HDU 1024

Max Sum Plus Plus

Problem Description

Now I think you have got an AC in Ignatius.L's "Max Sum" problem. To be a brave ACMer, we always challenge ourselves to more difficult problems. Now you are faced with a more difficult problem.

Given a consecutive number sequence S₁, S₂, S₃, S₄ ... S_x, ... S_n (1 ≤ x ≤ n ≤ 1,000,000, -32768 ≤ S_x ≤ 32767). We define a function sum(i, j) = S_i + ... + S_j (1 ≤ i ≤ j ≤ n).

Now given an integer m (m > 0), your task is to find m pairs of i and j which make sum(i₁, j₁) + sum(i₂, j₂) + sum(i₃, j₃) + ... + sum(i_m, j_m) maximal (i_x ≤ i_y ≤ j_x or i_x≤ j_y ≤ j_x is not allowed).

But I`m lazy, I don't want to write a special-judge module, so you don't have to output m pairs of i and j, just output the maximal summation of sum(i_x, j_x)(1 ≤ x ≤ m) instead. ^_^

 

Input

Each test case will begin with two integers m and n, followed by n integers S₁, S₂, S₃ ... S_n.
Process to the end of file.

 

Output

Output the maximal summation described above in one line.

 

Sample Input

1 3 1 2 3

2 6 -1 4 -2 3 -2 3

 

 

Sample Output

6

8

 

Hint

Huge input, scanf and dynamic programming is recommended.

 

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
using namespace std;
const int MAXN=1e6+5,INF=0x3f3f3f3f;
int a[MAXN],dp[MAXN],maxv[MAXN];
int main()
{
    int m,n;
    while(scanf("%d%d",&m,&n)!=EOF)
    {
        for(int i=1;i<=n;i++)
            scanf("%d",&a[i]),dp[i]=maxv[i]=-INF;
        dp[0]=0;
        int ans=-INF;
        for(int i=1;i<=n;i++)
        {
            for(int j=min(m,i);j>=1;j--)
            {
                dp[j]=max(dp[j]+a[i],maxv[j-1]+a[i]);
                maxv[j]=max(maxv[j],dp[j]);
            }
            ans=max(ans,dp[m]);
        }
        printf("%d
",ans);
    }
    return 0;
}