Create 53_Maximum_Subarray.md

Author: koji

53_Maximum_Subarray.md

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+## 53. Maximum Subarray
+
+```
+Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.
+
+ 
+
+Example 1:
+
+Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
+Output: 6
+Explanation: [4,-1,2,1] has the largest sum = 6.
+Example 2:
+
+Input: nums = [1]
+Output: 1
+Example 3:
+
+Input: nums = [5,4,-1,7,8]
+Output: 23
+ 
+
+Constraints:
+
+1 <= nums.length <= 3 * 104
+-105 <= nums[i] <= 105
+ 
+
+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.
+```
+
+```python
+def maxSubArray(self, nums: List[int]) -> int:
+ # Kadane's Algorithm
+ max_cur = nums[0]
+ max_global = nums[0]
+ 
+ for i in range(1, len(nums)):
+ max_cur = max(nums[i], max_cur + nums[i])
+ if max_cur > max_global:
+ max_global = max_cur
+ 
+ return max_global
+```
+
+```
+Runtime: 80 ms, faster than 15.49% of Python3 online submissions for Maximum Subarray.
+Memory Usage: 14.9 MB, less than 60.64% of Python3 online submissions for Maximum Subarray.
+```