Create Kadane's Algorithm.md

data_structures/arrays/Kadane's Algorithm.md

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+---
+title: "Kadane's Algorithm"
+sidebar_label: "Introduction to Kadane's Algorithm"
+description: "Kadane's Algorithm efficiently finds the maximum sum of a contiguous subarray. It is a fundamental algorithm for solving problems involving subarray sums."
+tags: [basic-dsa, data-structures, Kadane's Algorithm]
+---
+
+### Definition:
+
+Kadane’s Algorithm is used to find the **maximum sum of a contiguous subarray** within a given array. It efficiently handles both positive and negative numbers and works in **O(n)** time, making it a crucial tool for solving optimization problems related to arrays.
+
+### Characteristics:
+
+- **Linear Time Complexity**:
+
+  - The algorithm processes the array in a single pass, ensuring **O(n)** time complexity.
+
+- **Handles Negative Numbers**:
+
+  - It can deal with arrays containing both positive and negative numbers, ensuring the correct maximum sum is found.
+
+- **Space Complexity: O(1)**
+  - Only a few extra variables are used, making the space usage constant.
+
+### Python Implementation:
+
+```python
+def max_subarray(nums):
+    """
+    Find the maximum sum of a contiguous subarray using Kadane's Algorithm.
+    Args:
+        nums (list): List of integers.
+    Returns:
+        int: Maximum sum of any contiguous subarray.
+    """
+    max_sum = curr_sum = nums[0]
+    for num in nums[1:]:
+        curr_sum = max(num, curr_sum + num)
+        max_sum = max(max_sum, curr_sum)
+    return max_sum
+
+# Example usage
+if __name__ == "__main__":
+    arr = [-2, 1, -3, 4, -1, 2, 1, -5, 4]
+    result = max_subarray(arr)
+    print("Maximum subarray sum:", result)  # Output: 6
+```