A. Max Sum Plus Plus
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 (子段1: 4;子段2:3 -2 3)
Sample Output
6
8
Hint
Huge input, scanf and dynamic programming is recommended. 题意:求最大M子段和
#include <iostream>
#include<cmath>
#include<cstring>
using namespace std;
const int MAX=;
const int INF=0x7fffffff;
int a[MAX];
int b[MAX];
int c[MAX];
int main()
{
int m,n;
while(cin>>n>>m)
{
for(int i=;i<=m;i++)
cin>>a[i];
memset(b,,sizeof(b));
memset(c,,sizeof(c));
int maxn;
for(int i=;i<=n;i++)
{
maxn=(-)*INF;
for(int j=i;j<=m;j++)
{
b[j]=max(b[j-]+a[j],c[j-]+a[j]);
c[j-]=maxn;
if(b[j]>maxn)
maxn=b[j];
}
}
cout<<maxn<<endl;
}
return ;
}