LeetCode | maximum subsequence 0053. Maximum Subarray and [Python]

LeetCode 0053. Maximum Subarray largest sub-sequence and Easy [] [] [Dynamic Programming Python]

Problem

LeetCode

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.

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.

problem

Power button

Given an array of integers nums, and find a maximum sub-arrays having a continuous (subarray least one element), and to return to its maximum.

Example:

输入: [-2,1,-3,4,-1,2,1,-5,4],
输出: 6
解释: 连续子数组 [4,-1,2,1] 的和最大，为 6。

Advanced:

If you have implemented a complexity of O (n) of the solution, try to solve a more sophisticated use of divide and conquer.

Thinking

Dynamic Programming

Find dp recurrence formula. dp equal to the number of each position together with the foregoing dp, dp is a current negative side do not add up.

Time complexity: O (len (the nums))
spatial complexity: O (. 1)

Python code

class Solution(object):
    def maxSubArray(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        if not nums:
            return 0
        dp = 0
        sum = -0xFFFFFFFF
        for i in range(len(nums)):
            dp = nums[i] + (dp if dp > 0 else 0)  # if dp > 0: dp = nums[i] + dp, else: dp = nums[i]
            sum = max(sum, dp)
        return sum

Code address

GitHub link