题目描述

给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。

样例

示例:

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。

算法1

动态规划

C++ 代码

class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int res = INT_MIN, gen = INT_MIN;
        for(auto x : nums)
        {
            if(gen < 0) gen = x;
            else
                gen += x;
            res = max(res, gen);
        }
        return res;
    }
};

算法2

分治算法

class Solution {
public:
    int func(vector<int>& a, int from, int to)
    {
        if(from == to)
            return a[from];
        int mid = (from + to) / 2;
        int m1 = func(a, from, mid);
        int m2 = func(a, mid + 1, to);
        int i, left = a[mid], now = a[mid];
        for(i = mid - 1; i >= from; --i)
        {
            now += a[i];
            left = max(now, left);
        }

        int right = a[mid + 1];
        now = a[mid + 1];
        for(i = mid + 2; i <= to; ++i)
        {
            now += a[i];
            right = max(now, right);
        }
        int m3 = left + right;
        return max(m1, max(m2, m3));
    }
    int maxSubArray(vector<int>& nums) {
        return func(nums, 0, nums.size() - 1);
    }
};