#53: Maximum Subarray

Author: papilo-cloud

Array/max_subarray.py

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+# 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 <= 105
+# -104 <= nums[i] <= 104
+
+
+from typing import List
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        # Solved using Kadane's Algorithm
+        current_sum = nums[0]
+        max_sum = nums[0]
+
+        for i in range(1, len(nums)):
+            current_sum = max(nums[i], current_sum + nums[i])
+            max_sum = max(current_sum, max_sum)
+        return max_sum

Dynamic_programming/max_subarray.py

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+# 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 <= 105
+# -104 <= nums[i] <= 104
+
+
+from typing import List
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        # Solved using Kadane's Algorithm
+        current_sum = nums[0]
+        max_sum = nums[0]
+
+        for i in range(1, len(nums)):
+            current_sum = max(nums[i], current_sum + nums[i])
+            max_sum = max(current_sum, max_sum)
+        return max_sum