Update 2.10-minimum-window-sort-medium.md

2.-pattern-two-pointers/2.10-minimum-window-sort-medium.md

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-# 2.10 Minimum Window Sort \(medium\)
+Given an array, find the length of the smallest subarray that, when sorted, results in the entire array being sorted.
 
+📥 Examples
+Example 1
+Input: [1, 3, 2, 0, -1, 7, 10]
+Output: 5
+Explanation: The subarray [3, 2, 0, -1, 7] must be sorted to sort the entire array.
+
+Example 2
+Input: [1, 2, 5, 3, 7, 10, 9, 12]
+Output: 5
+Explanation: The subarray [5, 3, 7, 10, 9] must be sorted.
+
+💡 Approach: Sliding Window Strategy
+We need to:
+
+Find the first element out of order from the start.
+
+Find the first element out of order from the end.
+
+Determine the minimum and maximum of the subarray between them.
+
+Expand the window left/right if the min/max affect the elements outside.
+
+Return the length of this window.
+
+🧠 Java Code
+java
+Copy
+Edit
+public int shortestWindowToSort(int[] arr) {
+    int low = 0, high = arr.length - 1;
+
+    // Step 1: Move 'low' forward while array is sorted
+    while (low < arr.length - 1 && arr[low] <= arr[low + 1]) {
+        low++;
+    }
+
+    // Array is already sorted
+    if (low == arr.length - 1) return 0;
+
+    // Step 2: Move 'high' backward while array is sorted
+    while (high > 0 && arr[high] >= arr[high - 1]) {
+        high--;
+    }
+
+    // Step 3: Find min and max in the subarray
+    int subarrayMin = Integer.MAX_VALUE;
+    int subarrayMax = Integer.MIN_VALUE;
+    for (int k = low; k <= high; k++) {
+        subarrayMin = Math.min(subarrayMin, arr[k]);
+        subarrayMax = Math.max(subarrayMax, arr[k]);
+    }
+
+    // Step 4: Expand window to the left
+    while (low > 0 && arr[low - 1] > subarrayMin) {
+        low--;
+    }
+
+    // Step 5: Expand window to the right
+    while (high < arr.length - 1 && arr[high + 1] < subarrayMax) {
+        high++;
+    }
+
+    return high - low + 1;
+}
+⏱ Time Complexity
+O(N) — Only a few linear scans through the array.
+
+💾 Space Complexity
+O(1) — Constant space, no extra data structures used.
+
+✅ Summary
+We don’t sort the array; we find the part that needs sorting.
+
+Expand the range if sorting the subarray still doesn’t fix the full array.
+
+Efficient and clean solution — great for interviews and real-world use.