🚀 LeetCode Daily Task: Minimum Operations to Make a Uni-Value Grid (2033)

[Antim-IWP]

🚀 LeetCode Daily Task: Minimum Operations to Make a Uni-Value Grid (2033)

Difficulty: Medium
📅 Today's Challenge: Improve problem-solving skills by solving LeetCode Problem #2033.

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📝 Problem Statement

You are given a 2D integer grid of size m x n and an integer x.
In one operation, you can either add or subtract x from any element in the grid.

A uni-value grid is a grid where all elements are equal.

Your task: Find the minimum number of operations required to make the grid uni-value. If it is not possible, return -1.

💡 Example 1:

Input: grid = [[2,4],[6,8]], x = 2
Output: 4
Explanation:
- Add `x` to `2` once.
- Subtract `x` from `6` once.
- Subtract `x` from `8` twice.
Total operations: `4`

💡 Example 2:

Input: grid = [[1,5],[2,3]], x = 1
Output: 5

💡 Example 3:

Input: grid = [[1,2],[3,4]], x = 2
Output: -1
Explanation: It is impossible to make every element equal.

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🛠 Constraints:

• 1 ≤ m, n ≤ 10^5
• 1 ≤ m * n ≤ 10^5
• 1 ≤ x, grid[i][j] ≤ 10^4

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🎯 How to Contribute [Click Here]

✅ Step 1: Fork this repository.
✅ Step 2: Clone the repository.

git clone https://github.com/YOUR-USERNAME/Optimism-Educator.git

✅ Step 3: Create a new branch.

git checkout -b feature-leetcode2033

✅ Step 4: Solve the problem in Python, Java, or C++.
✅ Step 5: Submit a Pull Request (PR).

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📂 File Structure

📦 LeetCode_Daily_Tasks
 ┣ 📂 Solutions
 ┃ ┣ 📜 2033_Minimum_Operations.py
 ┃ ┣ 📜 2033_Minimum_Operations.java
 ┃ ┣ 📜 2033_Minimum_Operations.cpp
 ┣ 📜 README.md

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🔥 Want to Participate?

🌟 Star the repo & Join the Discussion [HERE] 🚀
💬 Discuss solutions, share tips, and collaborate!

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🔗 Useful Links

📌 LeetCode Problem Link: [Click Here]
📌 Optimism Educator GitHub: [Visit Here]
📌 How to Contribute Guide: [Click Here]

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💡 Let's learn, code, and grow together! 🚀

[iamAntimPal]

✅ Intuition and Approach

To make a grid uni-value, all values must be equal. We can add or subtract x from any element, any number of times.

🧠 Key Observations:

• The difference between any two values in the grid must be divisible by x for it to be possible.
• So we must check if every grid value modulo x is the same.
• If possible, the optimal target value (to minimize operations) is the median of the values.

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🪜 Steps:

1. Flatten the grid into a list.
2. Check if all values modulo x are the same.
3. Sort the list.
4. Choose the median as the target.
5. Calculate total operations:
   For each value: abs(value - median) // x
6. Return the total.

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🧪 Examples

Example 1:

grid = [[2, 4], [6, 8]], x = 2
Flattened: [2, 4, 6, 8] → Median: 5 or 6
Target: 6
Operations: |2-6|//2 + |4-6|//2 + |6-6| + |8-6|//2 = 2 + 1 + 0 + 1 = 4

Example 3:

grid = [[1,2],[3,4]], x = 2
Some elements are odd, others even → Can't make equal with steps of 2 → return -1

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✅ Python Code

def min_operations(grid, x):
    # Flatten the grid
    flat = [num for row in grid for num in row]
    
    # Modulo check: all values should have same remainder mod x
    remainder = flat[0] % x
    if any(val % x != remainder for val in flat):
        return -1

    # Sort to find the median
    flat.sort()
    median = flat[len(flat) // 2]
    
    # Compute operations
    return sum(abs(val - median) // x for val in flat)

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🛠 Constraints:

• Time Complexity: O(n log n) for sorting
• Space Complexity: O(n) for flattened list