[LeetCode] 53. Maximum Subarray_Easy tag: Dynamic Programming

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: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

这个题目思路跟[LeetCode] 198. House Robber _Easy tag: Dynamic Programming很像, 我们只需要得到动态方程式, A[i] 是maxsum which contains nums[i] for sure, 
then   A[i] = max(A[i-1] + nums[i], nums[i]), init:  A[0] = nums[0]

1. Constraints
1) size  >= 1
2) elsement will be integer

2. Ideas

Dynamic Programming     T: O(n)    S; O(1)  using rolling array

3. Code
3.1)     S: O(n)

class Solution:
    def maxSum(self, nums):
        n = len(nums)
        dp = [0] * n
        dp[0], ans = nums[0], nums[0]
        for i in range(1, n):
            dp[i] = max(dp[i-1] + nums[i], nums[i])
            ans = max(ans, dp[i])
        return ans

 

3.2)   S; O(1)   using rolling array

class Solution:
    def maxSum(self, nums):
        n = len(nums)
        dp = [0]*2
        dp[0], ans = nums[0], nums[0]
        for i in range(1, n):
            dp[i%2] = max(dp[i%2 -1] + nums[i], nums[i])
            ans = max(ans, dp[i%2])
        return ans

 

4. Test cases