hdu1227_Fast Food

Fast Food

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2874    Accepted Submission(s): 1245

Problem Description

The fastfood chain McBurger owns several restaurants along a highway. Recently, they have decided to build several depots along the highway, each one located at a restaurant and supplying several of the restaurants with the needed ingredients. Naturally, these depots should be placed so that the average distance between a restaurant and its assigned depot is minimized. You are to write a program that computes the optimal positions and assignments of the depots. 

To make this more precise, the management of McBurger has issued the following specification: You will be given the positions of n restaurants along the highway as n integers d1 < d2 < ... < dn (these are the distances measured from the company's headquarter, which happens to be at the same highway). Furthermore, a number k (k <= n) will be given, the number of depots to be built. 

The k depots will be built at the locations of k different restaurants. Each restaurant will be assigned to the closest depot, from which it will then receive its supplies. To minimize shipping costs, the total distance sum, defined as



must be as small as possible.

Write a program that computes the positions of the k depots, such that the total distance sum is minimized. 

 

Input

The input file contains several descriptions of fastfood chains. Each description starts with a line containing the two integers n and k. n and k will satisfy 1 <= n <= 200, 1 <= k <= 30, k <= n. Following this will n lines containing one integer each, giving the positions di of the restaurants, ordered increasingly.

The input file will end with a case starting with n = k = 0. This case should not be processed. 

 

Output

For each chain, first output the number of the chain. Then output a line containing the total distance sum. 

Output a blank line after each test case.

 

Sample Input

6 3
5
6
12
19
20
27
0 0

 

Sample Output

Chain 1
Total distance sum = 8

 

题意：在一条路上有n个商店，要你在这条路上放k个仓库，最终问你这些商店到这些仓库的最短距离和是多少？

思路：与hdu1300完全相同，这里的距离可以初始化d[i][j]表示从i到j归一个仓库管理的话，距离的和是多少。

dp[i][j]为有i个仓库，管理前j个商店的最短距离

状态转移方程：dp[i][j] = min(dp[i-1][k]+d[k+1][j],dp[i][j])

#include<bits/stdc++.h>
#define INF 0xfffffff
using namespace std;
int dis[250];
int dp[35][250];
int main(){
    int n,kk,t = 1;
    while(scanf("%d%d",&n,&kk) && n+kk){
        memset(dp,0,sizeof(dp));
        for(int i = 1; i <= 205; i++)
            dp[0][i] = INF;
        for(int i = 1; i <= n; i++)
            scanf("%d",&dis[i]);
        for(int i = 1; i <= kk; i++)//!!车间
            for(int j = 1; j <= n; j++){//!!qian j
                int minn = INF;
                for(int k = 1; k <= j; k++){//!! cong k dao j
                    int mid = (k+j) >> 1;
                    int v = 0;
                    for(int l = k; l <=j; l++)
                        if(l > mid)v+=dis[l]-dis[mid];
                        else v+=dis[mid]-dis[l];
                    minn = min(v+dp[i-1][k-1],minn);
                }
                dp[i][j] = minn;
            }
        printf("Chain %d\nTotal distance sum = %d\n\n",t++,dp[kk][n]);
    }

}