POJ 2479 Maximum sum(双向DP)

Posted 2020-09-17 lxjshuju

Maximum sum

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 36100		Accepted: 11213

Description

Given a set of n integers: A={a1, a2,..., an}, we define a function d(A) as below:

Your task is to calculate d(A).

Input

The input consists of T(<=30) test cases. The number of test cases (T) is given in the first line of the input. 
Each test case contains two lines. The first line is an integer n(2<=n<=50000). The second line contains n integers: a1, a2, ..., an. (|ai| <= 10000).There is an empty line after each case.

Output

Print exactly one line for each test case. The line should contain the integer d(A).

Sample Input

1

10
1 -1 2 2 3 -3 4 -4 5 -5

Sample Output

13

Hint

In the sample, we choose {2,2,3,-3,4} and {5}, then we can get the answer. 

Huge input,scanf is recommended.

1000ms。50000个数，所以每次处理的时间复杂度不能超过nlogn，否则会超时。所以要让最后扫描一次就能求出答案。

基本思路就是第一次遍历先定义2个数组，分别记录前i项和（含i）与后n-i+1项和（含i）。
第二次遍历再定义2个数组。分别记录以i为终点（含i）的最大子段和与以i为起点（含i）的最大子段和。

第三次遍历再定义2个数组，分别记录第i项（含i）的之前的最大子段和与第i项（含i）的之后的最大子段和。最后遍历一遍数组求出i之前（含i）子段和与i之后（不含i）子段和的最大值就可以。

#include<stack>
#include<queue>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#pragma commment(linker,"/STACK: 102400000 102400000")
#define lson a,b,l,mid,cur<<1
#define rson a,b,mid+1,r,cur<<1|1
using namespace std;
const double eps=1e-6;
const int MAXN=50050;

int num[MAXN],n,prev[MAXN],afte[MAXN],ans1[MAXN],ans2[MAXN],fans1[MAXN],fans2[MAXN],sum;


int main()
{
#ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
#endif // ONLINE_JUDGE
    int tcase;
    scanf("%d",&tcase);
    while(tcase--)
    {
        scanf("%d",&n);
        memset(prev,0,sizeof(prev));//前i项和（含i）
        memset(afte,0,sizeof(afte));//后n-i+1项和（含i）
        memset(ans1,0,sizeof(ans1));//以i为终点（含i）的最大子段和
        memset(ans2,0,sizeof(ans2));//以i为起点（含i）的最大子段和
        memset(fans1,0,sizeof(fans1));//第i项（含i）的之前的最大子段和
        memset(fans2,0,sizeof(fans2));//第i项（含i）的之后的最大子段和
        sum=0;
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&num[i]);
            prev[i]=prev[i-1]+num[i];
            sum+=num[i];
        }
        if(n==2)
        {
            printf("%d\n",sum);
            continue;
        }
        for(int i=n;i>=1;i--)
            afte[i]=afte[i+1]+num[i];
        int minn=0;
        for(int i=0;i<n;i++)
        {
            minn=min(prev[i],minn);
            ans1[i+1]=prev[i+1]-minn;
            //printf("%d\n",ans1[i+1]);
        }
        minn=0;
        for(int i=n+1;i>0;i--)
        {
            minn=min(afte[i],minn);
            ans2[i-1]=afte[i-1]-minn;
            //printf("%d\n",ans2[i-1]);
        }
        int maxx=-99999999;
        for(int i=1;i<=n;i++)
        {
            maxx=max(maxx,ans1[i]);
            fans1[i]=maxx;
        }
        maxx=-99999999;
        for(int i=n;i>=1;i--)
        {
            maxx=max(maxx,ans2[i]);
            fans2[i]=maxx;
        }
        int ans=-99999999;
        for(int i=1;i<n;i++)
            ans=max(ans,fans1[i]+fans2[i+1]);//题目规定区间不能有交集
        printf("%d\n",ans);
    }
    return 0;
}