Typescript

Array

Reverse Array

let arr=[1,2,3,4,5];
reverseArr(arr);
console.log(arr);
function reverseArr(arr:number[]){
    let left=0;
    let right=arr.length-1;
    while(left<right){
        let temp=arr[left];
        arr[left]=arr[right];
        arr[right]=temp;
        left++;
        right--;
    }
}

minMaxArray

const arr=[1,3,4,6,7,5];
getMinMax(arr);
function getMinMax(arr:number[]){
let n=arr.length;
secondLargest(arr);
secondSmallest(arr);
}
function secondLargest(arr:number[]){
    let largest=-Infinity;
    let secondLargest=-Infinity;
    for(let i=0;i<arr.length;i++){
        if(arr[i]>largest){
            secondLargest=largest;
            largest=arr[i];
        }else if(arr[i]>=secondLargest && arr[i]!=largest){
            secondLargest=arr[i];
        }
    }
    console.log("largest",largest);
    console.log("secondLargest",secondLargest);

}
function secondSmallest(arr:number[]){
    let smallest=Infinity;
    let secondSmallest=Infinity;
    for(let i=0;i<arr.length;i++){
        if(arr[i]<arr[smallest]){
            secondSmallest=smallest;
            smallest=arr[i];
        }else if(arr[i]<=secondSmallest && arr[i]!=smallest){
            secondSmallest=arr[i];
        }
    }
     console.log("smallest", smallest);
  console.log("second smallest", secondSmallest);
}

Kth smallest

let arr = [1, 2, 3, 29, 344, 23];
let k = 4;
kSmallest(arr, k);

function kSmallest(arr: number[], k: number): void {
    if (k > 0 && k <= arr.length) {
        arr.sort((a, b) => a - b);
        console.log(arr[k - 1]);
    } else {
        console.log("Invalid value of k");
    }
}

Sort (0,1,2)

let arr=[0,2,1,2,0];
sortArray(arr);
function swap(arr:number[],first:number,second:number):void{
    [arr[first],arr[second]]=[arr[second],arr[first]];
}
function sortArray(arr:number[]){
    let n=arr.length;
    let low=0,mid=0,high=n-1;
    while(mid<=high){
        if(arr[mid]==0){
            swap(arr,low++,mid++);
        }else if(arr[mid]==2){
            swap(arr,mid,high--);
        }else{
            mid++;
        }
    }
    console.log(arr);
}

Move Negative left

let arr=[-1,2,3,-3,4,-5];
sortArray(arr);
function sortArray(arr:number[]){
    let n=arr.length;
    let j=0;
    for(let i=0;i<arr.length;i++){
        if(arr[i]<0){
            if(i!=j){
                let temp=arr[i];
                arr[i]=arr[j];
                arr[j]=temp;
            }
            j++;
        }
    }
    console.log(arr);
}

Find Union and InterSection

let arr1 = [1, 2, 3, 5, 6, 7, 8, 23];
let arr2 = [2, 3, 4, 5, 6];
const { union, intersection } = findUnionAndIntersection(arr1, arr2);

console.log("Union:", union);
console.log("Intersection:", intersection);

function findUnionAndIntersection(arr1: number[], arr2: number[]): { union: number[], intersection: number[] } {
    const map = new Map<number, number>();
    for (const item of arr1) {
        map.set(item, (map.get(item) || 0) + 1);
    }

    const unionSet = new Set(arr1);
    const intersection: number[] = [];

    for (const item of arr2) {
        if (map.has(item) && map.get(item)! > 0) {
            map.set(item, map.get(item)! - 1);
            intersection.push(item);
        }
        unionSet.add(item);  // add item to the union set
    }

    return {
        union: Array.from(unionSet),  // convert the Set back to an array for the union
        intersection
    };
}

Cyclic Rotate Array

let arr=[1,2,3,4,4,6,8];
let k=2;
rotateLeft(arr,k);
rotateRight(arr,k);
function reverse(arr:number[],l:number,r:number):void{
    while(l<r){
        let temp=arr[l];
        arr[l]=arr[r];
        arr[r]=temp;
        l++;
        r--;
    }
}
function rotateLeft(arr:number[],k:number):void{
let n=arr.length;
    reverse(arr,0,k-1);
    reverse(arr,k,n-1);
    reverse(arr,0,n-1);
    console.log("reverse left= ",arr);
}
function rotateRight(arr:number[], k:number):void {
  let n = arr.length;
  reverse(arr, 0, n - k - 1);
  reverse(arr, n - k, n - 1);
  reverse(arr, 0, n - 1);
  console.log("reverse right = ", arr);
}

Sub Array Kadane

const arr=[3,4,5,6,-1];
const n=arr.length;
const maxSum=maxSubArray(arr,n);
console.log(`The maximum subarray sum is: ${maxSum}`);
function maxSubArray(arr:number[],n:number):number{
    let max=Number.MIN_SAFE_INTEGER;
    let sum=0;
    for(let i=0;i<n;i++){
        sum+=arr[i];
        if(sum>max){
            max=sum;
        }if(sum<0){
            sum=0;
        }
    }
    return max;
}

Minimise Height

const arr=[1,3,4,5,67,7];
const k=2;
console.log(getMinDiff(arr,arr.length,k));
function getMinDiff(arr:number[], n:number, k:number):number{
if(n==1){
    return 0;
}
arr.sort((a,b)=>a-b);
let ans=arr[n-1]-arr[0];
let small=arr[0]+k;
let big=arr[n-1]-k;
if(small>big){
    [small,big]=[big,small];
}
for (let i = 1; i < n - 1; i++) {
    const height = arr[i];
    const subtract = height - k;
    const add = height + k;

    if (subtract >= small || add <= big) {
      continue;
    }

    if (big - subtract <= add - small) {
      small = subtract;
    } else {
      big = add;
    }
  }

  return Math.min(ans, big - small);
}

Minimum Number of Jump

let arr = [2, 3, 4, 5, 2, 3, 4, 8, 12];
let n = arr.length;
console.log("Minimum Jumps: ", minJumpBruteForce(arr, n));

function minJumpBruteForce(arr: number[], n: number): number {
    // If array has only one element, no jumps are needed
    if (n === 1) return 0;
    
    // If the first element is 0, we can't make any jump
    if (arr[0] === 0) return -1;
    
    let rng = arr[0];  // Maximum range reachable with current jump
    let sl = arr[0];   // Steps left in the current jump
    let jp = 1;        // Number of jumps taken

    for (let i = 1; i < n; i++) {
        // Check if we've reached the end
        if (i === n - 1) return jp;
        
        // Update the maximum range reachable
        rng = Math.max(rng, i + arr[i]);
        sl--;  // Decrease steps left in the current jump range

        // If steps left become zero, we need another jump
        if (sl === 0) {
            jp++;  // Increase jump count

            // If the current maximum range is less than or equal to `i`, we can't move forward
            if (rng <= i) return -1;

            // Reset the steps left to reach `rng` from current position `i`
            sl = rng - i;
        }
    }

    // If we never reach the last index, return -1
    return -1;
}

Find Duplicates

let arr = [1, 3, 4, 2, 3]; // Corrected array where 3 is the duplicate.
console.log("Duplicate no: ", findDuplicate(arr));

function findDuplicate(arr: number[]): number {
    let slow = arr[0];
    let fast = arr[0];
    
    // Phase 1: Detect cycle using slow and fast pointers
    do {
        slow = arr[slow];         // move slow by 1 step
        fast = arr[arr[fast]];    // move fast by 2 steps
    } while (slow !== fast);      // continue until they meet

    // Phase 2: Find the entry point of the cycle (duplicate number)
    fast = arr[0];  // Reset fast to the beginning of the array
    while (slow !== fast) {
        slow = arr[slow];   // move both slow and fast by 1 step
        fast = arr[fast];
    }
    
    return slow;  // Both pointers now point to the duplicate number
}

Merge

let arr1=[1,4,8,10];
let arr2=[2,3,4];
let n=4;
let m=3;
merge(arr1,arr2,n,m);
console.log("The merged arrays are: ");
console.log("arr1[] = " + arr1.join(" "));
console.log("arr2[] = " + arr2.join(" "));
function merge(arr1:number[],arr2:number[],n:number,m:number):void{
    let left=n-1;
    let right=0;
    while(left>0 && right<m){
        if(arr1[left]>arr2[right]){
            [arr1[left],arr2[right]]=[arr2[right],arr1[left]];
            left--;
            right++;
        }else{
            break;
        }
    }
    arr1.sort((a, b) => a - b);
  arr2.sort((a, b) => a - b);
}

MergeIntervals

const arr = [
  [1, 3],
  [8, 10],
  [2, 6],
  [15, 18],
];
const ans = mergeOverlappingInterval(arr);
console.log("The merged intervals are:");
for (let it of ans) {
  console.log(`[${it[0]}, ${it[1]}]`);
}

function mergeOverlappingInterval(arr: number[][]): number[][] {
  let n = arr.length;
  arr.sort((a, b) => a[0] - b[0]);  // Sort intervals by the starting point

  const ans: number[][] = [arr[0]];  // Initialize the result with the first interval
  for (let i = 1; i < n; i++) {
    const last = ans[ans.length - 1];  // Get the last interval in the result
    const curr = arr[i];  // Get the current interval

    // Check if there is an overlap
    if (curr[0] <= last[1]) {
      // Merge the intervals by updating the end of the last interval
      last[1] = Math.max(curr[1], last[1]);
    } else {
      // No overlap, so add the current interval to the result
      ans.push(curr);
    }
  }

  return ans;  // Return the merged intervals
}

Next Permutation

let a = [2, 4, 5, 6, 77, 6];
let ans = nextGreaterPermutation(a);
console.log("The next permutation is: [" + ans.join(" ") + "]");

function nextGreaterPermutation(arr: number[]): number[] {
    let n = arr.length;
    let index = -1;

    // Step 1: Find the first index where arr[i] < arr[i+1]
    for (let i = n - 2; i >= 0; i--) {
        if (arr[i] < arr[i + 1]) {
            index = i;
            break;
        }
    }

    // Step 2: If no such index is found, reverse the array
    if (index === -1) {
        arr.reverse();
        return arr;
    }

    // Step 3: Find the smallest number greater than arr[index] from the right side
    for (let i = n - 1; i > index; i--) {
        if (arr[i] > arr[index]) {
            [arr[i], arr[index]] = [arr[index], arr[i]]; // Swap them
            break;
        }
    }

    // Step 4: Reverse the subarray to the right of index
    arr.splice(index + 1, n - index - 1, ...arr.slice(index + 1).reverse());

    return arr;
}

Count Inversion

const a: number[] = [5, 4, 3, 2, 1];
const cnt: number = numberOfInversionsOptimal(a);
console.log("The number of inversions is: " + cnt);

function numberOfInversionsNaive(arr: number[]): number {
  let count = 0;
  for (let i = 0; i < arr.length; i++) {
    for (let j = i + 1; j < arr.length; j++) { // Changed 'i' to 'i+1' for proper comparison
      if (arr[i] > arr[j]) {
        count++;
      }
    }
  }
  return count;
}

function mergeSort(arr: number[], low: number, high: number): number {
  let count = 0;
  if (low >= high) return count;
  let mid = Math.floor((low + high) / 2);
  count += mergeSort(arr, low, mid);
  count += mergeSort(arr, mid + 1, high);
  count += merge(arr, low, mid, high);
  return count;
}

function merge(arr: number[], low: number, mid: number, high: number): number {
  const temp: number[] = [];
  let left = low;
  let right = mid + 1;
  let count = 0;

  while (left <= mid && right <= high) {
    if (arr[left] <= arr[right]) {
      temp.push(arr[left]);
      left++;
    } else {
      temp.push(arr[right]);
      count += mid - left + 1;
      right++;
    }
  }

  while (left <= mid) {
    temp.push(arr[left]);
    left++;
  }

  while (right <= high) {
    temp.push(arr[right]);
    right++;
  }

  for (let i = low; i <= high; i++) {
    arr[i] = temp[i - low];
  }

  return count;
}

function numberOfInversionsOptimal(arr: number[]): number {
  return mergeSort(arr, 0, arr.length - 1);
}

Stock Buy And Sell

let arr=[7,1,4,6,8,2];
let n=arr.length;
let maxProfit=getMaxProfit(arr,n);
console.log("Max Profit: ", maxProfit);
function getMaxProfit(arr:number[], n:number):number{
    let ans=0;
    let minPrice=Infinity;
    for(let i=0;i<n;i++){
        minPrice=Math.min(minPrice,arr[i]);
        ans=Math.max(ans,arr[i]-minPrice);
    }
    return ans;
}

Compare Pair Sum

let arr: number[] = [1, 5, 7, 1];
let k: number = 6;
let n: number = arr.length;
console.log("The number of pairs with sum:", k, ":", countPairs(arr, n, k));

function countPairs(arr: number[], n: number, k: number): number {
    let count = 0;
    const freqMap = new Map<number, number>(); // Explicitly specifying the type of the map
    for (let i = 0; i < n; i++) {
        const required = k - arr[i];
        if (freqMap.has(required)) {
            count += freqMap.get(required)!; // Use non-null assertion since we know the value exists
        }
        freqMap.set(arr[i], (freqMap.get(arr[i]) || 0) + 1);
    }
    return count;
}

Common Elements 3 sorted Array

let A: number[] = [1, 5, 10, 20, 40, 80],
    n1: number = A.length;
let B: number[] = [6, 7, 20, 80, 100],
    n2: number = B.length;
let C: number[] = [3, 4, 15, 20, 30, 70, 80, 120],
    n3: number = C.length;

console.log("ans: ", commonElements(A, B, C, n1, n2, n3));

// TC: O(n1 + n2 + n3) SC: O(1)
function commonElements(arr1: number[], arr2: number[], arr3: number[], n1: number, n2: number, n3: number): number[] {
  let i = 0, j = 0, k = 0;
  let res: number[] = [];
  let last: number = Number.MIN_SAFE_INTEGER;
  
  while (i < n1 && j < n2 && k < n3) {
    if (arr1[i] === arr2[j] && arr1[i] === arr3[k] && arr1[i] !== last) {
      res.push(arr1[i]);
      last = arr1[i];
      i++;
      j++;
      k++;
    } else if (Math.min(arr1[i], arr2[j], arr3[k]) === arr1[i]) {
      i++;
    } else if (Math.min(arr1[i], arr2[j], arr3[k]) === arr2[j]) {
      j++;
    } else {
      k++;
    }
  }
  
  if (res.length === 0) {
    return [-1];
  }
  
  return res;
}

Rearrange by Sign

let a: number[] = [1, -2, 3, -4, 5, -6];
let n: number = a.length;
let ans = rearrangeBySign(a, n);
console.log(ans.join(" "));

function rearrangeBySign(a: number[], n: number): number[] {
    let ans = new Array(n);
    let posIndex = 0;
    let negIndex = 1;

    // First, place negative numbers at odd indices and positive numbers at even indices
    for (let i = 0; i < n; i++) {
        if (a[i] < 0) {
            ans[negIndex] = a[i];
            negIndex += 2; // Move to next odd index
        } else {
            ans[posIndex] = a[i];
            posIndex += 2; // Move to next even index
        }
    }

    // In case there are more positives or negatives and you still have unfilled spots, fill them in the remaining spots
    if (posIndex < n) {
        for (let i = 0; i < n; i++) {
            if (ans[i] === undefined) {
                ans[i] = a[i];
            }
        }
    }
    
    return ans;
}

Sub Array k0

let arr: number[] = [4, 2, -3, 1, 6];
let n: number = arr.length;
let k: number = 0;

console.log("Subarray with sum k:", findSubarrayOptimal(arr, n, k));

// TC: O(n^2) - Naive solution
function findSubarrayNaive(arr: number[], n: number, k: number): boolean {
  let isPresent = false;

  for (let i = 0; i < n; i++) {
    let sum = 0;
    for (let j = i; j < n; j++) {
      sum += arr[j];
      if (sum === k) {
        isPresent = true;
        break;
      }
    }
    if (isPresent) break;
  }
  return isPresent;
}

// TC: O(n) - Optimal solution using prefix sum and hash set
function findSubarrayOptimal(arr: number[], n: number, k: number): boolean {
  let sum = 0;
  let isPresent = false;
  let prefixSum = new Set<number>();

  for (let i = 0; i < n; i++) {
    sum += arr[i];

    // Check if the current sum is equal to k, or if the difference (sum - k) exists in the prefixSum set
    if (sum === k || prefixSum.has(sum - k)) {
      isPresent = true;
      break;
    }

    // Add the current sum to the prefixSum set for future checks
    prefixSum.add(sum);
  }

  return isPresent;
}

Max Product Sub Array

let arr: number[] = [6, -3, -10, 0, 2];
let n: number = arr.length;
console.log("Max Product: ", getMaxProduct(arr, n));

function getMaxProduct(arr: number[], n: number): number {
    let maxEnd = arr[0];
    let minEnd = arr[0];
    let maxProd = arr[0];

    for (let i = 1; i < n; i++) {
        if (arr[i] < 0) {
            // Swap maxEnd and minEnd when encountering a negative number
            let temp = maxEnd;
            maxEnd = minEnd;
            minEnd = temp;
        }

        // Calculate max and min products ending at the current position
        maxEnd = Math.max(arr[i], maxEnd * arr[i]);
        minEnd = Math.min(arr[i], minEnd * arr[i]);

        // Update maxProd with the maximum product found so far
        maxProd = Math.max(maxProd, maxEnd);
    }

    return maxProd;
}

Longes Consecutive Sucessive

let arr: number[] = [100, 200, 1, 3, 4];
let ans = longestSuccessive(arr);
console.log("The longest consecutive sequence is:", ans);

function longestSuccessive(arr: number[]): number {
    let n = arr.length;
    if (n === 0) return 0;

    let longest = 1;
    let st = new Set(arr);

    for (let it of st) {
        // Only start counting sequence if it's the beginning of a sequence
        if (!st.has(it - 1)) {
            let cnt = 1;
            let x = it;
            while (st.has(x + 1)) {
                x += 1;
                cnt += 1;
            }
            longest = Math.max(longest, cnt);
        }
    }
    return longest;
}

Element Appear NK times

let arr: number[] = [2, 2, 1, 1, 1, 2, 2];
let n: number = arr.length;
let k: number = 2;

// Naive Approach: Check each element and count its frequency
function majorityElementNaive(arr: number[], n: number, k: number): number {
  for (let i = 0; i < n; i++) {
    let cnt = 0;
    for (let j = 0; j < n; j++) {
      if (arr[i] == arr[j]) {
        cnt++;
      }
    }
    if (cnt > Math.floor(n / k)) {
      return arr[i];
    }
  }
  return -1;
}

// Better Approach: Use a hashmap to store frequencies
function majorityElementBetter(arr: number[], n: number, k: number): number[] {
  let result: number[] = [];
  const freqMap = new Map<number, number>();
  const threshold = Math.floor(n / k) + 1;

  for (let i = 0; i < n; i++) {
    freqMap.set(arr[i], (freqMap.get(arr[i]) || 0) + 1);

    // If frequency meets threshold, add to result and remove from map to prevent duplicates
    if (freqMap.get(arr[i]) === threshold) {
      result.push(arr[i]);
      freqMap.delete(arr[i]);
    }
  }
  return result;
}

// Majority Element for n/2 using Boyer-Moore Voting Algorithm
function majorityElementHalf(arr: number[]): number {
  let count = 0;
  let candidate: number | undefined;

  for (let num of arr) {
    if (count === 0) {
      candidate = num;
    }
    count += (num === candidate) ? 1 : -1;
  }

  // Verify candidate frequency
  let verifyCount = arr.filter(num => num === candidate).length;
  return verifyCount > Math.floor(arr.length / 2) ? candidate! : -1;
}

// Majority Elements for n/3 using Extended Boyer-Moore Voting Algorithm
function majorityElementThird(arr: number[]): number[] {
  let n = arr.length;
  let count1 = 0, count2 = 0;
  let candidate1: number | undefined, candidate2: number | undefined;

  for (let num of arr) {
    if (candidate1 === num) {
      count1++;
    } else if (candidate2 === num) {
      count2++;
    } else if (count1 === 0) {
      candidate1 = num;
      count1 = 1;
    } else if (count2 === 0) {
      candidate2 = num;
      count2 = 1;
    } else {
      count1--;
      count2--;
    }
  }

  // Verify candidates
  count1 = arr.filter(num => num === candidate1).length;
  count2 = arr.filter(num => num === candidate2).length;
  let result: number[] = [];
  let threshold = Math.floor(n / 3) + 1;

  if (count1 >= threshold) result.push(candidate1!);
  if (count2 >= threshold) result.push(candidate2!);

  return result;
}

// Testing the functions
console.log("Naive Approach Majority Element:", majorityElementNaive(arr, n, k));
console.log("Better Approach Majority Element:", majorityElementBetter(arr, n, k));
console.log("Boyer-Moore Voting (n/2 Majority):", majorityElementHalf(arr));
console.log("Extended Boyer-Moore Voting (n/3 Majority):", majorityElementThird(arr));

Max Profit 2 Data

let price: number[] = [2, 30, 15, 10, 8, 25, 80];
let n: number = price.length;
console.log("Maximum Profit = ", maxProfitOptimal(price, n));

// Function to calculate maximum profit with two transactions (O(2n) approach)
function maxProfit(arr: number[], n: number): number {
  let profit: number[] = Array(n).fill(0);
  let maxPrice = arr[n - 1];

  // Traverse from the right to find maximum selling profit
  for (let i = n - 2; i >= 0; i--) {
    if (arr[i] > maxPrice) {
      maxPrice = arr[i];
    }
    profit[i] = Math.max(profit[i + 1], maxPrice - arr[i]);
  }

  let minPrice = arr[0];

  // Traverse from the left to find maximum buying profit
  for (let i = 1; i < n; i++) {
    if (arr[i] < minPrice) {
      minPrice = arr[i];
    }
    profit[i] = Math.max(profit[i - 1], profit[i] + (arr[i] - minPrice));
  }

  return profit[n - 1];
}

// Optimized function to calculate maximum profit with two transactions (O(n) approach)
function maxProfitOptimal(arr: number[], n: number): number {
  let first_buy = -Infinity;
  let first_sell = 0;
  let second_buy = -Infinity;
  let second_sell = 0;

  for (let i = 0; i < n; i++) {
    first_buy = Math.max(first_buy, -arr[i]); // max profit after buying the first stock
    first_sell = Math.max(first_sell, first_buy + arr[i]); // max profit after selling the first stock
    second_buy = Math.max(second_buy, first_sell - arr[i]); // max profit after buying the second stock
    second_sell = Math.max(second_sell, second_buy + arr[i]); // max profit after selling the second stock
  }

  return second_sell; // maximum profit with at most two transactions
}

Subset of Other Array

let a1: number[] = [11, 7, 1, 13, 21, 3, 7, 3];
let n: number = a1.length;
let a2: number[] = [11, 3, 7, 1, 7];
let m: number = a2.length;
console.log(isSubsetOptimal(a1, a2, n, m));

// Naive approach to check if `a2` is a subset of `a1` (TC: O(n^2))
function isSubsetNaive(a1: number[], a2: number[], n: number, m: number): string {
  let count = 0;

  for (let i = 0; i < m; i++) {
    let found = false;
    for (let j = 0; j < n; j++) {
      if (a1[j] === a2[i]) {
        count++;
        a1[j] = -1; // Mark as used
        found = true;
        break;
      }
    }
    if (!found) {
      return "No"; // Element from a2 not found in a1
    }
  }

  return m === count ? "Yes" : "No";
}

// Optimal approach using a hashmap to check if `a2` is a subset of `a1` (TC: O(n + m))
function isSubsetOptimal(a1: number[], a2: number[], n: number, m: number): string {
  let freq = new Map<number, number>();

  // Count frequencies of elements in a1
  for (let i = 0; i < n; i++) {
    freq.set(a1[i], (freq.get(a1[i]) || 0) + 1);
  }

  // Check elements of a2 in the frequency map
  for (let num of a2) {
    if (!freq.has(num)) {
      return "No";
    }
    freq.set(num, freq.get(num)! - 1);
    if (freq.get(num)! < 0) {
      return "No";
    }
  }

  return "Yes";
}

Three Sum

let arr: number[] = [-1, 0, 1, 2, -1, -4];
let n: number = arr.length;
let k: number = 0;
let res = tripletOptimal(n, arr, k);
console.log("triplets: ", res);

// Optimal approach (TC: O(n log n) + O(n^2), SC: O(no. of triplets))
function tripletOptimal(n: number, arr: number[], val: number): number[][] {
  let ans: number[][] = [];
  arr.sort((a, b) => a - b);

  for (let i = 0; i < n; i++) {
    if (i !== 0 && arr[i] === arr[i - 1]) continue;

    let j = i + 1;
    let k = n - 1;
    while (j < k) {
      let sum = arr[i] + arr[j] + arr[k];
      if (sum < val) {
        j++;
      } else if (sum > val) {
        k--;
      } else {
        ans.push([arr[i], arr[j], arr[k]]);
        j++;
        k--;

        // Skip duplicates for the second and third elements
        while (j < k && arr[j] === arr[j - 1]) j++;
        while (j < k && arr[k] === arr[k + 1]) k--;
      }
    }
  }

  return ans;
}

Trapping RainWater

function trappingRainwater(height: number[]): number {
  if (height.length === 0) return 0;

  let left = 0;
  let right = height.length - 1;
  let leftMax = 0;
  let rightMax = 0;
  let waterTrapped = 0;

  while (left <= right) {
    if (height[left] <= height[right]) {
      if (height[left] >= leftMax) {
        leftMax = height[left];
      } else {
        waterTrapped += leftMax - height[left];
      }
      left++;
    } else {
      if (height[right] >= rightMax) {
        rightMax = height[right];
      } else {
        waterTrapped += rightMax - height[right];
      }
      right--;
    }
  }

  return waterTrapped;
}

// Example usage:
const height = [0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1];
console.log("Trapped Rainwater:", trappingRainwater(height));

Factorial of large number

function largeNumberFactorial(n: number): number[] {
  let result: number[] = [1]; // Initialize result to handle large numbers

  for (let i = 2; i <= n; i++) {
    multiply(i, result);
  }

  return result.reverse(); // Reverse the array for readability
}

function multiply(x: number, result: number[]): void {
  let carry = 0;
  
  for (let i = 0; i < result.length; i++) {
    let product = result[i] * x + carry;
    result[i] = product % 10;
    carry = Math.floor(product / 10);
  }

  while (carry > 0) {
    result.push(carry % 10);
    carry = Math.floor(carry / 10);
  }
}

// Example usage:
const n = 100;
console.log(`Factorial of ${n}:`, largeNumberFactorial(n).join(""));

Binary Search

Find X in Array

let arr: number[] = [3, 4, 6, 7, 9, 12, 16];
let target: number = 6;
let index = search(arr, target);
if (index == -1) {
    console.log("The target is not present");
} else {
    console.log("The target is at index:", index);
}

function search(arr: number[], target: number): number {
    return binarySearch(arr, target);
}

function binarySearch(arr: number[], target: number): number {
    let low = 0;
    let high = arr.length - 1; // Set high to the last valid index

    while (low <= high) { // Adjust condition to <=
        let mid = Math.floor((low + high) / 2);
        if (arr[mid] === target) {
            return mid;
        } else if (arr[mid] < target) {
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }
    return -1;
}

Lower Bound

let arr: number[] = [3, 5, 9, 12];
let x: number = 9;
let index = lowerBound(arr, arr.length, x);
console.log("The lower bound is at index:", index);

function lowerBound(arr: number[], n: number, x: number): number {
    let low = 0, high = n - 1;
    let ans = n; // Initialize ans with n, indicating "not found" if all elements are less than x

    while (low <= high) {
        let mid = Math.floor((low + high) / 2);
        if (arr[mid] >= x) {
            ans = mid; // Update ans with the current mid index
            high = mid - 1; // Move left to find the lowest index
        } else {
            low = mid + 1; // Move right if arr[mid] < x
        }
    }
    return ans;
}

Upper Bound

let arr: number[] = [3, 5, 8, 9, 15, 19];
let x: number = 9;
let ind = upperBoundOptimal(arr, arr.length, x);
console.log("The upper bound is at index:", ind);

// TC: O(log n)
function upperBoundOptimal(arr: number[], n: number, x: number): number {
  let low = 0;
  let high = n - 1;
  let ans = n; // Initialize ans with n, indicating "not found" if all elements are less than or equal to x

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);
    if (arr[mid] > x) {
      ans = mid; // Update ans with the current mid index
      high = mid - 1; // Move left to find the lowest index with arr[mid] > x
    } else {
      low = mid + 1; // Move right if arr[mid] <= x
    }
  }
  return ans;
}

Search Insert Position

let arr:number[]=[1,3,4,7];
let x=6;
let index=searchInsert(arr,x);
console.log("The index is: ",index);
function searchInsert(arr:number[], x:number):number{
    let n=arr.length;
    let low=0;
    let high=n-1;
    let ans=n;
    while(low<=high){
        let mid=Math.floor((low+high)/2);
        if(arr[mid]>=x){
            ans=mid;
            high=mid-1;
        }else{
            low=mid+1;
        }
        
    }
    return ans;
}

Floor Ceil

let arr: number[] = [3, 4, 4, 7, 8, 10];
let n: number = arr.length;
let x: number = 8;
let ans = getFloorAndCeil(arr, n, x);
console.log("The floor and ceil are:", ans[0], ans[1]);

function getFloorAndCeil(arr: number[], n: number, x: number): [number, number] {
  let floor = findFloor(arr, n, x);
  let ceil = findCeil(arr, n, x);
  return [floor, ceil];
}

function findFloor(arr: number[], n: number, x: number): number {
  let low = 0;
  let high = n - 1;
  let ans = -1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);
    if (arr[mid] <= x) {
      ans = arr[mid];
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
  return ans;
}

function findCeil(arr: number[], n: number, x: number): number {
  let low = 0;
  let high = n - 1;
  let ans = -1;

  while (low <= high) {
    let mid = Math.floor((low + high) / 2);
    if (arr[mid] >= x) {
      ans = arr[mid];
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  return ans;
}

First Last Occurance

let arr:number[]=[3,4,5,6,12,12,32];
let n:number=arr.length;
let k:number=12;
let ans=getLastOccurance(arr,n,k);
console.log("answer: ",ans);
function getLastOccurance(arr:number[],n:number,k:number):number{
    let low=0,high=n-1,result=-1;
    while(low<=high){
        let mid=Math.floor(low+(high-low)/2);
        if(arr[mid]==k){
            result=mid;
            high=mid-1;
        }
        else if(k<arr[mid]){
            high=mid-1;
        }else{
            low=mid+1;
        }
    }
    return result;
}

Count Occurance

Search In Rotate

Polly Fills

Filter

interface Array<T> {
  myOwnFilter(callback: (element: T, index: number) => boolean): T[];
}

Array.prototype.myOwnFilter = function <T>(callback: (element: T, index: number) => boolean): T[] {
  let newArr: T[] = [];
  this.forEach((element: T, index: number) => {
    if (callback(element, index)) {
      newArr.push(element);
    }
  });
  return newArr;
};

let arr: number[] = [1, 3, 2, 4, 9, 5, 8, 6];

const arrFiltered = arr.myOwnFilter((element, index) => {
  return element > 4;
});

console.log(arrFiltered);

For Each

interface Array<T> {
  myForEach(callback: (element: T, index: number) => void): void;
}

Array.prototype.myForEach = function <T>(callback: (element: T, index: number) => void): void {
  for (let i = 0; i < this.length; i++) {
    callback(this[i], i);
  }
};

const arr: number[] = [1, 2, 3, 4, 5];

arr.myForEach((element, index) => {
  console.log(`Element at index ${index}: ${element}`);
});

Map

// Adding myOwnMap method to Array prototype
interface Array<T> {
  myOwnMap<U>(callback: (element: T, index: number) => U): U[];
  myOwnReduce(callback: (accumulator: T, currentValue: T, index?: number, array?: T[]) => T, initialValue?: T): T;
}

Array.prototype.myOwnMap = function <T, U>(callback: (element: T, index: number) => U): U[] {
  const newArr: U[] = [];

  this.forEach((element: T, index: number) => {
    const result = callback(element, index);
    newArr.push(result);
  });

  return newArr;
};

const arr = [1, 3, 2, 4, 9, 5, 8, 6];

const arr2 = arr.myOwnMap((element, index) => {
  return element * 5;
});

console.log("Mapped Array:", arr2);

Reduce

// Extending the Array interface to include myOwnReduce
interface Array<T> {
  myOwnReduce<U>(
    callback: (accumulator: U, currentValue: T, index: number, array: T[]) => U,
    initialValue?: U
  ): U;
}

// Adding myOwnReduce method to Array prototype
Array.prototype.myOwnReduce = function <T, U>(
  this: T[],
  callback: (accumulator: U, currentValue: T, index: number, array: T[]) => U,
  initialValue?: U
): U {
  if (this.length === 0 && initialValue === undefined) {
    throw new TypeError("Reduce of empty array with no initial value");
  }

  let accumulator: U = initialValue !== undefined ? initialValue : (this[0] as unknown as U);
  const startIndex = initialValue !== undefined ? 0 : 1;

  for (let i = startIndex; i < this.length; i++) {
    accumulator = callback(accumulator, this[i], i, this);
  }

  return accumulator;
};

// Example usage
const arr = [1, 2, 3, 4];
const sum = arr.myOwnReduce<number>((accumulator, currentValue) => {
  return accumulator + currentValue;
}, 0);

console.log("Reduced Sum:", sum); // Output: Reduced Sum: 10

Regex

const string: string = "all your string base belong to us";
const regex: RegExp = /base/;
const isExisting: boolean = regex.test(string);
console.log(isExisting);

Sliding Window

Longest Sub String No Repeating Char

let s: string = "abcabcbb";
console.log(lengthOfLongestSubString(s));

function lengthOfLongestSubString(s: string): number {
  let n = s.length;
  let left = 0;
  let right = 0;
  let charSet = new Set<string>(); // TypeScript: explicitly specifying the type of elements in the set
  let maxLen = 0;

  while (right < n) {
    if (!charSet.has(s[right])) {
      charSet.add(s[right]);
      maxLen = Math.max(maxLen, right - left + 1);
      right++;
    } else {
      charSet.delete(s[left]);
      left++;
    }
  }

  return maxLen;
}

Max Sub Array Size K

function slidingWindowFixed(arr: number[], k: number): number | null {
  const n = arr.length;
  if (n < k) return null;

  let left = 0;
  let right = 0;
  let maxSum = 0;
  let currSum = 0;
  const windowSet = new Set<number>();

  while (right < n) {
    if (!windowSet.has(arr[right]) && windowSet.size < k) {
      windowSet.add(arr[right]);
      currSum += arr[right];
      right++;
    } else {
      windowSet.delete(arr[left]);
      currSum -= arr[left];
      left++;
    }

    if (windowSet.size === k) {
      maxSum = Math.max(maxSum, currSum);
      windowSet.delete(arr[left]);
      currSum -= arr[left];
      left++;
    }
  }
  return maxSum;
}
function ifNotDistinct(arr: number[], k: number): number | null {
  const n = arr.length;
  if (n < k) return null;

  let left = 0;
  let right = 0;
  let maxSum = 0;
  let currentSum = 0;

  while (right < n) {
    currentSum += arr[right];

    if (right - left + 1 === k) {
      maxSum = Math.max(maxSum, currentSum);
      currentSum -= arr[left];
      left++;
    }

    right++;
  }

  return maxSum;
}
let arr = [1, 5, 4, 2, 9, 9, 9];
let k = 3;

console.log(slidingWindowFixed(arr, k)); // Output: Max sum of distinct elements within a sliding window
console.log(ifNotDistinct(arr, k));     // Output: Max sum of a fixed-size sliding window

First Negative Number of Size K

let arr: number[] = [-8, 2, 3, -6, 10];
let k: number = 2;
console.log(slidingWindowFixed(arr, k));

function slidingWindowFixed(arr: number[], k: number): number[] {
    const n = arr.length;
    let left = 0;
    let right = 0;
    let window: number[] = [];
    let result: number[] = [];

    while (right < n) {
        // Add negative numbers to the window
        if (arr[right] < 0) {
            window.push(arr[right]);
        }

        console.log(window); // Debugging: logging window contents

        // When the window size reaches 'k', process the window
        if (right - left + 1 === k) {
            // If there are no negative numbers in the window, push 0 to the result
            if (window.length === 0) {
                result.push(0);
            } else {
                // Otherwise, push the first negative number in the window (i.e., window[0])
                result.push(window[0]);

                // If the element at the left of the window is the same as the first negative number,
                // remove it from the window
                if (arr[left] === window[0]) {
                    window.shift();
                }
            }
            // Slide the window to the right
            left++;
        }
        right++;
    }

    return result;
}

Max Of All Sub Array

function slidingWindowFixed(arr: number[], k: number): number[] {
  const n = arr.length;
  let left = 0;
  let right = 0;
  const ans: number[] = [];
  let maxNum = Number.MIN_VALUE;

  while (right < n) {
    // Update the maximum number in the current window
    if (arr[right] > maxNum) {
      maxNum = arr[right];
    }

    // Check if the window size equals k
    if (right - left + 1 === k) {
      ans.push(maxNum); // Add the maximum value to the result array

      // If the leftmost element was the maximum, recalculate for the new window
      if (arr[left] === maxNum) {
        maxNum = Number.MIN_VALUE;
        for (let i = left + 1; i <= right; i++) {
          maxNum = Math.max(maxNum, arr[i]);
        }
      }

      left++; // Slide the window
    }

    right++; // Expand the window
  }

  return ans;
}

// Example Usage
const arr: number[] = [1, 2, 3, 1, 4, 5, 2, 3, 6];
const k: number = 3;
console.log(slidingWindowFixed(arr, k)); // Output: [3, 3, 4, 5, 5, 5, 6]

Max Consecutive longest Ones

function longestOnes(arr: number[], k: number): number {
  const n: number = arr.length;
  let left: number = 0;
  let right: number = 0;
  let window: number = 0; // Count of `1`s in the current window
  let ans: number = 0;

  while (right < n) {
    // Expand the window to include the current element
    window += arr[right];

    // If the window condition is violated, shrink from the left
    while (window + k < right - left + 1) {
      window -= arr[left];
      left++;
    }

    // Update the maximum size of the window
    ans = Math.max(ans, right - left + 1);
    right++;
  }

  return ans;
}

// Example Usage
const arr: number[] = [
  0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1,
];
const k: number = 3;
console.log(longestOnes(arr, k)); // Output: 10

Max Fruit

function findMaxFruits(arr: number[]): number {
  const n: number = arr.length;
  let left: number = 0;
  let right: number = 0;
  let ans: number = 0;

  const map: Map<number, number> = new Map();

  while (right < n) {
    // Add the current fruit to the map
    map.set(arr[right], (map.get(arr[right]) || 0) + 1);

    // If there are more than 2 distinct types of fruits, shrink the window
    while (map.size > 2) {
      const leftFruit = arr[left];
      const count = map.get(leftFruit) || 0;

      if (count === 1) {
        map.delete(leftFruit);
      } else {
        map.set(leftFruit, count - 1);
      }
      left++;
    }

    // Update the maximum length
    ans = Math.max(ans, right - left + 1);

    right++;
  }

  return ans;
}

// Example Usage
const arr: number[] = [1, 2, 1, 1, 3, 4, 2, 2, 2, 2, 4];
console.log(findMaxFruits(arr)); // Output: 5

Character Replacement

function characterReplacement(s: string, k: number): number {
  const n: number = s.length;
  const charCount: number[] = new Array(26).fill(0);
  let maxCount: number = 0;
  let maxLen: number = 0;
  let left: number = 0;

  for (let right = 0; right < n; right++) {
    const charIndex: number = s.charCodeAt(right) - "A".charCodeAt(0);
    charCount[charIndex]++;
    maxCount = Math.max(maxCount, charCount[charIndex]);

    // Check if the current window is valid
    while (right - left + 1 - maxCount > k) {
      const leftIndex: number = s.charCodeAt(left) - "A".charCodeAt(0);
      charCount[leftIndex]--;
      left++;
    }

    // Update the maximum length
    maxLen = Math.max(maxLen, right - left + 1);
  }

  return maxLen;
}

// Example Usage
const s: string = "AABABBA";
const k: number = 1;
console.log(characterReplacement(s, k)); // Output: 4

Num SubArray with sum

function numSubarraysWithSum(nums: number[], goal: number): number {
  const prefixSumCount: Map<number, number> = new Map();
  let sum: number = 0;
  let count: number = 0;

  for (const num of nums) {
    // Add current number to the cumulative sum
    sum += num;

    // If the cumulative sum equals the goal, increment the count
    if (sum === goal) {
      count++;
    }

    // Check if there exists a prefix sum that satisfies the condition
    if (prefixSumCount.has(sum - goal)) {
      count += prefixSumCount.get(sum - goal)!;
    }

    // Update the prefixSumCount map
    prefixSumCount.set(sum, (prefixSumCount.get(sum) || 0) + 1);
  }

  return count;
}

// Example Usage
const nums: number[] = [1, 0, 1, 0, 1];
const goal: number = 2;
console.log(numSubarraysWithSum(nums, goal)); // Output: 4

Number of Sub Arrays

function numberOfSubarrays(nums: number[], k: number): number {
  const n: number = nums.length;
  let left: number = 0;
  let right: number = 0;
  let niceSubArray: number = 0;
  let result: number = 0;
  let countOdd: number = 0;

  while (right < n) {
    // Count odd numbers in the current window
    if (nums[right] % 2 !== 0) {
      countOdd++;
    }

    // When the current window has exactly k odd numbers
    if (countOdd === k) {
      niceSubArray = 0;
    }

    // Shrink the window from the left while maintaining k odd numbers
    while (countOdd >= k) {
      if (nums[left] % 2 !== 0) {
        countOdd--;
      }
      left++;
      niceSubArray++;
    }

    // Add the count of valid subarrays for the current window
    result += niceSubArray;
    right++;
  }

  return result;
}

// Example Usage
const nums: number[] = [1, 1, 2, 1, 1];
const k: number = 3;
console.log(numberOfSubarrays(nums, k)); // Output: 2

Number of substring

function numberOfSubstrings(s: string): number {
  const freq: Record<string, number> = { a: 0, b: 0, c: 0 };
  const n: number = s.length;
  let left: number = 0;
  let right: number = 0;
  let count: number = 0;
  let missing: number = 3; // Counts how many of 'a', 'b', 'c' are missing in the window

  while (right < n) {
    // Add the character at `right` to the frequency map
    if (++freq[s[right]] === 1) {
      missing--; // Decrease `missing` if a new character is added
    }

    // When all characters are present in the window
    while (missing === 0) {
      // All substrings starting from the current `left` to the end are valid
      count += n - right;

      // Remove the character at `left` from the window
      if (--freq[s[left]] === 0) {
        missing++; // Increase `missing` if a character is removed completely
      }
      left++; // Shrink the window
    }

    right++; // Expand the window
  }

  return count;
}

// Example Usage
const s: string = "abcabc";
console.log(numberOfSubstrings(s)); // Output: 10

Sorting

Selection Sort

let arr: number[] = [13, 46, 24, 52, 20, 9];
let n: number = arr.length;
console.log("Selection Sort: ", selectionSort(arr, n));

// TC: O(n^2) SC: O(1)
function selectionSort(arr: number[], n: number): number[] {
  for (let i = 0; i < n - 1; i++) {
    let min: number = i;
    for (let j = i + 1; j < n; j++) {
      if (arr[j] < arr[min]) {
        min = j;
      }
    }
    let temp: number = arr[i];
    arr[i] = arr[min];
    arr[min] = temp;
  }
  return arr;
}

Quick Sort

const arr: number[] = [4, 6, 2, 5, 7, 9, 1, 3];
console.log("Before Using Quicksort: ", arr);
sortArray(arr);
console.log("After Quicksort: ", arr);

function partition(arr: number[], low: number, high: number): number {
  const pivot: number = arr[low];
  let i: number = low;
  let j: number = high;

  while (i < j) {
    while (arr[i] <= pivot && i <= high - 1) {
      i++;
    }

    while (arr[j] > pivot && j >= low + 1) {
      j--;
    }

    if (i < j) {
      const temp: number = arr[i];
      arr[i] = arr[j];
      arr[j] = temp;
    }
  }

  const temp: number = arr[low];
  arr[low] = arr[j];
  arr[j] = temp;
  return j;
}

function quickSort(arr: number[], low: number, high: number): void {
  if (low < high) {
    const pIndex: number = partition(arr, low, high);
    quickSort(arr, low, pIndex - 1);  // Recursively sort the left part
    quickSort(arr, pIndex + 1, high); // Recursively sort the right part
  }
}

function sortArray(arr: number[]): number[] {
  quickSort(arr, 0, arr.length - 1);
  return arr;
}

Merge Sort

let arr: number[] = [13, 46, 24, 52, 20, 9];
let n: number = arr.length;
mergeSort(arr, 0, n - 1);
console.log("Merge sort: ", arr);

// Time complexity: O(n log n)  // Space complexity: O(n)
function mergeSort(arr: number[], low: number, high: number): void {
  if (low >= high) return;
  
  let mid: number = Math.floor((low + high) / 2);
  mergeSort(arr, low, mid);         // Sort the left half
  mergeSort(arr, mid + 1, high);    // Sort the right half
  merge(arr, low, mid, high);       // Merge both halves
}

function merge(arr: number[], low: number, mid: number, high: number): void {
  const temp: number[] = [];
  let left: number = low;
  let right: number = mid + 1;

  while (left <= mid && right <= high) {
    if (arr[left] <= arr[right]) {
      temp.push(arr[left]);
      left++;
    } else {
      temp.push(arr[right]);
      right++;
    }
  }

  // Add remaining elements from the left part
  while (left <= mid) {
    temp.push(arr[left]);
    left++;
  }

  // Add remaining elements from the right part
  while (right <= high) {
    temp.push(arr[right]);
    right++;
  }

  // Copy the sorted elements back into the original array
  for (let i = low; i <= high; i++) {
    arr[i] = temp[i - low];
  }
}

Insertion Sort

let arr:number[]=[23,23,43,34,5,6];
let n:number=arr.length;
insertionSort(arr,n);
console.log("Insertion sort: ", arr);
function insertionSort(arr:number[],n:number):number[]{
    for(let i=0;i<n;i++){
        let j=i;
        while(j>0 && arr[j-1]>arr[j]){
            let temp=arr[j];
            arr[j]=arr[j-1];
            arr[j-1]=temp;
            j--;
        }
    }
    return arr;
}

Buuble Sort

let arr: number[] = [12, 3, 2, 45, 34];
let n: number = arr.length;
bubbleSort(arr, n);
console.log("Bubble Sort:", arr);

function bubbleSort(arr: number[], n: number): void {
    for (let turn = 0; turn < n - 1; turn++) {
        for (let j = 0; j < n - turn - 1; j++) {  // Fixed range for `j`
            if (arr[j] < arr[j + 1]) {  // Sort in descending order
                let temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }
}

String

Remove Outer most String

let s: string = "(()())(())";
let ans: string = removeOuterParentheses(s);
console.log("ans: ", ans);

function removeOuterParentheses(s: string): string {
  let res: string = "";
  let bal: number = 0;
  
  for (let ch of s) {
    if (ch === "(") {
      if (bal > 0) {
        res += "(";
      }
      bal++;
    } else if (ch === ")") {
      bal--;
      if (bal > 0) {
        res += ")";
      }
    }
  }

  return res;
}

Reverse String

let str: string = "hello";
let ans = reverse(str);
console.log("ans: ", ans);

function reverse(str: string): string {
  let strArr = str.split("");
  let low = 0;
  let high = strArr.length - 1; // Adjusted high index to length - 1

  while (low < high) {
    [strArr[low], strArr[high]] = [strArr[high], strArr[low]];
    low++;
    high--;
  }

  return strArr.join("");
}

Reverse Word

let str:string="this is and amazing program";
console.log(reverseWords(str));
function reverseWords(str:string){
    let reversedWord="";
    let reversedStr="";
     for (let i = 0; i < str.length; i++) {
    if (str[i] !== " ") {
      reversedWord = str[i] + reversedWord;
    } else {
      reversedStr += reversedWord + " ";
      reversedWord = "";
    }
  }
  // Handle the last word
  reversedStr += reversedWord;
  return reversedStr;
}

Duplicate Char String

let str: string = "test string";
printDuplicate(str);
console.log(str);

function printDuplicate(str: string) {
    const charCount: { [key: string]: number } = {};  // Using an object to store character counts
    for (let i = 0; i < str.length; i++) {
        const char = str[i];  // Getting the character at index i
        if (charCount[char]) {
            charCount[char]++;
        } else {
            charCount[char] = 1;
        }
    }

    console.log("Character counts:", charCount);
    return charCount;
}

Odd Number In String

let num: string = "52";
let largestOdd = largestOddNumber(num);
console.log(largestOdd);  // This will now print the correct output

function largestOddNumber(num: string): string {
    for (let i = num.length - 1; i >= 0; i--) {
        if (parseInt(num[i]) % 2 === 1) {
            return num.substring(0, i + 1);  // Extracts the substring from the start to the first odd digit
        }
    }
    return "";  // If no odd digit found, return an empty string
}

Longest Common Prefix

let strs: string[] = ["flower", "flow", "flight"];
let ans: string = longestCommonPrefix(strs);
console.log("ans: ", ans);

function longestCommonPrefix(strs: string[]): string {
  if (strs.length === 0) {
    return "";
  }

  const reference: string = strs[0];

  for (let i = 0; i < reference.length; i++) {
    const char: string = reference[i];
    for (let j = 1; j < strs.length; j++) {
      if (i >= strs[j].length || strs[j][i] !== char) {
        return reference.slice(0, i);
      }
    }
  }
  return reference;
}

Palindrome

let s: string = "abba";
console.log(isPalindrome(s));  // Output will be true or false

function isPalindrome(s: string): boolean {
    let left = 0, right = s.length - 1;
    while (left < right) {
        if (s[left] !== s[right]) {
            return false;  // Return false if not a palindrome
        }
        left++;
        right--;
    }
    return true;  // Return true if palindrome
}

Isomorphic String

function isIsomorphic(s: string, t: string): boolean {
  if (s.length !== t.length) return false;

  const mpp = new Map<string, string>();

  for (let i = 0; i < s.length; i++) {
    const original = s[i];
    const replacement = t[i];
    if (!mpp.has(original)) {
      // Ensure no character in `t` is already mapped to another character in `s`
      if (![...mpp.values()].includes(replacement)) {
        mpp.set(original, replacement);
      } else {
        return false;
      }
    } else {
      const mappedChar = mpp.get(original);
      if (mappedChar !== replacement) {
        return false;
      }
    }
  }
  return true;
}

let s: string = "egg";
let t: string = "add";
console.log("ans: ", isIsomorphic(s, t));  // Output will be true or false

Check if Valid Anagram

function isValidAnagramOptimal(s: string, t: string): boolean {
  // If lengths are different, they cannot be anagrams
  if (s.length !== t.length) {
    return false;
  }

  // Initialize a frequency array for characters (assuming uppercase English letters)
  let freq = new Array(26).fill(0);

  // Count the frequency of characters in s
  for (let i = 0; i < s.length; i++) {
    freq[s.charCodeAt(i) - "A".charCodeAt(0)]++;
  }

  // Subtract the frequency of characters in t
  for (let i = 0; i < t.length; i++) {
    freq[t.charCodeAt(i) - "A".charCodeAt(0)]--;
  }

  // Check if all frequencies are zero, meaning the strings are anagrams
  for (let i = 0; i < 26; i++) {
    if (freq[i] !== 0) {
      return false;
    }
  }

  return true;
}

// Example usage:
let s: string = "INTEGER";
let t: string = "TEGERNI";
console.log(isValidAnagramOptimal(s, t));  // Output: true

Sort Char Freq

function freqSort(s: string): string {
  let map = new Map<string, number>();  // Map to store character frequencies
  let str = "";

  // Populate the map with the frequency of each character
  for (let i = 0; i < s.length; i++) {
    if (!map.has(s[i])) {
      map.set(s[i], 1);
    } else {
      map.set(s[i], map.get(s[i])! + 1); // Using non-null assertion for the value
    }
  }

  // Sort the map entries by frequency in descending order
  const newMap = new Map([...map.entries()].sort((a, b) => b[1] - a[1]));

  // Build the final string based on the sorted frequencies
  for (let [i, j] of newMap) {
    str += i.repeat(j);
  }

  return str;
}

// Example usage:
let s: string = "tree";
console.log("ans: ", freqSort(s));  // Output: "eetr"

Max Depth Parenthesis

function maxDepth(s: string): number {
  let maxDepth = 0;
  let currDept = 0;

  for (let i = 0; i < s.length; i++) {
    let ch = s[i];
    if (ch === "(") {
      currDept++;
      maxDepth = Math.max(maxDepth, currDept);
    } else if (ch === ")") {
      currDept--;
    }
  }
  return maxDepth;
}

// Example usage:
let s: string = "(1+(2*3)+((8)/4))+1";
console.log(maxDepth(s));  // Output: 3

Roman To Integer

function romanToInt(s: string): number {
  let map = new Map<string, number>();
  map.set("I", 1);
  map.set("V", 5);
  map.set("X", 10);
  map.set("L", 50);
  map.set("C", 100);
  map.set("D", 500);
  map.set("M", 1000);

  let result = 0;
  for (let i = 0; i < s.length; i++) {
    let curr = map.get(s[i])!;
    let next = map.get(s[i + 1])!;
    if (curr < next) {
      result -= curr; // Subtract the current value if it's less than the next
    } else {
      result += curr; // Add the current value otherwise
    }
  }
  return result;
}

// Example usage:
let s: string = "LVIII";
console.log("ans: ", romanToInt(s));  // Output: 58

Integer to Roman

function integerToRomanNaive(num: number): string {
  const map = new Map<number, string>();
  map.set(1, "I");
  map.set(5, "V");
  map.set(10, "X");
  map.set(50, "L");
  map.set(100, "C");
  map.set(500, "D");
  map.set(1000, "M");

  let base = 1;
  const result: string[] = [];
  while (num > 0) {
    const last = num % 10;
    if (last < 4) {
      for (let k = last; k > 0; k--) {
        result.unshift(map.get(base)!);
      }
    } else if (last == 4) {
      result.unshift(...[map.get(base)!, map.get(base * 5)!]);
    } else if (last == 5) {
      result.unshift(map.get(base * 5)!);
    } else if (last < 9) {
      for (let k = last; k > 5; k--) {
        result.unshift(map.get(base)!);
      }
      result.unshift(map.get(base * 5)!);
    } else {
      result.unshift(...[map.get(base)!, map.get(base * 10)!]);
    }
    base *= 10;
    num = (num - last) / 10;
  }
  return result.join("");
}

function integerToRomanOptimal(num: number): string {
  const map: [string, number][] = [
    ["M", 1000],
    ["CM", 900],
    ["D", 500],
    ["CD", 400],
    ["C", 100],
    ["XC", 90],
    ["L", 50],
    ["XL", 40],
    ["X", 10],
    ["IX", 9],
    ["V", 5],
    ["IV", 4],
    ["I", 1],
  ];

  let res = "";

  for (const [roman, val] of map) {
    while (num >= val) {
      res += roman;
      num -= val;
    }
  }
  return res;
}

// Example usage:
let num: number = 58;
console.log("ans: ", integerToRomanOptimal(num)); // Output: "LVIII"

Count Distinct Character

let str: string = "aabab";
let k: number = 2;
console.log("ans: ", countSubstringsWithKDistinctCharsOptimal(str, k));

function countSubstringsWithKDistinctCharsBruteForce(str: string, k: number): number {
  let n: number = str.length;
  let count: number = 0;

  for (let i = 0; i < n; i++) {
    for (let j = i; j < n; j++) {
      const substring: string = str.slice(i, j + 1);
      const distinctChars = new Set(substring);
      if (distinctChars.size === k) {
        count++;
      }
    }
  }
  return count;
}

function most_k_chars(s: string, k: number): number {
  if (!s) {
    return 0;
  }

  const char_count: { [key: string]: number } = {};
  let num: number = 0;
  let left: number = 0;

  for (let i = 0; i < s.length; i++) {
    char_count[s[i]] = (char_count[s[i]] || 0) + 1;
    while (Object.keys(char_count).length > k) {
      char_count[s[left]] -= 1;
      if (char_count[s[left]] === 0) {
        delete char_count[s[left]];
      }
      left += 1;
    }
    num += i - left + 1;
  }
  return num;
}

function countSubstringsWithKDistinctCharsOptimal(str: string, k: number): number {
  return most_k_chars(str, k) - most_k_chars(str, k - 1);
}

Longest Palindrome

let s: string = "babad";
console.log(longestPalindromeOptimal(s));

// TC: O(n^3), SC: O(1)
function longestPalindrome(s: string): string {
  let n: number = s.length;
  let longest: string = "";
  for (let i = 0; i < n; i++) {
    for (let j = i + 1; j <= n; j++) {
      const substring: string = s.slice(i, j);
      if (isPalindrome(substring) && substring.length > longest.length) {
        longest = substring;
      }
    }
  }
  return longest;
}

function isPalindrome(str: string): boolean {
  const n: number = str.length;
  for (let i = 0; i < Math.floor(n / 2); i++) {
    if (str[i] !== str[n - 1 - i]) {
      return false;
    }
  }
  return true;
}

function expandOverCenter(str: string, left: number, right: number): string {
  let n: number = str.length;
  while (left >= 0 && right < n && str[left] === str[right]) {
    left--;
    right++;
  }
  return str.slice(left + 1, right);
}

function longestPalindromeOptimal(s: string): string {
  const n: number = s.length;
  let maxPalindrome: string = "";
  for (let i = 0; i < n; i++) {
    const palindrom1: string = expandOverCenter(s, i, i);
    const palindrom2: string = expandOverCenter(s, i, i + 1);

    if (palindrom1.length > maxPalindrome.length) {
      maxPalindrome = palindrom1;
    }
    if (palindrom2.length > maxPalindrome.length) {
      maxPalindrome = palindrom2;
    }
  }
  return maxPalindrome;
}

Sum of beauty

let s: string = "aabcb";
console.log(sumOfBeautiesOptimal(s));

function sumOfBeautiesNaive(s: string): number {
  let n: number = s.length;
  let beautySum: number = 0;

  for (let i = 0; i < n; i++) {
    for (let j = i + 1; j < n; j++) {
      const substring: string = s.slice(i, j);
      beautySum += calculateBeauty(substring);
    }
  }
  return beautySum;
}

function calculateBeauty(substring: string): number {
  const charCount: Map<string, number> = new Map();
  let maxCount: number = 0;
  let minCount: number = Number.MAX_VALUE;

  for (let i = 0; i < substring.length; i++) {
    const char: string = substring[i];
    charCount.set(char, (charCount.get(char) || 0) + 1);
    maxCount = Math.max(maxCount, charCount.get(char)!);
    minCount = Math.min(minCount, charCount.get(char)!);
  }
  return maxCount - minCount;
}

function sumOfBeautiesOptimal(s: string): number {
  let beautySum: number = 0;
  const limit: number = s.length;

  for (let i = 0; i < limit; i++) {
    const freq: number[] = new Array(26).fill(0);
    for (let j = i; j < limit; j++) {
      freq[s.charCodeAt(j) - "a".charCodeAt(0)]++;
      beautySum += calculateBeautyFreq(freq);
    }
  }
  return beautySum;
}

function calculateBeautyFreq(freq: number[]): number {
  let max: number = -Infinity;
  let min: number = Infinity;

  for (let i = 0; i < 26; i++) {
    if (freq[i] !== 0) {
      max = Math.max(max, freq[i]);
      min = Math.min(min, freq[i]);
    }
  }
  return max - min;
}

Atoi

function atoi(str: string): number {
  // Remove leading whitespace
  str = str.trim();

  // Check for empty string
  if (!str) return 0;

  // Initialize variables
  let sign: number = 1;
  let result: number = 0;
  let index: number = 0;

  // Determine sign
  if (str[index] === '-') {
    sign = -1;
    index++;
  } else if (str[index] === '+') {
    index++;
  }

  // Convert characters to integer until a non-digit is encountered
  while (index < str.length && str[index] >= '0' && str[index] <= '9') {
    const digit: number = str.charCodeAt(index) - '0'.charCodeAt(0);
    result = result * 10 + digit;
    index++;
    
    // Handle overflow for 32-bit signed integer range
    if (result * sign < -2147483648) return -2147483648;
    if (result * sign > 2147483647) return 2147483647;
  }

  return result * sign;
}
console.log(atoi("42"));

Stack

Stack Using Array

const myStack: string[] = [];
myStack.push("a");
myStack.push("b");
myStack.push("c");
console.log(myStack); // Output: ['a', 'b', 'c']

myStack.pop();
myStack.push("e");
myStack.push("f");
console.log(myStack); // Output: ['a', 'b', 'e', 'f']

Stack Using LinkedList

class StackNode {
  value: string;
  next: StackNode | null;

  constructor(value: string) {
    this.value = value;
    this.next = null;
  }
}

class Stack {
  top: StackNode | null;
  size: number;

  constructor() {
    this.top = null;
    this.size = 0;
  }

  push(val: string): void {
    const newNode = new StackNode(val);
    if (this.size === 0) {
      this.top = newNode;
    } else {
      newNode.next = this.top;
      this.top = newNode;
    }
    this.size++;
  }

  getTop(): string | null {
    if (this.size === 0) return null;
    return this.top?.value || null;
  }

  pop(): string | null {
    if (this.size === 0) return null;
    const node = this.top;
    if (node) {
      this.top = node.next;
      this.size--;
      return node.value;
    }
    return null;
  }
}

// Testing the Stack
const stack = new Stack();
stack.push("a");
stack.push("b");
stack.push("c");
stack.push("d");

console.log(stack.pop()); // Output: "d"
console.log(stack.pop()); // Output: "c"
console.log(stack.pop()); // Output: "b"
console.log(stack.pop()); // Output: "a"
console.log(stack.getTop()); // Output: null

Queue Using ArrayList

const queue:string[]=[];
queue.push("a");
queue.push("b");
queue.push("c");
queue.push("d");
console.log(queue);
queue.shift();
console.log(queue);

Queue using LinkedList

class QueueNode {
  value: string;
  next: QueueNode | null;

  constructor(value: string) {
    this.value = value;
    this.next = null;
  }
}

class Queue {
  front: QueueNode | null;
  back: QueueNode | null;
  size: number;

  constructor() {
    this.front = null;
    this.back = null;
    this.size = 0;
  }

  enque(value: string): void {
    const newNode = new QueueNode(value);
    if (this.size === 0) {
      this.front = newNode;
      this.back = newNode;
    } else {
      this.back!.next = newNode; // Use non-null assertion
      this.back = newNode;
    }
    this.size++;
  }

  deque(): string | null {
    if (this.size === 0) {
      return null;
    }

    const node = this.front; // Store the front node to return its value
    if (this.front !== null) { // Check if front is not null
      this.front = this.front.next;
    }
    if (this.size === 1) {
      this.back = null;
    }
    this.size--;

    return node!.value; // Use non-null assertion since node is not null here
  }
}

const queue: Queue = new Queue();
queue.enque("a");
queue.enque("b");
queue.enque("c");
queue.enque("d");
console.log(queue);
console.log(queue.front?.value);
console.log(queue.back?.value);
console.log(queue.deque());
queue.deque();
queue.deque();
queue.deque();
console.log(queue);

Valid Paranthesis

let str: string = "(])";
console.log(checkValidParenthesis(str));

function checkValidParenthesis(str: string): boolean {
  let n: number = str.length;
  let stack: string[] = [];
  
  for (let i: number = 0; i < n; i++) {
    if (str[i] === "(" || str[i] === "[" || str[i] === "{") {
      stack.push(str[i]);
    } else {
      if (stack.length === 0) return false;
      let ch: string = stack[stack.length - 1];
      if (
        (str[i] === ")" && ch === "(") ||
        (str[i] === "}" && ch === "{") ||
        (str[i] === "]" && ch === "[")
      ) {
        stack.pop();
      } else {
        return false;
      }
    }
  }
  return stack.length === 0;
}

Stack Using Queue

class Stack {
  private queue1: number[];
  private queue2: number[];

  constructor() {
    this.queue1 = [];
    this.queue2 = [];
  }

  // Adds a new element to the stack
  push(value: number): void {
    this.queue1.push(value);
  }

  // Removes the top element from the stack and returns it
  pop(): number | null {
    if (this.queue1.length === 0) return null;

    // Transfer elements from queue1 to queue2, leaving only the last one
    while (this.queue1.length > 1) {
      this.queue2.push(this.queue1.shift() as number);
    }

    // The last element in queue1 is the top element of the stack
    const poppedItem = this.queue1.shift() as number;

    // Swap queues to keep queue1 as the main queue
    [this.queue1, this.queue2] = [this.queue2, this.queue1];
    return poppedItem;
  }

  // Returns the top element of the stack without removing it
  top(): number | null {
    if (this.queue1.length === 0) return null;

    // Transfer elements from queue1 to queue2, leaving only the last one
    while (this.queue1.length > 1) {
      this.queue2.push(this.queue1.shift() as number);
    }

    // Get the top item and add it back to queue2
    const topItem = this.queue1.shift() as number;
    this.queue2.push(topItem);

    // Swap queues to keep queue1 as the main queue
    [this.queue1, this.queue2] = [this.queue2, this.queue1];
    return topItem;
  }

  // Checks if the stack is empty
  isEmpty(): boolean {
    return this.queue1.length === 0;
  }

  // Returns the size of the stack
  size(): number {
    return this.queue1.length;
  }
}

// Testing the Stack implementation
const stack: Stack = new Stack();
stack.push(1);
stack.push(2);
stack.push(3);

console.log(stack.pop()); // Output: 3
console.log(stack.top()); // Output: 2
console.log(stack.pop()); // Output: 2
console.log(stack.isEmpty()); // Output: false
console.log(stack.size()); // Output: 1

Queue Using Stack

class Queue{
    private stack1:number[];
    private stack2: number[];
    constructor(){
        this.stack1=[];
        this.stack2=[];
    }
    enqueue(value:number):void{
        this.stack1.push(value);
    }
    dequeue():number|null{
        if(this.stack2.length===0){
            if(this.stack1.length===0){
                return null;
            }
            while(this.stack1.length>0){
                this.stack2.push(this.stack1.pop() as number);
            }
        }
        return this.stack2.pop() || null;
    }
    front():number | null{
        if(this.stack2.length===0){
            if(this.stack1.length===0){
                return null;
            }
            while(this.stack1.length>0){
                this.stack2.push(this.stack1.pop()as number);
            }
        }
        return this.stack2[this.stack2.length-1]||null;
    }
isEmpty():boolean{
    return this.stack1.length===0&&this.stack2.length===0;
}
size():number{
    return this.stack1.length+this.stack2.length;
}
}
// Example usage:
const queue = new Queue();
queue.enqueue(1);
queue.enqueue(2);
queue.enqueue(3);

console.log(queue.dequeue()); // 1
console.log(queue.front()); // 2
console.log(queue.dequeue()); // 2
console.log(queue.isEmpty()); // false
console.log(queue.size()); // 1

Min Stack

class MinStack{
    private stack:number[];
    private minStack:number[];
    constructor(){
        this.stack=[];
        this.minStack=[];
    }
push(val:number):void{
    this.stack.push(val);
    if(this.minStack.length===0 || val<=this.minStack[this.minStack.length-1]){
        this.minStack.push(val);
    }
}
pop():void{
    if(this.stack.length===0)return;
    if(this.stack[this.stack.length-1]===this.minStack[this.minStack.length-1]){
        this.minStack.pop();
    }
    this.stack.pop();
}
top():number|null{
    if(this.stack.length===0) return null;
    return this.stack[this.stack.length-1];
}
getMin():number|null{
    if(this.minStack.length===0) return null;
    return this.minStack[this.minStack.length-1];
}
}
const minStack = new MinStack();
minStack.push(-2);
minStack.push(0);
minStack.push(-3);
console.log(minStack.getMin()); // Output: -3
minStack.pop();
console.log(minStack.top());    // Output: 0
console.log(minStack.getMin()); // Output: -2

Next Greater Element

const nums1: number[] = [4, 1, 2];
const nums2: number[] = [1, 3, 4, 2];
const result = nextGreaterElement(nums1, nums2);
console.log(result);

function nextGreaterElement(nums1: number[], nums2: number[]): number[] {
    const nextGreater = new Map<number, number>();
    const stack: number[] = [];

    for (const num of nums2) {
        while (stack.length > 0 && stack[stack.length - 1] < num) {
            nextGreater.set(stack.pop() as number, num);
        }
        stack.push(num);
    }

    const result: number[] = [];
    for (const num1 of nums1) {
        result.push(nextGreater.has(num1) ? nextGreater.get(num1)! : -1);
    }
    return result;
}

Next Smallest Element

let arr:number[]=[4,5,2,10,8];
console.log(nextSmallerElement(arr));
function nextSmallerElement(arr:number[]){
    let n:number=arr.length;
    let stack:number[]=[];
    let ans:number[]=[];
    ans[0]=-1;
for(let i=0;i<n;i++){
    while(stack.length>0 && stack[stack.length-1]>=arr[i]){
        stack.pop() as number;
    }
    if(stack.length===0){
        ans[i]=-1;
    }
    else{
        ans[i]=stack[stack.length-1];
    }
    stack.push(arr[i]);
}
return ans;
}

Trapping Rain Water

let arr: number[] = [0, 1, 2, 1, 4, 3, 3, 2];
let n: number = arr.length;
console.log(trapWater(arr, n));

function trapWater(arr: number[], n: number): number {
    let left = 0, right = n - 1;
    let waterTrapped = 0;
    let maxLeft = 0, maxRight = 0;

    while (left <= right) {
        if (arr[left] <= arr[right]) {
            if (arr[left] >= maxLeft) {
                maxLeft = arr[left];
            } else {
                waterTrapped += maxLeft - arr[left];
            }
            left++;
        } else {
            if (arr[right] >= maxRight) {
                maxRight = arr[right];
            } else {
                waterTrapped += maxRight - arr[right];
            }
            right--;
        }
    }
    return waterTrapped;
}

Sum of Sub Array Min

function subArrayMinOptimal(arr: number[], n: number): number {
  const mod = 10 ** 9 + 7;
  const left: number[] = new Array(n);
  const right: number[] = new Array(n);
  const stack: number[] = [];

  // Calculate the left boundary for each element
  for (let i = 0; i < n; i++) {
    while (stack.length > 0 && arr[stack[stack.length - 1]] > arr[i]) {
      stack.pop();
    }
    left[i] = stack.length === 0 ? -1 : stack[stack.length - 1];
    stack.push(i);
  }

  stack.length = 0; // Reset stack for right boundary calculation

  // Calculate the right boundary for each element
  for (let i = n - 1; i >= 0; i--) {
    while (stack.length !== 0 && arr[stack[stack.length - 1]] >= arr[i]) {
      stack.pop();
    }
    right[i] = stack.length === 0 ? n : stack[stack.length - 1];
    stack.push(i);
  }

  let sum = 0;

  // Calculate the sum of subarray minimums
  for (let i = 0; i < n; i++) {
    sum = (sum + (i - left[i]) * (right[i] - i) * arr[i]) % mod;
  }

  return sum;
}

// Example usage
const arr: number[] = [3, 1, 2, 4];
const n: number = arr.length;
console.log(subArrayMinOptimal(arr, n)); // Output: 17

Histogram

let arr:number[] = [2, 1, 5, 6, 2, 3, 1];
let n:number = arr.length;
console.log(largestArea(arr, n));

function largestArea(arr:number[],n:number){
    let stack:number[]=[];
    let leftSmall:number[]=new Array(n);
    let rightSmall:number[]=new Array(n);
    for(let i=0;i<n;i++){
  while (stack.length != 0 && arr[stack[stack.length - 1]] >= arr[i]) {
      stack.pop();
    }
    if (stack.length == 0) {
      leftSmall[i] = 0;
    } else {
      leftSmall[i] = stack[stack.length - 1] + 1;
    }
    stack.push(i);
  }

  while (stack.length !== 0) {
    stack.pop();
  }

  for (let i = n - 1; i >= 0; i--) {
    while (stack.length !== 0 && arr[stack[stack.length - 1]] >= arr[i]) {
      stack.pop();
    }
    if (stack.length == 0) {
      rightSmall[i] = n - 1;
    } else {
      rightSmall[i] = stack[stack.length - 1] - 1;
    }
    stack.push(i);
  }

  let maxA = 0;
  for (let i = 0; i < n; i++) {
    maxA = Math.max(maxA, arr[i] * (rightSmall[i] - leftSmall[i] + 1));
  }
  return maxA;
}

Asteroid Collision

function asteroidCollision(asteroids: number[]): number[] {
  const stack: number[] = [];

  for (let i = 0; i < asteroids.length; i++) {
    let add = true;
    while (stack.length !== 0 && asteroids[i] < 0 && stack[stack.length - 1] > 0) {
      if (Math.abs(asteroids[i]) > Math.abs(stack[stack.length - 1])) {
        stack.pop();
      } else if (Math.abs(asteroids[i]) === Math.abs(stack[stack.length - 1])) {
        stack.pop();
        add = false;
        break;
      } else {
        add = false;
        break;
      }
    }
    if (add) stack.push(asteroids[i]);
  }
  return stack;
}

// Example usage
let asteroids: number[] = [5, 10, -5];
console.log(asteroidCollision(asteroids)); // Output: [5, 10]

Sum of Sub Arrays Ranges

function subArrayRanges(arr: number[], n: number): number {
  let total = 0;

  for (let i = 0; i < n; i++) {
    let min = arr[i];
    let max = arr[i];
    for (let j = i; j < n; j++) {
      min = Math.min(min, arr[j]);
      max = Math.max(max, arr[j]);
      total += max - min;
    }
  }
  return total;
}

function subArrayRangesOptimal(arr: number[], n: number): number {
  const mod = 10 ** 9 + 7;
  let result = 0;
  let stack: number[] = [];

  const left: number[] = new Array(n).fill(0);
  const maxLeft: number[] = new Array(n).fill(0);
  const right: number[] = new Array(n).fill(0);
  const maxRight: number[] = new Array(n).fill(0);

  // Calculate left distances for minimums
  for (let i = 0; i < n; i++) {
    while (stack.length > 0 && arr[i] < arr[stack[stack.length - 1]]) {
      stack.pop();
    }
    left[i] = stack.length === 0 ? i + 1 : i - stack[stack.length - 1];
    stack.push(i);
  }

  stack = [];

  // Calculate right distances for minimums
  for (let i = n - 1; i >= 0; i--) {
    while (stack.length > 0 && arr[i] <= arr[stack[stack.length - 1]]) {
      stack.pop();
    }
    right[i] = stack.length === 0 ? n - i : stack[stack.length - 1] - i;
    stack.push(i);
  }

  stack = [];

  // Calculate left distances for maximums
  for (let i = 0; i < n; i++) {
    while (stack.length > 0 && arr[i] > arr[stack[stack.length - 1]]) {
      stack.pop();
    }
    maxLeft[i] = stack.length === 0 ? i + 1 : i - stack[stack.length - 1];
    stack.push(i);
  }

  stack = [];

  // Calculate right distances for maximums
  for (let i = n - 1; i >= 0; i--) {
    while (stack.length > 0 && arr[i] >= arr[stack[stack.length - 1]]) {
      stack.pop();
    }
    maxRight[i] = stack.length === 0 ? n - i : stack[stack.length - 1] - i;
    stack.push(i);
  }

  // Calculate the result using min and max distances
  for (let i = 0; i < n; i++) {
    result = (result + (maxLeft[i] * maxRight[i] - left[i] * right[i]) * arr[i]) % mod;
  }

  return result;
}

// Example usage:
let arr: number[] = [1, 2, 3];
let n: number = arr.length;
console.log(subArrayRanges(arr, n)); // Brute force approach
console.log(subArrayRangesOptimal(arr, n)); // Optimal approach

Remove K Digits

function removeKdigits(num: string, k: number): string {
  let stack: string[] = [];

  for (let digit of num) {
    while (k > 0 && stack.length > 0 && digit < stack[stack.length - 1]) {
      stack.pop();
      k--;
    }
    stack.push(digit);
  }

  // Remove any remaining digits from the end if k > 0
  stack.length = Math.max(stack.length - k, 0);

  // Join the stack to form the result string and remove leading zeros
  let result = stack.join("");
  result = result.replace(/^0+/, "");

  // Return "0" if the result is empty, otherwise the result
  return result === "" ? "0" : result;
}

// Example usage:
let num = "1432219";
let k = 3;
console.log(removeKdigits(num, k)); // Output: "1219"

LRU Cache

class LRUCache {
  private capacity: number;
  private cache: Map<number, DoublyLinkedListNode>;
  private order: DoublyLinkedList;

  constructor(capacity: number) {
    this.capacity = capacity;
    this.cache = new Map(); // Use a Map for key-value storage
    this.order = new DoublyLinkedList(); // Doubly linked list for maintaining order
  }

  get(key: number): number {
    if (this.cache.has(key)) {
      // Move the accessed item to the front
      const node = this.cache.get(key)!;
      this.order.moveToFront(node);
      return node.value;
    }
    return -1;
  }

  put(key: number, value: number): void {
    if (this.cache.has(key)) {
      // Update the existing key
      const node = this.cache.get(key)!;
      node.value = value;
      this.order.moveToFront(node);
    } else {
      // Add a new key
      if (this.cache.size === this.capacity) {
        // Remove the least recently used item
        const removedKey = this.order.removeFromEnd();
        if (removedKey !== null) this.cache.delete(removedKey);
      }
      const newNode = new DoublyLinkedListNode(key, value);
      this.cache.set(key, newNode);
      this.order.addToFront(newNode);
    }
  }
}

class DoublyLinkedListNode {
  key: number;
  value: number;
  prev: DoublyLinkedListNode | null;
  next: DoublyLinkedListNode | null;

  constructor(key: number, value: number) {
    this.key = key;
    this.value = value;
    this.prev = null;
    this.next = null;
  }
}

class DoublyLinkedList {
  private head: DoublyLinkedListNode;
  private tail: DoublyLinkedListNode;

  constructor() {
    this.head = new DoublyLinkedListNode(0, 0);
    this.tail = new DoublyLinkedListNode(0, 0);
    this.head.next = this.tail;
    this.tail.prev = this.head;
  }

  addToFront(node: DoublyLinkedListNode): void {
    const next = this.head.next!;
    node.prev = this.head;
    node.next = next;
    this.head.next = node;
    next.prev = node;
  }

  removeFromEnd(): number | null {
    if (this.tail.prev === this.head) return null;
    const lastNode = this.tail.prev!;
    this.removeNode(lastNode);
    return lastNode.key;
  }

  moveToFront(node: DoublyLinkedListNode): void {
    this.removeNode(node);
    this.addToFront(node);
  }

  private removeNode(node: DoublyLinkedListNode): void {
    const prevNode = node.prev!;
    const nextNode = node.next!;
    prevNode.next = nextNode;
    nextNode.prev = prevNode;
  }
}

// Example usage:
const lRUCache = new LRUCache(2);
lRUCache.put(1, 1);
lRUCache.put(2, 2);
console.log(lRUCache.get(1)); // Output: 1
lRUCache.put(3, 3); // LRU key was 2, evicts key 2
console.log(lRUCache.get(2)); // Output: -1
lRUCache.put(4, 4); // LRU key was 1, evicts key 1
console.log(lRUCache.get(1)); // Output: -1
console.log(lRUCache.get(3)); // Output: 3
console.log(lRUCache.get(4)); // Output: 4

Greedy

Fractional Knapsack

type Item = {
  value: number;
  weight: number;
};

function fractionalKnapsack(W: number, arr: Item[], n: number): number {
  // Sort items by value-to-weight ratio in descending order
  arr.sort((a, b) => b.value / b.weight - a.value / a.weight);

  let maxValue = 0; // Maximum value obtained
  let fractions: { item: Item; fraction: number }[] = []; // To track fractions of items used

  for (let item of arr) {
    if (item.weight <= W) {
      // If the entire item fits, take it completely
      maxValue += item.value;
      W -= item.weight;
      fractions.push({ item, fraction: 1 });
    } else {
      // If only a part of the item fits, take the fraction
      const fraction = W / item.weight;
      maxValue += item.value * fraction;
      fractions.push({ item, fraction });
      break; // Knapsack is full
    }
  }

  // Optionally, you can return `fractions` for more details
  return maxValue;
}

// Example Usage
const items: Item[] = [
  { value: 60, weight: 10 },
  { value: 100, weight: 20 },
  { value: 120, weight: 30 },
];

const capacity = 50;
console.log(fractionalKnapsack(capacity, items, items.length)); // Output: 240

Fractional Knapsack

Recursion

Atoi

function iterativeAtoi(str: string): number {
  let sign = 1;
  let base = 0;
  let i = 0;

  // Skip leading whitespace
  while (
    i < str.length &&
    (str[i] === " " || str[i] === "\t" || str[i] === "\n" || str[i] === "\r")
  ) {
    i++;
  }

  // Check for sign
  if (str[i] === "-" || str[i] === "+") {
    sign = str[i] === "-" ? -1 : 1;
    i++;
  }

  // Convert digits to integer
  while (i < str.length && str[i] >= "0" && str[i] <= "9") {
    if (
      base > Number.MAX_SAFE_INTEGER / 10 ||
      (base === Number.MAX_SAFE_INTEGER / 10 && +str[i] > 7)
    ) {
      return sign === 1 ? Number.MAX_SAFE_INTEGER : Number.MIN_SAFE_INTEGER;
    }
    base = 10 * base + (+str[i]);
    i++;
  }

  return base * sign;
}

function recursiveAtoi(str: string): number {
  let sign = 1;
  let base = 0;
  let i = 0;

  // Skip leading whitespace
  while (
    i < str.length &&
    (str[i] === " " || str[i] === "\t" || str[i] === "\n" || str[i] === "\r")
  ) {
    i++;
  }

  // Check for sign
  if (str[i] === "-" || str[i] === "+") {
    sign = str[i] === "-" ? -1 : 1;
    i++;
  }

  return convert(sign, str, i, base);
}

function convert(sign: number, str: string, i: number, base: number): number {
  if (i < str.length && str[i] >= "0" && str[i] <= "9") {
    if (
      base > Number.MAX_SAFE_INTEGER / 10 ||
      (base === Number.MAX_SAFE_INTEGER / 10 && +str[i] > 7)
    ) {
      return sign === 1 ? Number.MAX_SAFE_INTEGER : Number.MIN_SAFE_INTEGER;
    }
    base = 10 * base + (+str[i]);
    return convert(sign, str, i + 1, base);
  }

  return base * sign;
}

// Example Usage
console.log(iterativeAtoi("-123")); // Output: -123
console.log(iterativeAtoi("+123")); // Output: 123
console.log(iterativeAtoi("/123")); // Output: 0 (invalid input)

console.log(recursiveAtoi("-123")); // Output: -123
console.log(recursiveAtoi("+123")); // Output: 123
console.log(recursiveAtoi("/123")); // Output: 0 (invalid input)

Pow XN

function myPowIterative(x: number, n: number): number {
  if (n === 0) return 1;

  let result = 1;
  let base = x;
  let exponent = Math.abs(n);

  while (exponent > 0) {
    if (exponent % 2 === 1) {
      result *= base;
    }
    base *= base;
    exponent = Math.floor(exponent / 2);
  }

  return n < 0 ? 1 / result : result;
}

function myPowRecursive(x: number, n: number): number {
  if (n === 0) return 1;

  if (n < 0) {
    x = 1 / x;
    n = -n;
  }

  return n % 2 === 0
    ? myPowRecursive(x * x, Math.floor(n / 2))
    : x * myPowRecursive(x * x, Math.floor(n / 2));
}

// Example Usage
console.log(myPowIterative(2, 3));   // Output: 8
console.log(myPowIterative(2, -3));  // Output: 0.125

console.log(myPowRecursive(2, 3));   // Output: 8
console.log(myPowRecursive(2, -3));  // Output: 0.125

Count Good Number

const MOD = 10 ** 9 + 7;

function countGoodDigitStrings(N: number): number {
  let count = 0;

  function isGoodDigitString(s: string): boolean {
    for (let i = 0; i < s.length; i++) {
      if (i % 2 === 0 && +s[i] % 2 !== 0) return false; // Even positions must have even digits
      if (i % 2 === 1 && ![2, 3, 5, 7].includes(+s[i])) return false; // Odd positions must have prime digits
    }
    return true;
  }

  for (let num = 0; num < Math.pow(10, N); num++) {
    const paddedNum = num.toString().padStart(N, "0");
    if (isGoodDigitString(paddedNum)) {
      count++;
    }
  }

  return count % MOD;
}

function countGoodDigitStringsOptimal(N: number): number {
  let count = 1;

  if (N % 2 === 0) {
    count *= modPow(4, Math.floor(N / 2)); // 4 choices for even positions
    count *= modPow(5, Math.floor(N / 2)); // 5 choices for odd positions
    count %= MOD;
  } else {
    count *= modPow(4, Math.floor(N / 2)); // 4 choices for even positions
    count *= modPow(5, Math.floor((N + 1) / 2)); // 5 choices for odd positions
    count %= MOD;
  }

  return count;
}

function modPow(base: number, exponent: number): number {
  if (exponent === 0) return 1;

  let result = 1;
  base = base % MOD;

  while (exponent > 0) {
    if (exponent % 2 === 1) {
      result = (result * base) % MOD;
    }
    base = (base * base) % MOD;
    exponent = Math.floor(exponent / 2);
  }

  return result % MOD;
}

// Example Usage:
console.log(countGoodDigitStrings(2)); // Output for the brute-force approach
console.log(countGoodDigitStringsOptimal(50)); // Output for the optimized approach

Binary String With consecutive 1s

function generateAllStrings(k: number): void {
  if (k <= 0) {
    return;
  }
  
  const str: string[] = new Array(k);
  
  // Start with the first character as "0"
  str[0] = "0";
  generateAllStringsUtil(k, str, 1);

  // Start with the first character as "1"
  str[0] = "1";
  generateAllStringsUtil(k, str, 1);
}

function generateAllStringsUtil(k: number, str: string[], n: number): void {
  // Base case: If the string length reaches k, print it
  if (n === k) {
    console.log(str.join(""));
    return;
  }

  // If the previous character is "1", only "0" can follow
  if (str[n - 1] === "1") {
    str[n] = "0";
    generateAllStringsUtil(k, str, n + 1);
  }

  // If the previous character is "0", both "0" and "1" can follow
  if (str[n - 1] === "0") {
    str[n] = "0";
    generateAllStringsUtil(k, str, n + 1);

    str[n] = "1";
    generateAllStringsUtil(k, str, n + 1);
  }
}

// Example usage
const k = 3;
generateAllStrings(k);

Generate Paranthesis

function generateParenthesis(n: number): string[] {
  const result: string[] = [];
  generateAllParenthesis(result, "(", 1, 0, n);
  return result;
}

function generateAllParenthesis(
  result: string[],
  str: string,
  open: number,
  close: number,
  n: number
): void {
  // Base case: If the number of open and close parentheses equals n, add to result
  if (open === n && close === n) {
    result.push(str);
    return;
  }

  // If the number of open parentheses is less than n, add an open parenthesis
  if (open < n) {
    generateAllParenthesis(result, str + "(", open + 1, close, n);
  }

  // If the number of close parentheses is less than open, add a close parenthesis
  if (close < open) {
    generateAllParenthesis(result, str + ")", open, close + 1, n);
  }
}

// Example usage
const n = 3;
console.log(generateParenthesis(n));

Seq of strings

const str: string = "abc";
const ans: string[] = [];
getAllSubsequence(0, str, ans, "");
console.log("ans: ", ans);

function getAllSubsequence(
  i: number,
  str: string,
  ans: string[],
  current: string
): void {
  // Base case: If the current index reaches the string's length, add the current subsequence to the result
  if (i === str.length) {
    ans.push(current);
    return;
  }

  // Include the current character in the subsequence
  getAllSubsequence(i + 1, str, ans, current + str[i]);

  // Exclude the current character from the subsequence
  getAllSubsequence(i + 1, str, ans, current);
}

Sub Sequence with sum k

const arr: number[] = [2, 5, 8, 4, 6, 11];
const targetSum: number = 13;
const ans: number[][] = [];
const v: number[] = [];

subSeq(0, arr, targetSum, ans, 0, v);
console.log(ans);

function subSeq(
  i: number,
  arr: number[],
  targetSum: number,
  ans: number[][],
  currSum: number,
  v: number[]
): void {
  // Base case: When the current index reaches the end of the array
  if (i === arr.length) {
    // If the current sum equals the target sum, add the current sequence to the result
    if (currSum === targetSum) {
      ans.push([...v]);
    }
    return;
  }

  // Include the current element in the subsequence
  subSeq(i + 1, arr, targetSum, ans, currSum + arr[i], [...v, arr[i]]);

  // Exclude the current element from the subsequence
  subSeq(i + 1, arr, targetSum, ans, currSum, v);
}

Find Combination Sum

const arr: number[] = [2, 3, 5];
const target: number = 8;
const ans: number[][] = [];

findCombinationSum(0, arr, target, ans, []);
console.log(ans);

function findCombinationSum(
  i: number,
  arr: number[],
  target: number,
  ans: number[][],
  ds: number[]
): void {
  // Base case: If we have reached the end of the array
  if (i === arr.length) {
    // If the target is exactly 0, add the current combination to the result
    if (target === 0) {
      ans.push([...ds]);
    }
    return;
  }

  // Include the current element in the combination if it is less than or equal to the target
  if (arr[i] <= target) {
    ds.push(arr[i]); // Add the current element to the combination
    findCombinationSum(i, arr, target - arr[i], ans, ds); // Recurse with the reduced target
    ds.pop(); // Backtrack to explore other combinations
  }

  // Exclude the current element and move to the next
  findCombinationSum(i + 1, arr, target, ans, ds);
}

Combination

function findCombinationSum(
  i: number,
  arr: number[],
  target: number,
  ans: number[][],
  ds: number[]
): void {
  if (target === 0) {
    ans.push([...ds]); // Add the current combination to the results
    return;
  }

  for (let j = i; j < arr.length; j++) {
    // Skip duplicate elements to avoid duplicate combinations
    if (j > i && arr[j] === arr[j - 1]) continue;

    // Break the loop if the current number exceeds the target
    if (arr[j] > target) break;

    // Include the current element in the combination
    ds.push(arr[j]);

    // Recursively call for the next index with a reduced target
    findCombinationSum(j + 1, arr, target - arr[j], ans, ds);

    // Backtrack by removing the current element from the combination
    ds.pop();
  }
}

// Input
const candidates: number[] = [10, 1, 2, 7, 6, 1, 5].sort((a, b) => a - b); // Sort the array
const target: number = 8;
const ans: number[][] = [];

// Function call
findCombinationSum(0, candidates, target, ans, []);

// Output the results
console.log(ans);

Sub set sum

// Function to calculate all subset sums
function subSetSum(arr: number[], n: number): number[] {
  const ans: number[] = [];
  subSetSumHelper(0, arr, n, ans, 0);
  return ans;
}

function subSetSumHelper(
  index: number,
  arr: number[],
  n: number,
  ans: number[],
  sum: number
): void {
  if (index === n) {
    ans.push(sum); // Add the current sum to the answer array
    return;
  }

  // Include the current element in the sum
  subSetSumHelper(index + 1, arr, n, ans, sum + arr[index]);

  // Exclude the current element from the sum
  subSetSumHelper(index + 1, arr, n, ans, sum);
}

// Function to generate all subsets
function subSet(
  index: number,
  arr: number[],
  n: number,
  ans: number[][],
  ds: number[]
): void {
  if (index === n) {
    ans.push([...ds]); // Add a copy of the current subset to the answer array
    return;
  }

  // Include the current element in the subset
  subSet(index + 1, arr, n, ans, [...ds, arr[index]]);

  // Exclude the current element from the subset
  subSet(index + 1, arr, n, ans, ds);
}

// Input array
const arr: number[] = [3, 1, 2];
const n: number = arr.length;

// Calculate subset sums
console.log("Subset sums: ", subSetSum(arr, n));

// Generate subsets
const subsets: number[][] = [];
subSet(0, arr, n, subsets, []);
console.log("Subsets: ", subsets);

Subset sum2

function subsetWithDup(arr: number[], n: number): number[][] {
  const ans: number[][] = [];
  
  // Sort the array to ensure duplicates are adjacent
  arr.sort((a, b) => a - b);
  
  subSetHelper(0, arr, n, ans, []);
  
  return ans;
}

function subSetHelper(
  index: number,
  arr: number[],
  n: number,
  ans: number[][],
  ds: number[]
): void {
  // Add a copy of the current subset to the result
  ans.push([...ds]);

  // Loop through the array starting from the current index
  for (let i = index; i < n; i++) {
    // Skip duplicate elements at the same recursion level
    if (i !== index && arr[i] === arr[i - 1]) continue;

    // Include the current element in the subset
    ds.push(arr[i]);

    // Recursively call for the next index
    subSetHelper(i + 1, arr, n, ans, ds);

    // Backtrack: remove the last element
    ds.pop();
  }
}

// Input array
const arr: number[] = [1, 2, 2];
const n: number = arr.length;

// Generate subsets
console.log("Unique subsets: ", subsetWithDup(arr, n));

combination sum3

function combinationSum3(k: number, n: number): number[][] {
  const ans: number[][] = [];
  
  // Call the helper function for backtracking
  backtrack(1, k, n, ans, [], 0);
  
  return ans;
}

function backtrack(
  index: number,
  k: number,
  n: number,
  ans: number[][],
  ds: number[],
  sum: number
): void {
  // If the subset has exactly `k` numbers and their sum equals `n`, add to the result
  if (ds.length === k && sum === n) {
    ans.push([...ds]);
    return;
  }

  // Stop recursion if the subset length exceeds `k` or the sum exceeds `n`
  if (ds.length >= k || sum > n) {
    return;
  }

  // Iterate from the current index to 9
  for (let i = index; i <= 9; i++) {
    // Include the current number in the subset
    ds.push(i);

    // Recursively call for the next index
    backtrack(i + 1, k, n, ans, ds, sum + i);

    // Backtrack: remove the last element
    ds.pop();
  }
}

// Input parameters
const k: number = 3;
const n: number = 7;

// Get all combinations
console.log("Combinations: ", combinationSum3(k, n));

Letter combination

const digit: string = "234";

const map: { [key: string]: string } = {
  2: "abc",
  3: "def",
  4: "ghi",
  5: "jkl",
  6: "mno",
  7: "pqrs",
  8: "tuv",
  9: "wxyz",
};

console.log(letterCombination(digit));

function letterCombination(digit: string): string[] {
  if (!digit) return [];
  
  const ans: string[] = [];
  
  // Call the helper function for backtracking
  backtrack(0, ans, digit, "");
  
  return ans;
}

function backtrack(
  i: number,
  ans: string[],
  digit: string,
  curr: string
): void {
  // If the current index reaches the length of digits, add the combination
  if (i === digit.length) {
    ans.push(curr);
    return;
  }

  // Iterate over the letters mapped to the current digit
  for (const letter of map[digit[i]]) {
    backtrack(i + 1, ans, digit, curr + letter);
  }
}

Palindrome Partitioning

const s: string = "aabb";
console.log(palindromePartition(s));

function palindromePartition(s: string): string[][] {
  const ans: string[][] = [];
  backtrack(0, s, ans, []);
  return ans;
}

function backtrack(
  index: number,
  s: string,
  ans: string[][],
  ds: string[]
): void {
  // Base case: if the current index reaches the end of the string
  if (index === s.length) {
    ans.push([...ds]);
    return;
  }

  // Explore all substrings starting from the current index
  for (let i = index; i < s.length; i++) {
    if (isPalindrome(s, index, i)) {
      ds.push(s.substring(index, i + 1)); // Add the palindrome substring
      backtrack(i + 1, s, ans, ds); // Recurse for the next part of the string
      ds.pop(); // Backtrack
    }
  }
}

function isPalindrome(s: string, start: number, end: number): boolean {
  while (start < end) {
    if (s[start++] !== s[end--]) {
      return false;
    }
  }
  return true;
}

Word Search

const board: string[][] = [
  ["A", "B", "C", "E"],
  ["S", "F", "C", "S"],
  ["A", "D", "E", "E"],
];
const word: string = "SEE";

console.log(wordSearch(board, word));

function wordSearch(board: string[][], word: string): boolean {
  const n: number = board.length;
  const m: number = board[0].length;

  for (let i = 0; i < n; i++) {
    for (let j = 0; j < m; j++) {
      if (board[i][j] === word[0]) {
        if (searchNext(board, word, i, j, 0, n, m)) {
          return true;
        }
      }
    }
  }
  return false;
}

function searchNext(
  board: string[][],
  word: string,
  row: number,
  col: number,
  index: number,
  n: number,
  m: number
): boolean {
  // Base case: if we've matched the entire word
  if (index === word.length) {
    return true;
  }

  // Boundary and validity checks
  if (
    row < 0 ||
    col < 0 ||
    row >= n ||
    col >= m ||
    board[row][col] !== word[index] ||
    board[row][col] === "!"
  ) {
    return false;
  }

  // Save the current character and mark it as visited
  const temp: string = board[row][col];
  board[row][col] = "!";

  // Explore in all 4 directions
  const top = searchNext(board, word, row - 1, col, index + 1, n, m);
  const bottom = searchNext(board, word, row + 1, col, index + 1, n, m);
  const left = searchNext(board, word, row, col - 1, index + 1, n, m);
  const right = searchNext(board, word, row, col + 1, index + 1, n, m);

  // Restore the current cell
  board[row][col] = temp;

  // Return true if any direction leads to a solution
  return top || bottom || left || right;
}

NQueens

const n: number = 4;
console.log(solveNQueens(n));

function solveNQueens(n: number): string[][] {
  const board: string[][] = Array.from({ length: n }, () => Array(n).fill("."));
  const ans: string[][] = [];
  backtrack(0, board, ans);
  return ans;
}

function backtrack(col: number, board: string[][], ans: string[][]): void {
  if (col === board.length) {
    ans.push(board.map((row) => row.join("")));
    return;
  }

  for (let row = 0; row < board.length; row++) {
    if (validate(board, row, col)) {
      board[row][col] = "Q";
      backtrack(col + 1, board, ans);
      board[row][col] = ".";
    }
  }
}

function validate(board: string[][], row: number, col: number): boolean {
  let tempRow = row;
  let tempCol = col;

  // Check upper diagonal (top-left)
  while (row >= 0 && col >= 0) {
    if (board[row][col] === "Q") return false;
    row--;
    col--;
  }

  row = tempRow;
  col = tempCol;

  // Check left side
  while (col >= 0) {
    if (board[row][col] === "Q") return false;
    col--;
  }

  row = tempRow;
  col = tempCol;

  // Check lower diagonal (bottom-left)
  while (col >= 0 && row < board.length) {
    if (board[row][col] === "Q") return false;
    col--;
    row++;
  }

  return true;
}

ratInMaze

const maze: number[][] = [
  [1, 0, 0, 0],
  [1, 1, 0, 1],
  [1, 1, 0, 0],
  [0, 1, 1, 1],
];
const n: number = maze.length;
const result = findPaths(n, maze);
console.log(result);

function findPaths(n: number, m: number[][]): string[] {
  const paths: string[] = [];
  const path: string[] = new Array(n).fill("");
  const directions: string[] = ["D", "L", "R", "U"];
  const visited: boolean[][] = Array.from({ length: n }, () => Array(n).fill(false));

  function isSafe(x: number, y: number, visited: boolean[][]): boolean {
    return x >= 0 && x < n && y >= 0 && y < n && m[x][y] === 1 && !visited[x][y];
  }

  function findPath(x: number, y: number, visited: boolean[][], index: number): void {
    if (x === n - 1 && y === n - 1) {
      paths.push(path.join(""));
      return;
    }

    visited[x][y] = true;

    for (const dir of directions) {
      const newX: number = x + (dir === "U" ? -1 : dir === "D" ? 1 : 0);
      const newY: number = y + (dir === "L" ? -1 : dir === "R" ? 1 : 0);

      if (isSafe(newX, newY, visited)) {
        path[index] = dir;
        findPath(newX, newY, visited, index + 1);
      }
    }

    visited[x][y] = false;
  }

  findPath(0, 0, visited, 0);

  return paths.sort();
}

word break

const s1: string = "leetcode";
const wordDict1: string[] = ["leet", "code"];
console.log(wordBreakRecursion(s1, wordDict1)); // Output: true

const s2: string = "applepenapple";
const wordDict2: string[] = ["apple", "pen"];
console.log(wordBreakRecursion(s2, wordDict2)); // Output: true

const s3: string = "catsandog";
const wordDict3: string[] = ["cats", "dog", "sand", "and", "cat"];
console.log(wordBreakRecursion(s3, wordDict3)); // Output: false

function wordBreakRecursion(s: string, wordDict: string[]): boolean {
  function canSegment(s: string): boolean {
    if (s === "") {
      return true;
    }

    for (const word of wordDict) {
      if (s.startsWith(word) && canSegment(s.slice(word.length))) {
        return true;
      }
    }
    return false;
  }

  return canSegment(s);
}

nColoring

const N: number = 4;
const M: number = 3;
const graph: number[][] = [
  [0, 1, 1, 1],
  [1, 0, 1, 0],
  [1, 1, 0, 1],
  [1, 0, 1, 0],
];
console.log(graphColoring(graph, M, N));

function graphColoring(graph: number[][], M: number, N: number): boolean {
  const color: number[] = new Array(N).fill(-1);

  function isSafe(vertex: number, c: number): boolean {
    for (let i = 0; i < N; i++) {
      if (graph[vertex][i] === 1 && color[i] === c) {
        return false;
      }
    }
    return true;
  }

  function graphColorUtil(vertex: number): boolean {
    if (vertex === N) {
      return true;
    }

    for (let c = 1; c <= M; c++) {
      if (isSafe(vertex, c)) {
        color[vertex] = c;
        if (graphColorUtil(vertex + 1)) {
          return true;
        }
        color[vertex] = -1; // Backtrack
      }
    }
    return false;
  }

  return graphColorUtil(0);
}

sudoku

const board = [
  ["5", "3", ".", ".", "7", ".", ".", ".", "."],
  ["6", ".", ".", "1", "9", "5", ".", ".", "."],
  [".", "9", "8", ".", ".", ".", ".", "6", "."],
  ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
  ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
  ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
  [".", "6", ".", ".", ".", ".", "2", "8", "."],
  [".", ".", ".", "4", "1", "9", ".", ".", "5"],
  [".", ".", ".", ".", "8", ".", ".", "7", "9"],
];

solveSudoku(board);
console.log(board);

function solveSudoku(board) {
  for (let i = 0; i < 9; i++) {
    for (let j = 0; j < 9; j++) {
      if (board[i][j] === ".") {
        for (let c = "1"; c <= "9"; c++) {
          if (isValid(board, i, j, c)) {
            board[i][j] = c.toString();
            if (solveSudoku(board)) return true;
            else board[i][j] = ".";
          }
        }
        return false; // No valid number found for this cell
      }
    }
  }
  return true; // All cells are filled
}

function isValid(board, row, col, c) {
  c = c.toString(); // Convert c to a string for comparison
  for (let i = 0; i < 9; i++) {
    if (board[i][col] === c) {
      return false; // Check column
    }
    if (board[row][i] === c) {
      return false; // Check row
    }
    if (
      board[3 * Math.floor(row / 3) + Math.floor(i / 3)][
        3 * Math.floor(col / 3) + (i % 3)
      ] === c
    ) {
      return false; // Check 3x3 subgrid
    }
  }
  return true; // No conflicts found, it's valid
}

Matrix

Spiral Traversal

function printSpiral(mat: number[][]): number[] {
  let ans: number[] = [];
  let n: number = mat.length;
  let m: number = mat[0].length;
  let top: number = 0,
    left: number = 0,
    right: number = m - 1,
    bottom: number = n - 1;

  while (top <= bottom && left <= right) {
    // Traverse from left to right
    for (let i = left; i <= right; i++) {
      ans.push(mat[top][i]);
    }
    top++;

    // Traverse from top to bottom
    for (let i = top; i <= bottom; i++) {
      ans.push(mat[i][right]);
    }
    right--;

    // Traverse from right to left
    if (top <= bottom) {
      for (let i = right; i >= left; i--) {
        ans.push(mat[bottom][i]);
      }
      bottom--;
    }

    // Traverse from bottom to top
    if (left <= right) {
      for (let i = bottom; i >= top; i--) {
        ans.push(mat[i][left]);
      }
      left++;
    }
  }

  return ans;
}

// Example matrix
let mat: number[][] = [
  [1, 2, 3, 4],
  [5, 6, 7, 8],
  [9, 10, 11, 12],
  [13, 14, 15, 16],
];

// Call function and log result
let ans: number[] = printSpiral(mat);
for (let i = 0; i < ans.length; i++) {
  console.log(ans[i] + " ");
}

Search Element Matrix

const mat: number[][] = [
  [1, 2, 3, 4],
  [5, 6, 7, 8],
  [9, 10, 11, 12],
];

let n: number = mat.length;
let m: number = mat[0].length;
let target: number = 8;

let ans: number[] = searchMatrixOptimal(mat, n, m, target);
console.log("ans: ", ans);

// TC: O(n*m) SC: O(1)
function searchMatrixNaive(mat: number[][], n: number, m: number, target: number): number[] {
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < m; j++) {
      if (mat[i][j] === target) {
        return [i, j];
      }
    }
  }
  return [-1, -1];
}

// TC: O(N + logM) SC: O(1)
function searchMatrixBetter(mat: number[][], n: number, m: number, target: number): number[] {
  for (let i = 0; i < n; i++) {
    if (mat[i][0] <= target && target <= mat[i][m - 1]) {
      return binarySearch(mat[i], target, i);
    }
  }
  return [-1, -1];
}

function binarySearch(arr: number[], target: number, i: number): number[] {
  let n: number = arr.length;
  let low: number = 0,
    high: number = n - 1;
  while (low <= high) {
    let mid: number = Math.floor((low + high) / 2);
    if (arr[mid] === target) {
      return [i, mid];
    } else if (target > arr[mid]) {
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
  return [-1, -1];
}

// TC: O(log(n*m)) SC: O(1)
function searchMatrixOptimal(arr: number[][], n: number, m: number, target: number): number[] {
  let low: number = 0;
  let high: number = n * m - 1;

  while (low <= high) {
    let mid: number = Math.floor((low + high) / 2);
    let row: number = Math.floor(mid / m);
    let col: number = mid % m;
    if (arr[row][col] === target) return [row, col];
    else if (arr[row][col] < target) low = mid + 1;
    else high = mid - 1;
  }

  return [-1, -1];
}

Median Row Matrix

let arr: number[][] = [
  [1, 3, 8],
  [2, 3, 4],
  [1, 2, 5],
];
let row: number = arr.length;
let col: number = arr[0].length;
let ans: number = findMedianOptimal(arr, row, col);
console.log("ans", ans);

// Naive approach: O(row * col * log(row * col))
function findMedianNaive(arr: number[][], row: number, col: number): number {
  let median: number[] = new Array(row * col);

  let index: number = 0;
  for (let i = 0; i < row; i++) {
    for (let j = 0; j < col; j++) {
      median[index] = arr[i][j];
      index++;
    }
  }

  median.sort((a, b) => a - b);
  return median[Math.floor((row * col) / 2)];
}

// Optimized approach: O(row * log(col))
function findMedianOptimal(arr: number[][], row: number, col: number): number {
  let low: number = 1;
  let high: number = 1000000000;
  let n: number = row;
  let m: number = col;
  while (low <= high) {
    let mid: number = Math.floor((low + high) >> 1);
    let cnt: number = 0;
    for (let i = 0; i < n; i++) {
      cnt += countSmallerThanMid(arr[i], mid, col);
    }
    if (cnt <= (n * m) / 2) low = mid + 1;
    else high = mid - 1;
  }
  return low;
}

// Helper function to count elements smaller than or equal to `mid` in a sorted row
function countSmallerThanMid(arr: number[], mid: number, n: number): number {
  let l: number = 0;
  let h: number = n - 1;
  while (l <= h) {
    let md: number = (l + h) >> 1;
    if (arr[md] <= mid) {
      l = md + 1;
    } else {
      h = md - 1;
    }
  }
  return l;
}

Row With Max 1s

const matrix: number[][] = [
  [1, 1, 1],
  [0, 0, 1],
  [0, 0, 0],
];
const n: number = 3;
const m: number = 3;

console.log(
  "The row with maximum no. of 1's is: " + rowWithMax1Optimal(matrix, n, m)
);

// Naive approach: O(n * m) SC: O(1)
function rowWithMax1Naive(mat: number[][], n: number, m: number): number {
  let maxCount: number = 0;
  let index: number = -1;
  for (let i = 0; i < n; i++) {
    let count: number = 0;
    for (let j = 0; j < m; j++) {
      if (mat[i][j] === 1) {
        count++;
      }
    }
    if (count > maxCount) {
      maxCount = count;
      index = i;
    }
  }
  return index;
}

// Helper function: Binary search to find the lower bound of 1 in a row
function lowerBound(arr: number[], n: number, target: number): number {
  let low: number = 0;
  let high: number = n - 1;
  let ans: number = n;
  while (low <= high) {
    let mid: number = Math.floor((low + high) / 2);
    if (arr[mid] >= target) {
      ans = mid;
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  return ans;
}

// Optimized approach: O(n * log m) SC: O(1)
function rowWithMax1Optimal(mat: number[][], n: number, m: number): number {
  let maxCount: number = 0;
  let index: number = -1;
  for (let i = 0; i < n; i++) {
    // Count the number of 1's in the row using binary search
    let count: number = m - lowerBound(mat[i], m, 1);
    if (count > maxCount) {
      maxCount = count;
      index = i;
    }
  }
  return index;
}

Sorted Matrix

let mat: number[][] = [
  [40, 94, 73, 98, 27],
  [58, 89, 87, 95, 9],
  [95, 28, 34, 74, 32],
  [19, 46, 78, 64, 80],
  [72, 62, 86, 16, 99],
];

let n: number = mat.length;
console.log("before: ", mat);
sortMatrixOptimal(mat, n);
console.log("after: ", mat);

function sortMatrix(mat: number[][], n: number): void {
  let temp: number[] = new Array(n * n);
  let k: number = 0;
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      temp[k++] = mat[i][j];
    }
  }
  temp.sort((a, b) => a - b);
  k = 0;
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      mat[i][j] = temp[k++];
    }
  }
}

function sortMatrixOptimal(matrix: number[][], n: number): number[][] {
  const numRows: number = matrix.length;
  const numCols: number = matrix[0].length;
  let flatArray: number[] = [].concat(...matrix);
  let index: number = 0;
  flatArray.sort((a, b) => a - b);
  let res: number[][] = new Array(numRows);

  for (let i = 0; i < numRows; i++) {
    for (let j = 0; j < numCols; j++) {
      matrix[i][j] = flatArray[index];
      index++;
    }
  }
  return matrix;
}

function sortMatrixRowWiseColWise(mat: number[][], n: number): void {
  sortByRow(mat, n);
  transpose(mat, n);
  sortByRow(mat, n);
  transpose(mat, n);
}

function sortByRow(mat: number[][], n: number): void {
  for (let i = 0; i < n; i++) {
    mat[i].sort((a, b) => a - b);
  }
}

function transpose(mat: number[][], n: number): void {
  for (let i = 0; i < n; i++) {
    for (let j = i + 1; j < n; j++) {
      let temp: number = mat[i][j];
      mat[i][j] = mat[j][i];
      mat[j][i] = temp;
    }
  }
}

Find Pair Matrix

let mat: number[][] = [
  [1, 2, -1, -4, -20],
  [-8, -3, 4, 2, 1],
  [3, 8, 6, 1, 3],
  [-4, -1, 1, 7, -6],
  [0, -4, 10, -5, 1],
];
let n: number = mat.length;
let ans: number = findPairOptimal(mat, n);
console.log("ans: ", ans);

// TC: O(n^4) SC: O(1)
function findPairNaive(mat: number[][], n: number): number {
  let maxVal: number = Number.MIN_VALUE;
  for (let i = 0; i < n - 1; i++) {
    for (let j = 0; j < n - 1; j++) {
      for (let k = i + 1; k < n; k++) {
        for (let l = j + 1; l < n; l++) {
          if (maxVal < mat[k][l] - mat[i][j]) {
            maxVal = mat[k][l] - mat[i][j];
          }
        }
      }
    }
  }
  return maxVal;
}

function findPairOptimal(mat: number[][], n: number): number {
  let maxValue: number = Number.MIN_VALUE;
  let maxArr: number[][] = new Array(n);

  for (let i = 0; i < n; i++) {
    maxArr[i] = new Array(n);
  }

  maxArr[n - 1][n - 1] = mat[n - 1][n - 1];
  let maxv: number = mat[n - 1][n - 1];

  for (let j = n - 2; j >= 0; j--) {
    if (mat[n - 1][j] > maxv) maxv = mat[n - 1][j];
    maxArr[n - 1][j] = maxv;
  }

  maxv = mat[n - 1][n - 1];
  for (let i = n - 2; i >= 0; i--) {
    if (mat[i][n - 1] > maxv) maxv = mat[i][n - 1];
    maxArr[i][n - 1] = maxv;
  }

  for (let i = n - 2; i >= 0; i--) {
    for (let j = n - 2; j >= 0; j--) {
      // Update maxValue
      if (maxArr[i + 1][j + 1] - mat[i][j] > maxValue)
        maxValue = maxArr[i + 1][j + 1] - mat[i][j];

      // Set maxArr (i, j)
      maxArr[i][j] = Math.max(
        mat[i][j],
        Math.max(maxArr[i][j + 1], maxArr[i + 1][j])
      );
    }
  }

  return maxValue;
}

Rotate by 90

let arr: number[][] = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
];
let rotated: number[][] = rotateMatOptimal(arr);
console.log("rotated matrix: ", rotated);

// TC: O(n^2) SC: O(n^2)
function rotateMatNaive(arr: number[][]): number[][] {
  let n: number = arr.length;
  let ans: number[][] = [[], [], []];
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      ans[j][n - i - 1] = arr[i][j];
    }
  }
  return ans;
}

// TC: O(n^2 + n^2) SC: O(1)
function rotateMatOptimal(arr: number[][]): number[][] {
  let n: number = arr.length;
  let m: number = arr[0].length;
  
  // Transpose the matrix (i.e., swapping rows with columns)
  for (let i = 0; i < n; i++) {
    for (let j = i; j < m; j++) {
      let temp: number = arr[i][j];
      arr[i][j] = arr[j][i];
      arr[j][i] = temp;
    }
  }

  // Reverse each row to complete the 90-degree rotation
  for (let i = 0; i < n; i++) {
    for (let j = 0; j < Math.floor(n / 2); j++) {
      let temp: number = arr[i][j];
      arr[i][j] = arr[i][n - 1 - j];
      arr[i][n - 1 - j] = temp;
    }
  }

  return arr;
}

kth smallest element

const matrix: number[][] = [
  [1, 5, 9],
  [10, 11, 13],
  [12, 13, 15],
];

const k: number = 8;
const result: number = kthSmallest(matrix, k);
console.log(result); // Output: 13

// TC: O(log(N) * R * log(C))
function kthSmallest(matrix: number[][], k: number): number {
  const rows: number = matrix.length;
  const cols: number = matrix[0].length;
  let low: number = matrix[0][0];
  let high: number = matrix[rows - 1][cols - 1];

  while (low <= high) {
    const mid: number = low + Math.floor((high - low) / 2);
    const smallerElements: number = countSmallerElements(matrix, mid);

    if (smallerElements < k) {
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }

  return low;
}

function countSmallerElements(matrix: number[][], target: number): number {
  let count: number = 0;

  for (let i = 0; i < matrix.length; i++) {
    const row: number[] = matrix[i];
    let start: number = 0;
    let end: number = row.length - 1;

    while (start <= end) {
      const mid: number = start + Math.floor((end - start) / 2);

      if (row[mid] <= target) {
        start = mid + 1;
      } else {
        end = mid - 1;
      }
    }

    count += start;
  }

  return count;
}

common element

function commonElements(mat: number[][]): void {
  const m: number = mat.length;
  const n: number = mat[0].length;
  const common: Map<number, boolean> = new Map();

  // Add elements of the first row to the map
  for (let j = 0; j < n; j++) {
    common.set(mat[0][j], true);
  }

  // Process the remaining rows
  for (let i = 1; i < m; i++) {
    const row: number[] = mat[i];
    const currentRow: Map<number, boolean> = new Map();

    for (let j = 0; j < n; j++) {
      if (common.has(row[j])) {
        currentRow.set(row[j], true);
      }
    }

    // Clear common map and set it to current row elements
    common.clear();
    for (const [key] of currentRow) {
      common.set(key, true);
    }
  }

  // Print the common elements
  for (const [key] of common) {
    console.log(key + " ");
  }
}

// Example usage:
const mat: number[][] = [
  [1, 2, 1, 4, 8],
  [3, 7, 8, 5, 1],
  [8, 7, 7, 3, 1],
  [8, 1, 2, 7, 9],
];

commonElements(mat);

Heaps

Max Heap

 class BinaryHeap {
  private list: number[];

  constructor() {
    this.list = [];
  }

  // Helper method to maintain max heap property
  private maxHeapify(arr: number[], n: number, i: number): void {
    let largest = i;
    let l = 2 * i + 1;
    let r = 2 * i + 2;

    // Check if left child is larger than the root
    if (l < n && arr[l] > arr[largest]) {
      largest = l;
    }

    // Check if right child is larger than the largest so far
    if (r < n && arr[r] > arr[largest]) {
      largest = r;
    }

    // If largest is not root, swap and heapify the affected subtree
    if (largest !== i) {
      [arr[i], arr[largest]] = [arr[largest], arr[i]];
      this.maxHeapify(arr, n, largest);
    }
  }

  // Insert a new element into the heap
  insert(num: number): void {
    const size = this.list.length;
    if (size === 0) {
      this.list.push(num);
    } else {
      this.list.push(num);
      for (let i = Math.floor(this.list.length / 2) - 1; i >= 0; i--) {
        this.maxHeapify(this.list, this.list.length, i);
      }
    }
  }

  // Delete a specific element from the heap
  delete(num: number): void {
    let size = this.list.length;
    let i = 0;
    // Find the index of the element to delete
    for (i = 0; i < size; i++) {
      if (this.list[i] === num) {
        break;
      }
    }

    // Swap the element with the last element and remove the last element
    [this.list[i], this.list[size - 1]] = [this.list[size - 1], this.list[i]];
    this.list.splice(size - 1);

    // Re-heapify the heap after deletion
    for (let i = Math.floor(this.list.length / 2) - 1; i >= 0; i--) {
      this.maxHeapify(this.list, this.list.length, i);
    }
  }

  // Find the maximum element in the heap
  findMax(): number | undefined {
    return this.list[0];
  }

  // Delete the maximum element from the heap
  deleteMax(): void {
    if (this.list.length > 0) {
      this.delete(this.list[0]);
    }
  }

  // Get the size of the heap
  size(): number {
    return this.list.length;
  }

  // Check if the heap is empty
  isEmpty(): boolean {
    return this.list.length === 0;
  }

  // Get the list of elements in the heap
  getList(): number[] {
    return this.list;
  }
}

// Example usage
const heap = new BinaryHeap();
heap.insert(3);
heap.insert(4);
heap.insert(9);
heap.insert(5);
heap.insert(2);
console.log(heap.getList());

heap.delete(9);
console.log(heap.getList());

heap.insert(7);
console.log(heap.getList());

Min Heap

class BinaryHeap {
  private list: number[];

  constructor() {
    this.list = [];
  }

  // Helper method to maintain min heap property
  private minHeapify(arr: number[], n: number, i: number): void {
    let smallest = i;
    let l = 2 * i + 1;
    let r = 2 * i + 2;

    // Check if left child is smaller than the root
    if (l < n && arr[l] < arr[smallest]) {
      smallest = l;
    }

    // Check if right child is smaller than the smallest so far
    if (r < n && arr[r] < arr[smallest]) {
      smallest = r;
    }

    // If smallest is not root, swap and heapify the affected subtree
    if (smallest !== i) {
      [arr[i], arr[smallest]] = [arr[smallest], arr[i]];
      this.minHeapify(arr, n, smallest);
    }
  }

  // Insert a new element into the heap
  insert(num: number): void {
    this.list.push(num);
    let size = this.list.length;
    // Fix the heap property by performing min-heapify from the last parent node
    for (let i = Math.floor(size / 2) - 1; i >= 0; i--) {
      this.minHeapify(this.list, size, i);
    }
  }

  // Delete a specific element from the heap
  delete(num: number): void {
    let size = this.list.length;
    let i = 0;
    // Find the index of the element to delete
    for (i = 0; i < size; i++) {
      if (this.list[i] === num) {
        break;
      }
    }

    // If element was found, swap with the last element and remove it
    if (i < size) {
      [this.list[i], this.list[size - 1]] = [this.list[size - 1], this.list[i]];
      this.list.splice(size - 1);
      // Re-heapify the heap after deletion
      for (let i = Math.floor(this.list.length / 2) - 1; i >= 0; i--) {
        this.minHeapify(this.list, this.list.length, i);
      }
    }
  }

  // Find the minimum element in the heap
  findMin(): number | undefined {
    return this.list[0];
  }

  // Delete the minimum element from the heap
  deleteMin(): void {
    if (this.list.length > 0) {
      this.delete(this.list[0]);
    }
  }

  // Get the size of the heap
  size(): number {
    return this.list.length;
  }

  // Check if the heap is empty
  isEmpty(): boolean {
    return this.list.length === 0;
  }

  // Get the list of elements in the heap
  getList(): number[] {
    return this.list;
  }
}

// Example usage
const heap = new BinaryHeap();
heap.insert(3);
heap.insert(4);
heap.insert(9);
heap.insert(5);
heap.insert(2);

console.log(heap.getList()); // Min-Heap after insertions

heap.delete(9); // Delete element 9
console.log(heap.getList()); // Min-Heap after deletion

heap.insert(7); // Insert 7
console.log(heap.getList()); // Min-Heap after inserting 7

Greedy

Linked List

class Node {
  val: number;
  next: Node | null;

  constructor(val: number) {
    this.val = val;
    this.next = null;
  }
}

class LinkedList {
  head: Node | null;

  constructor() {
    this.head = null;
  }

  // Add a value to the end of the list
  add(val: number): void {
    if (this.head === null) {
      this.head = new Node(val);
      return;
    }
    let curr = this.head;
    while (curr.next !== null) {
      curr = curr.next;
    }
    curr.next = new Node(val);
  }

  // Add a value to the beginning of the list
  addFirst(val: number): Node | null {
    let curr = new Node(val);
    curr.next = this.head;
    this.head = curr;
    return this.head;
  }

  // Add a value to the end of the list (similar to add)
  addLast(val: number): void {
    let curr = this.head;
    while (curr && curr.next !== null) {
      curr = curr.next;
    }
    if (curr) {
      curr.next = new Node(val);
    } else {
      this.head = new Node(val);
    }
  }

  // Check if the list contains a certain value
  contains(val: number): boolean {
    let curr = this.head;
    while (curr !== null) {
      if (curr.val === val) {
        return true;
      }
      curr = curr.next;
    }
    return false;
  }

  // Get the value at a specific index
  get(index: number): number {
    if (index < 0) {
      throw new Error("Index out of bounds");
    }
    let curr = this.head;
    let i = 0;
    while (i < index && curr !== null) {
      curr = curr.next;
      i++;
    }
    if (curr !== null) {
      return curr.val;
    } else {
      throw new Error("Index out of bounds");
    }
  }

  // Peek at the value of the first node
  peek(): number {
    if (this.head === null) {
      throw new Error("List is empty");
    }
    return this.head.val;
  }

  // Remove and return the value of the first node
  poll(): number {
    if (this.head === null) {
      throw new Error("List is empty");
    }
    let value = this.head.val;
    this.head = this.head.next;
    return value;
  }

  // Pop (remove) the first node (alias for poll)
  pop(): number {
    return this.poll();
  }

  // Push a new value at the beginning of the list (alias for addFirst)
  push(element: number): Node | null {
    return this.addFirst(element);
  }

  // Remove a node at a specific index
  remove(index: number): void {
    if (index < 0) {
      throw new Error("Index out of bounds");
    }
    if (index === 0) {
      if (this.head !== null) {
        this.head = this.head.next;
        return;
      } else {
        throw new Error("Index out of bounds");
      }
    }
    let curr = this.head;
    let prev: Node | null = null;
    let i = 0;
    while (i < index && curr !== null) {
      prev = curr;
      curr = curr.next;
      i++;
    }

    if (curr !== null) {
      if (prev !== null) {
        prev.next = curr.next;
      }
    } else {
      throw new Error("Index out of bounds");
    }
  }

  // Get the size of the list
  size(): number {
    let count = 0;
    let curr = this.head;
    while (curr !== null) {
      count++;
      curr = curr.next;
    }
    return count;
  }

  // Create a cycle in the linked list (for testing)
  createCircle(startIndex: number, cycleIndex: number): void {
    if (this.head === null) {
      throw new Error("Cannot create a cycle in an empty list.");
    }

    let currIndex = 0;
    let currNode: Node | null = this.head;
    let startNode: Node | null = null;
    let endNode: Node | null = null;

    while (currNode !== null) {
      if (currIndex === startIndex) {
        startNode = currNode;
      }
      if (currIndex === cycleIndex) {
        endNode = currNode;
      }
      currNode = currNode.next;
      currIndex++;
    }

    if (startNode === null || endNode === null) {
      throw new Error("Invalid cycle position or start index.");
    }

    endNode.next = startNode;
  }

  // Print the list, detecting cycles to avoid infinite loops
  print(): void {
    let curr = this.head;
    let visitedNodes = new Set<Node>();
    let str = "";

    while (curr !== null) {
      if (visitedNodes.has(curr)) {
        console.log("Cycle detected. Stopping print.");
        break;
      }
      visitedNodes.add(curr);
      str += curr.val + "->";
      curr = curr.next;
    }

    if (curr === null) {
      console.log(str + "null (end of list)");
    }
  }
}

// Example usage
const list = new LinkedList();
list.add(10);
list.add(20);
list.add(30);
list.addFirst(5);
list.addLast(40);
list.print(); // 5->10->20->30->40->null

list.remove(2);
list.print(); // 5->10->30->40->null

console.log(list.get(2)); // 30

Find Middle Node

import { LinkedList } from "./01.linked-list"; // Assuming the LinkedList and Node classes are exported correctly from the other file

function middleNode(list: LinkedList): Node | null {
  if (list.head === null) {
    return null; // Empty list, no middle node
  }

  let slow: Node | null = list.head;
  let fast: Node | null = list.head;

  while (fast !== null && fast.next !== null) {
    slow = slow.next;
    fast = fast.next.next;
  }

  return slow;
}

const list = new LinkedList();
list.add("a");
list.add("b");
list.add("c");
list.add("d");
list.add("e");
list.add("f");
list.createCircle(1, 2);
list.print();

const middle = middleNode(list);
if (middle !== null) {
  console.log("Middle node:", middle.val);
} else {
  console.log("The list is empty.");
}

Reverse LinkedList

import { LinkedList, Node } from "./01.linked-list"; // Assuming LinkedList and Node are properly exported

// Create an instance of LinkedList
const list = new LinkedList();
list.add("a");
list.add("b");
list.add("c");
list.add("d");
list.add("e");
list.add("f");

// Iterative Reverse Function
function reverse(list: LinkedList): void {
  let prev: Node | null = null;
  let curr: Node | null = list.head;
  let next: Node | null = null;

  while (curr !== null) {
    next = curr.next;
    curr.next = prev;
    prev = curr;
    curr = next;
  }

  list.head = prev;
}

// Recursive Reverse Function
function reverseList(node: Node | null): Node | null {
  if (node === null || node.next === null) {
    return node;
  }

  let newHead = reverseList(node.next);
  node.next.next = node;
  node.next = null;
  
  return newHead;
}

// Reverse the list using the iterative method
reverse(list);

// Print the reversed list
list.print();

// Reverse the list using the recursive method and update the head of the list
const newHead = reverseList(list.head);
list.head = newHead;

// Print the recursively reversed list
list.print();

Detect Cycle

import { LinkedList, Node } from "./01.linked-list"; // Assuming LinkedList and Node are properly exported

const list = new LinkedList();
list.add(1);
list.add(2);
list.add(3);
list.add(4);
list.add(5);
list.add(6);
list.createCircle(1, 5); // Creates a cycle between node 1 and 5
list.print();

// Check for cycle using the optimal approach
console.log("Cycle detected:", detectCycleOptimal(list.head));

// Naive cycle detection using a set
function detectCycleNaive(head: Node | null): boolean {
  const set = new Set<Node>();
  while (head !== null) {
    if (set.has(head)) return true; // Checking the node reference directly
    set.add(head);
    head = head.next;
  }
  return false;
}

// Optimal cycle detection using slow and fast pointers
function detectCycleOptimal(head: Node | null): boolean {
  if (head === null || head.next === null) return false;

  let slow: Node | null = head;
  let fast: Node | null = head;

  while (fast !== null && fast.next !== null) {
    fast = fast.next.next;  // Move fast pointer two steps
    slow = slow.next;       // Move slow pointer one step

    if (fast === slow) {
      return true; // Cycle detected when slow and fast pointers meet
    }
  }
  return false; // No cycle detected
}

5.Find Starting Index

import { LinkedList, Node } from "./01.linked-list"; // Assuming LinkedList and Node are correctly exported

// Create the linked list
const list = new LinkedList();
list.add(1);
list.add(2);
list.add(3);
list.add(4);
list.add(5);
list.add(6);
list.createCircle(1, 5); // Creates a cycle between node 1 and 5
list.print();

// Check for cycle using the optimal approach
console.log("ans:", detectCycleOptimal(list.head));

// Naive cycle detection (returns the node's value where the cycle starts)
function detectCycleNaive(head: Node | null): number | null {
  const set = new Set<Node>();
  while (head !== null) {
    if (set.has(head)) return head.val; // If a node is revisited, return its value (cycle start)
    set.add(head);
    head = head.next;
  }
  return null; // No cycle detected
}

// Optimal cycle detection (returns the node's value where the cycle starts)
function detectCycleOptimal(head: Node | null): number | null {
  let fast: Node | null = head;
  let slow: Node | null = head;
  let entry: Node | null = head;

  while (fast !== null && fast.next !== null) {
    fast = fast.next.next;
    slow = slow.next;

    // Cycle detected
    if (slow === fast) {
      // Move slow pointer back to the head
      while (slow !== entry) {
        slow = slow.next;
        entry = entry.next;
      }
      return slow.val; // Return the node's value where the cycle starts
    }
  }

  return null; // No cycle detected
}

Length of Loop

import { LinkedList, Node } from "./01.linked-list"; // Assuming LinkedList and Node are exported from the module

// Create the linked list and add nodes
const list = new LinkedList();
list.add(1);
list.add(2);
list.add(3);
list.add(4);
list.add(5);
list.add(6);
list.createCircle(2, 5); // Creates a cycle between nodes 2 and 5
list.print();

// Check for cycle length using the optimal approach
console.log("Cycle Length: ", lengthOfLoop(list.head));

// Naive approach to calculate the length of the loop in the linked list
function lengthOfLoopNaive(head: Node | null): number | null {
  const set = new Set<Node>();
  let totalLength = 0;
  let length = 0;
  let entry = head;

  while (head !== null) {
    if (set.has(head)) {
      // Cycle detected, count the length of the cycle
      while (entry !== head) {
        entry = entry.next;
        length++;
      }
      return totalLength - length; // Return the length of the cycle
    }
    set.add(head);
    totalLength++;
    head = head.next;
  }

  return null; // No cycle detected
}

// Optimal approach (Floyd's Cycle-Finding Algorithm) to calculate the length of the loop
function lengthOfLoop(head: Node | null): number | false {
  let slow: Node | null = head;
  let fast: Node | null = head;
  let length = 0;

  // Detect cycle using slow and fast pointers
  while (fast !== null && fast.next !== null) {
    fast = fast.next.next;
    slow = slow.next;

    if (slow === fast) {
      // Cycle detected, now calculate the length of the cycle
      do {
        length++;
        fast = fast.next;
      } while (slow !== fast);

      return length; // Return the length of the cycle
    }
  }

  return false; // No cycle detected
}

7, Check If LL Palindrome

// Assuming LinkedList and Node are defined in the linked list module
import { LinkedList, Node } from "./01.linked-list";

const list = new LinkedList();
list.add(1);
list.add(2);
list.add(3);
list.add(3);
list.add(2);
list.add(1);
list.print();

// Check if the linked list is a palindrome
console.log("Ans: ", isPalindrome(list.head));

function isPalindromeNaive(head: Node | null): boolean {
  let ans: number[] = [];
  while (head !== null) {
    ans.push(head.val);
    head = head.next;
  }

  let n = ans.length;
  for (let i = 0; i < Math.floor(n / 2); i++) {
    if (ans[i] !== ans[n - 1 - i]) return false;
  }
  return true;
}

function isPalindrome(head: Node | null): boolean {
  if (head == null || head.next == null) return true;

  let slow: Node | null = head;
  let fast: Node | null = head;

  // Move slow to the middle of the list
  while (fast !== null && fast.next !== null) {
    slow = slow.next;
    fast = fast.next.next;
  }

  // Reverse the second half of the list
  slow.next = reverse(slow.next);
  slow = slow.next;

  let temp: Node | null = head;
  while (slow !== null) {
    if (temp!.val !== slow.val) return false;
    slow = slow.next;
    temp = temp.next;
  }

  return true;
}

function reverse(head: Node | null): Node | null {
  let prev: Node | null = null;
  let curr: Node | null = head;
  let next: Node | null = null;

  while (curr !== null) {
    next = curr.next;
    curr.next = prev;
    prev = curr;
    curr = next;
  }

  return prev;
}

Odd Even LL

// Assuming LinkedList and Node are defined in the linked list module
import { LinkedList, Node } from "./01.linked-list";

const list = new LinkedList();
list.add(2);
list.add(1);
list.add(3);
list.add(5);
list.add(6);
list.add(4);
list.add(7);

console.log("Original List:");
list.print();

// Call the function to rearrange the list (odd-even positions)
console.log(oddEvenNaive(list.head));

function oddEvenNaive(head: Node | null): Node | null {
  if (head == null) return null;

  let odd: Node | null = head;
  let even: Node | null = head.next;
  let evenHead: Node | null = even;

  while (even !== null && even.next !== null) {
    odd.next = odd.next?.next ?? null;  // Move odd pointer to next odd node
    odd = odd.next ?? null;

    even.next = even.next?.next ?? null;  // Move even pointer to next even node
    even = even.next ?? null;
  }

  // Connect the end of the odd list to the head of the even list
  if (odd !== null) {
    odd.next = evenHead;
  }

  return head;
}

License

Dheerajjha451/DSA_Typescript

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