maximum-subarray

Maximum Subarray – LeetCode 53

Problem

Description

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

Example

For example, given the array [-2,1,-3,4,-1,2,1,-5,4],
the contiguous subarray [4,-1,2,1] has the largest sum = 6.

Answer

Original

Code

class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int res = INT_MIN, curSum = 0;
        for (int num : nums) {
            curSum = max(curSum + num, num);
            res = max(res, curSum);
        }
        return res;
    }
};

思路

这里使用动态规划，curSum保存局部最优解，res保存全局最优解。在curSum部分，选择当前值和累加值，意味着若累加值不能给当前值带来贡献则舍弃。这样将在一次遍历中生成所有局部最优解，然后通过res进行记录，最后返回答案。时间复杂度$O(n)$，空间复杂度$O(1)$。

Better

思路

更多的可以在Wiki看到