【NOIP2009】道路游戏

题面

https://www.luogu.org/problem/P1070

题解

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;


int n,m,p,ans=0;
int a[1050][1050],sum[1050][1050],oto[1050][1050],f[1050],cost[1050];

void suc(int &x){
  if (x==n) x=1; else x++;
}

int dfs(int x,int colled){
  if (x==m+1) {
    if (colled>ans) ans=colled;
    return 0;
  }
  if (f[x]!=-1) {
    if (colled+f[x]>ans) ans=colled+f[x];
    return f[x];
  }
  int i,j,ans0=0,t0;
  
  for (i=1;i<=n;i++)
    for (j=x;j<=min(x+p-1,m);j++) {
      t0=dfs(j+1,colled-cost[oto[i][x]]+sum[i][j]-sum[i][x-1]);
      ans0=max(ans0,-cost[oto[i][x]]+sum[i][j]-sum[i][x-1]+t0);
    }

  if (colled+ans0>ans) ans=colled+ans0;
  f[x]=ans0;
  return f[x];
}

int main() {
  int x,y,i,j;
  scanf("%d %d %d",&n,&m,&p);
  for (i=1;i<=n;i++)
    for (j=1;j<=m;j++) scanf("%d",&a[i][j]);
  for (i=1;i<=n;i++) {
    x=i; y=1;
    for (j=1;j<=m;j++) {
      sum[i][j]=sum[i][j-1]+a[x][y];
      oto[i][j]=x;
      suc(x); y++;
    }
  }
  for (i=1;i<=n;i++) scanf("%d",&cost[i]);
  memset(f,-1,sizeof(f));
  dfs(1,0);
  printf("%d
",ans);
}