uva348 Optimal Array Multiplication Sequence（DP）

题目链接：http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=11&page=show_problem&problem=284

 

水题

#include <iostream>
#include <cstring>
#include <cstdio>
#include <string>
#define f first
#define s second
#define ll long long
#define inf 1e17
using namespace std;
pair<ll,ll> p[15];
int n,ct;
ll dp[15][15];
int path[15][15];
ll DP(int x,int y){
   if(dp[x][y]!=inf) return dp[x][y];
   if(x==y) return dp[x][y]=0;
   if(x+1==y){
       path[x][y]=x;
       return dp[x][y]=p[x].f*p[y].s*p[x].s;
   }
   ll ret=(ll)1e17;
   for(int i=x;i<y;i++){
      ll now=DP(x,i)+DP(i+1,y)+p[x].f*p[y].s*p[i].s;
      if(now<ret){
         ret=now;
         path[x][y]=i;
      }
   }
   return dp[x][y]=ret;
}
void solve(int x,int y){
   if(x==y) {cout<<"A"<<ct++;return;}
   //if(path[x][y]==-1) return;
   cout<<"(";
   //if(path[x][y]==x&&x+1!=y) cout<<"A"<<ct++;
   solve(x,path[x][y]);
   //if(x+1==y) cout<<"A"<<ct++;
   cout<<" x ";
   //if(x+1==y) cout<<"A"<<ct++;
   solve(path[x][y]+1,y);
   //if(path[x][y]+1==y&&x+1!=y) cout<<"A"<<ct++;
   cout<<")";

}
int main(){
    //freopen("348","r",stdin);
    int cas=1;
    while(cin>>n&&n){
        for(int i=0;i<n;i++) cin>>p[i].f>>p[i].s;
        for(int i=0;i<15;i++){
           for(int j=0;j<15;j++){
              dp[i][j]=(ll)1e17;
           }
        }
        memset(path,-1,sizeof path);
        DP(0,n-1);
        printf("Case %d: ",cas++);
        ct=1;
        solve(0,n-1);
        cout<<endl;
    }
    return 0;
}