hdu 1024Max Sum Plus Plus

本文探讨了一种复杂版本的最大子序列和问题,该问题要求在给定的整数序列中找到多个不重叠子序列,使得这些子序列的和达到最大值。文章提供了一个高效的解决方案,并通过样例输入输出展示了解决方案的有效性。

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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 ... Sx, ... Sn (1 ≤ x ≤ n ≤ 1,000,000, -32768 ≤ Sx ≤ 32767). We define a function sum(i, j) = Si + ... + Sj (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(im, jm) maximal (ix ≤ iy ≤ jx or ix ≤ jy ≤ jx 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(ix, jx)(1 ≤ x ≤ m) instead. ^_^
 

Input
Each test case will begin with two integers m and n, followed by n integers S1, S2, S3 ... Sn.
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
题目是看懂了,但代码还没理解!!
#include<iostream>
using namespace std;
#define max(a,b) a>b?a:b
#define MAXN 1000000
int num[MAXN+50],now[MAXN+50],pre[MAXN+50];
int main()
{
 int m,n,i,j,k,ans,max_pre;
    while(cin>>m>>n)
    {
        for(i=1;i<=n;i++)
            scanf("%d",&num[i]);                    //数据太多所以用scanf
        memset(now,0,sizeof(now));
        memset(pre,0,sizeof(pre));
        for(i=1;i<=m;i++)
        {
   max_pre=-99999999;
            for(j=i;j<=n;j++)
            {
    
                now[j]=max(now[j-1]+num[j],pre[j-1]+num[j]);
                pre[j-1]=max_pre;
                if(now[j]>max_pre)
                    max_pre=now[j];
             //cout<<pre[j-1]<<'*'<<now[j-1]<<'*'<<now[j]<<'*'<<max_pre<<endl;
   }
   cout<<endl;
  }
        cout<<max_pre<<endl;
    }
 
    return 0;
}
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