solve(w03): 53. Maximum Subarray

Author: seungriyou

maximum-subarray/seungriyou.py

@@ -0,0 +1,44 @@
+# https://leetcode.com/problems/maximum-subarray/
+
+from typing import List
+
+class Solution:
+    def maxSubArray1(self, nums: List[int]) -> int:
+        """
+        [Complexity]
+            - TC: O(n)
+            - SC: O(n)
+
+        [Approach]
+            dp[i] = nums[i]까지 봤을 때, (1) nums[i]가 포함되면서 (2) 가장 sum이 큰 subarray의 sum 값
+                  = max(dp[i - 1] + num, num)
+        """
+
+        n = len(nums)
+        dp = [0] * n
+        dp[0] = nums[0]
+        max_sum = nums[0]
+
+        for i in range(1, n):
+            dp[i] = max(dp[i - 1] + nums[i], nums[i])
+            max_sum = max(max_sum, dp[i])
+
+        return max_sum
+
+    def maxSubArray(self, nums: List[int]) -> int:
+        """
+        [Complexity]
+            - TC: O(n)
+            - SC: O(1)
+
+        [Approach]
+            space optimized DP
+        """
+
+        prev = max_sum = nums[0]
+
+        for i in range(1, len(nums)):
+            prev = max(prev + nums[i], nums[i])
+            max_sum = max(max_sum, prev)
+
+        return max_sum