add solution: maximum-subarray

Author: dusunax

maximum-subarray/dusunax.py

@@ -0,0 +1,34 @@
+'''
+# 53. Maximum Subarray
+
+- use Kadane's Algorithm for efficiently finding the maximum subarray sum.
+
+## Time and Space Complexity
+
+```
+TC: O(n)
+SC: O(1)
+```
+
+#### TC is O(n):
+- iterating through the list just once to find the maximum subarray sum. = O(n)
+
+#### SC is O(1):
+- using a constant amount of extra space to store the current sum and the maximum sum. = O(1)
+'''
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        if len(nums) == 1:
+            return nums[0]
+
+        currentSum = 0 # SC: O(1)
+        maxSum = nums[0] # SC: O(1)
+
+        for i in range(len(nums)): # TC: O(n)
+            currentSum = max(currentSum + nums[i], nums[i]) # TC: O(1)
+            
+            if currentSum > maxSum: # TC: O(1)
+                maxSum = currentSum
+
+        return maxSum