ZOJ3469 Food Delivery[区间dp]

Food Delivery

When we are focusing on solving problems, we usually prefer to stay in front of computers rather than go out for lunch. At this time, we may call for food delivery.

Suppose there are N people living in a straight street that is just lies on an X-coordinate axis. The i^th person‘s coordinate is X_i meters. And in the street there is a take-out restaurant which has coordinates X meters. One day at lunchtime, each person takes an order from the restaurant at the same time. As a worker in the restaurant, you need to start from the restaurant, send food to theN people, and then come back to the restaurant. Your speed is V^-1 meters per minute.

You know that the N people have different personal characters; therefore they have different feeling on the time their food arrives. Their feelings are measured by Displeasure Index. At the beginning, the Displeasure Index for each person is 0. When waiting for the food, the i^th person will gain B_i Displeasure Index per minute.

If one‘s Displeasure Index goes too high, he will not buy your food any more. So you need to keep the sum of all people‘s Displeasure Index as low as possible in order to maximize your income. Your task is to find the minimal sum of Displeasure Index.

Input

The input contains multiple test cases, separated with a blank line. Each case is started with three integers N ( 1 <= N <= 1000 ), V ( V > 0), X ( X >= 0 ), then N lines followed. Each line contains two integers X_i ( X_i >= 0 ), B_i ( B_i >= 0), which are described above.

You can safely assume that all numbers in the input and output will be less than 2³¹ - 1.

Please process to the end-of-file.

Output

For each test case please output a single number, which is the minimal sum of Displeasure Index. One test case per line.

Sample Input

5 1 0
1 1
2 2
3 3
4 4
5 5

Sample Output

55

用f[i][j][0]表示送完[i,j]这个区间且送货员停在i 位置,的最小不满值,f[i][j][1]表示送完[i,j]这个区间且送货员停在j位置,的最小不满值。

转移显然。（详见这里）

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=1003;
int n,m,V,X;
int f[N][N][2];
struct data{
    int p,s;
    bool operator <(const data &a)const{
        return p<a.p;
    }
}d[N],tx;
int main(){
    while(~scanf("%d%d%d",&n,&V,&X)){
        for(int i=1;i<=n;i++) scanf("%d%d",&d[i].p,&d[i].s);
        d[++n].p=X;tx=d[n];memset(f,0x3f,sizeof f);
        sort(d+1,d+n+1);d[n+1]=(data){0,0};
        for(int i=1;i<=n;i++) d[i].s+=d[i-1].s;
        m=lower_bound(d+1,d+n+1,tx)-d;
        f[m][m][0]=f[m][m][1]=0;
        for(int j=m;j<=n;j++){
            for(int i=j-1;i;i--){
                f[i][j][0]=min(f[i+1][j][0]+(d[n].s-d[j].s+d[i].s)*(d[i+1].p-d[i].p),
                                  f[i+1][j][1]+(d[n].s-d[j].s+d[i].s)*(d[j].p-d[i].p));
                f[i][j][1]=min(f[i][j-1][0]+(d[n].s-d[j-1].s+d[i-1].s)*(d[j].p-d[i].p),
                                  f[i][j-1][1]+(d[n].s-d[j-1].s+d[i-1].s)*(d[j].p-d[j-1].p));
            }
        }
        printf("%d\n",min(f[1][n][0],f[1][n][1])*V);
    }
    return 0;
}