53-最大子序和.cpp

/*

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。

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。

*/

#include<iostream>
using namespace std;
#include<vector>

class Solution{
public:
    int maxSubArray(vector<int>& nums){
        /*
            动态规划
        */
        int pre = 0, maxAns = nums[0];
        for (const auto &x:nums){
            pre = max(pre+x, x);
            maxAns = max(maxAns, pre);
        }
        return maxAns;
    }
};

class Solution2{
    /*
    线段树， 详情见 https://leetcode-cn.com/problems/maximum-subarray/solution/zui-da-zi-xu-he-by-leetcode-solution/
    */
public:
    struct Status
    {
        int lSum, rSum, mSum, iSum;
    };

    Status pushUp(Status l, Status r)
    {
        int iSum = l.iSum + r.iSum;
        int lSum = max(l.lSum, l.iSum + r.lSum);
        int rSum = max(r.rSum, r.iSum + l.rSum);
        int mSum = max(max(l.mSum, r.mSum), l.rSum + r.lSum);
        return (Status){lSum, rSum, mSum, iSum};
    };

    Status get(vector<int> &a, int l, int r)
    {
        if (l == r)
        {
            return (Status){a[l], a[l], a[l], a[l]};
        }
        int m = (l + r) >> 1;
        Status lSub = get(a, l, m);
        Status rSub = get(a, m + 1, r);
        return pushUp(lSub, rSub);
    }

    int maxSubArray(vector<int> &nums)
    {
        return get(nums, 0, nums.size() - 1).mSum;
    }
};