feat(work): add Maximum Subarray solution (LeetCode 53)

work/1/Medium/Array/53.maximum-subarray.py

@@ -0,0 +1,58 @@
+"""
+53. Maximum Subarray
+Difficulty: Medium
+https://leetcode.com/problems/maximum-subarray/
+
+──────────────────────────────────────────────────
+
+Given an integer array nums, find the subarray with the largest sum,
+and return its sum.
+
+
+
+Example 1:
+
+Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
+Output: 6
+Explanation: The subarray [4,-1,2,1] has the largest sum 6.
+
+Example 2:
+
+Input: nums = [1]
+Output: 1
+Explanation: The subarray [1] has the largest sum 1.
+
+Example 3:
+
+Input: nums = [5,4,-1,7,8]
+Output: 23
+Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.
+
+
+
+Constraints:
+
+        • 1 <= nums.length <= 10^5
+
+        • -10^4 <= nums[i] <= 10^4
+
+
+
+Follow up: If you have figured out the O(n) solution, try coding
+another solution using the divide and conquer approach, which is more
+subtle.
+"""
+
+
+class Solution:
+    def maxSubArray(self, nums: list[int]) -> int:
+        best, total = nums[0], nums[0]
+
+        for i in range(1, len(nums)):
+            if total < 0:
+                total = nums[i]
+            else:
+                total = total + nums[i]
+            best = max(best, total)
+
+        return best