Leetcode 53

Author: Kondareddy1209

Leetcode/Leetcode_53.py

@@ -0,0 +1,102 @@
+"""
+=========================================================
+53. Maximum Subarray - Brute Force Approach
+=========================================================
+
+Problem:
+---------
+Given an integer array nums, find the contiguous subarray
+(containing at least one number) which has the largest sum,
+and return its sum.
+
+Example:
+---------
+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.
+
+---------------------------------------------------------
+Brute Force Intuition:
+---------------------------------------------------------
+Generate all possible contiguous subarrays and calculate
+their sums.
+
+Keep track of the maximum sum encountered so far.
+
+Instead of recalculating each subarray sum from scratch,
+we maintain a running sum:
+
+For every starting index i:
+    Initialize current_sum = 0
+
+    For every ending index j:
+        Add nums[j] to current_sum
+        Update max_sum
+
+---------------------------------------------------------
+Approach:
+---------------------------------------------------------
+1. Iterate through every possible starting index.
+2. For each starting index:
+      - Initialize current_sum = 0
+3. Extend the subarray one element at a time.
+4. Update the maximum subarray sum found so far.
+5. Return max_sum.
+
+---------------------------------------------------------
+Dry Run:
+---------------------------------------------------------
+nums = [-2,1,-3,4,-1,2,1,-5,4]
+
+i = 0
+    [-2]                -> -2
+    [-2,1]              -> -1
+    [-2,1,-3]           -> -4
+    ...
+
+i = 3
+    [4]                 -> 4
+    [4,-1]              -> 3
+    [4,-1,2]            -> 5
+    [4,-1,2,1]          -> 6   <-- Maximum
+
+Answer = 6
+
+---------------------------------------------------------
+Time Complexity:
+---------------------------------------------------------
+O(n²)
+
+Outer loop runs n times.
+Inner loop runs up to n times.
+
+---------------------------------------------------------
+Space Complexity:
+---------------------------------------------------------
+O(1)
+
+Only a few extra variables are used.
+
+=========================================================
+"""
+
+from typing import List
+
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        max_sum = float("-inf")
+
+        for i in range(len(nums)):
+            current_sum = 0
+
+            for j in range(i, len(nums)):
+                current_sum += nums[j]
+                max_sum = max(max_sum, current_sum)
+
+        return max_sum