ID: 53 Maximum Subarray (Dynamic Programming)

Author: Ankit-29

Dynamic_Programming/0053_Maximum_Subarray.py

@@ -0,0 +1,33 @@
+'''
+Given an integer array nums, find the contiguous subarray (containing at least one number) 
+which has the largest sum and return its sum.
+
+Input: [-2,1,-3,4,-1,2,1,-5,4],
+Output: 6
+Explanation: [4,-1,2,1] has the largest sum = 6.
+'''
+from typing import List
+class Solution:
+    ''' Approach #1 (Kadane's Algorithm) '''
+    '''
+        Simple idea of the Kadane’s algorithm is to look for all positive contiguous segments 
+        of the array (max_ending_here is used for this). And keep track of maximum sum contiguous 
+        segment among all positive segments (max_so_far is used for this). 
+        Each time we get a positive sum compare it with max_so_far and update max_so_far 
+        if it is greater than max_so_far
+        Reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem
+    '''
+    def maxSubArray(self, nums: List[int]) -> int:
+        best = nums[0]
+        curr = nums[0]
+        for idx in range(1,len(nums)):
+            curr = max(curr+nums[idx],nums[idx])
+            best = max(curr,best)
+        
+        return best
+
+
+if __name__ == '__main__':
+    sol = Solution()
+    nums = [-2,1,-3,4,-1,2,1,-5,4]
+    print(sol.maxSubArray(nums))