Create Kadanes.md

Author: Abhay182005dat

docs/dsa/Kadanes.md

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+---
+id: Algorithms
+title: Kadanes Algorithm
+sidebar_label: Algorithms
+sidebar_position: 2
+description: "Kadane's Algorithm efficiently finds the maximum sum contiguous subarray in a one-dimensional array. It's a dynamic programming technique named after its creator, Jay Kadane."
+---
+## Kadane's Algorithm:
+
+- **Purpose**: Finds the maximum sum of a contiguous subarray.
+- **Time Complexity**: O(n)
+- **Space Complexity**: O(1)
+- **Use Case**: Optimal for solving maximum subarray sum problems in linear time.
+### Simple Explanation
+Kadane's Algorithm:
+
+1. **Initialize**:
+   - Set `maxSum` to a very small number (e.g., negative infinity).
+   - Set `currentSum` to 0.
+
+2. **Iterate Through the Array**:
+   - For each element in the array:
+     - Add the element to `currentSum`.
+     - Update `maxSum` if `currentSum` is greater than `maxSum`.
+     - If `currentSum` becomes negative, reset it to 0.
+
+3. **Result**:
+   - The value of `maxSum` at the end of the iteration is the maximum sum of any contiguous subarray.
+### Code
+
+Input: arr = {-2,-3,4,-1,-2,1,5,-3}
+
+Output: 7
+
+Explanation: The subarray {4,-1, -2, 1, 5} has the largest sum 7.
+
+### Python
+
+    def max_sub_array(nums):
+          max_sum = float('-inf')
+          current_sum = 0
+    
+         for num in nums:
+            # Add the current number to the current_sum
+            current_sum += num
+            # Update max_sum if current_sum is greater
+            max_sum = max(max_sum, current_sum)
+            # Reset current_sum to 0 if it drops below 0
+            if current_sum < 0:
+                current_sum = 0
+            
+         return max_sum
+
+### C++
+    // Kadane's Algorithm to find the maximum sum of a contiguous subarray
+
+    #include <iostream>
+    #include <vector>
+    #include <algorithm>
+    #include <climits>
+
+    int maxSubArray(const std::vector<int>& nums) {
+    // Initialize max_sum to the lowest possible value and current_sum to 0
+    int max_sum = INT_MIN;
+    int current_sum = 0;
+
+    for (int num : nums) {
+        // Add the current number to the current_sum
+        current_sum += num;
+        // Update max_sum if current_sum is greater
+        max_sum = std::max(max_sum, current_sum);
+        // Reset current_sum to 0 if it drops below 0
+        if (current_sum < 0) {
+            current_sum = 0;
+        }
+    }
+
+    return max_sum;
+    }
+
+### Explanation
+Explanation:
+
+#### Initialization:
+
+  -`max_sum` is initialized to `INT_MIN` to handle arrays with all negative numbers.
+
+  -`current_sum` starts at `0`.
+
+#### Iteration:
+
+  -Traverse through each number in the array:
+  
+  -Add the number to `current_sum`.
+
+  -Update `max_sum` to be the maximum of `max_sum` and `current_sum`.
+
+  -If `current_sum` becomes negative, reset it to `0` to start a new subarray.
+
+