[LeetCode] [DP] 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.

A subarray is a contiguous part of an array.

 

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 <= 105
• -104 <= nums[i] <= 104

 

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        
        max = -10000
        result_max = -10000
        if len(nums)==1:
            return nums[0]
        for k in range(len(nums)):
            for i in range(len(nums) - k):
                window = nums[i:i + k +1]
                sumw = sum(window)
                if sumw > max:
                    max = sumw

            if max > result_max:
                result_max = max
        return result_max

# Brutal Force 로 첫 번째 시도. 역시나 Time Limit Exceed

# Credit to @Google 

class Solution:
    # @param A, a list of integers
    # @return an integer
    # 6:57
    
    def maxSubArray(self, A):
        if not A:
            return 0

        curSum = maxSum = A[0]
        for num in A[1:]:
            curSum = max(num, curSum + num) 
            # 누적합의 negative 가 커서, 다음 수가 starting 이 되는게 나은지 판단. 
            # fx = g(fx) 형태의 recursive 
            
            maxSum = max(maxSum, curSum)

        return maxSum