LeetCode 53. Maximum Subarray--动态规划--C++,Python解法

zhangpeterx

于 2019-09-26 14:51:53 发布

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本文介绍了LeetCode 53题的最大子数组和问题，通过动态规划求解，给出了Python和C++两种语言的解决方案。题目要求找到整数数组中连续子数组的最大和，并返回这个和。文章讨论了O(n)时间复杂度和O(1)空间复杂度的解题思路。

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题目地址：Maximum Subarray - 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.

这道题目是非常简单的动态规划题。

Python解法如下：

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        if nums == []:
            return 0
        result = nums[0]
        curr = nums[0]
        for i in range(1, len(nums)):
            curr = max(nums[i], nums[i]+curr)
            result = max(result, curr)
        return result

时间复杂度为O(n)，空间复杂度为O(1)。

C++解法如下：

class Solution {
public:
    int maxSubArray(vector<int> &nums) {
        if (nums.empty()) {
            return 0;
        }
        int result = nums[0], curr = nums[0];
        for (int i = 1; i < nums.size(); i++) {
            curr = std::max(nums[i], nums[i] + curr);
            result = std::max(result, curr);
        }
        return result;
    }
};