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Cutting Sticks

It is easy to notice that different selections in the order of cutting can led to different prices. For example, consider a stick of length 10 meters that has to be cut at 2, 4 and 7 meters from one end. There are several choices. One can be cutting first at 2, then at 4, then at 7. This leads to a price of 10 + 8 + 6 = 24 because the first stick was of 10 meters, the resulting of 8 and the last one of 6. Another choice could be cutting at 4, then at 2, then at 7. This would lead to a price of 10 + 4 + 6 = 20, which is a better price.

Your boss trusts your computer abilities to find out the minimum cost for cutting a given stick.

Input 

The next line consists of n positive numbers c_i ( 0 < c_i < l) representing the places where the cuts have to be done, given in strictly increasing order.

An input case with l = 0 will represent the end of the input.

Output 

Sample Input 

100
3
25 50 75
10
4
4 5 7 8
0

Sample Output 

The minimum cutting is 200.
The minimum cutting is 22.

区间dp：枚举区间长度进行dp

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<limits.h>
using namespace std;
const int maxn= 1000+10;
int dp[maxn][maxn];
int a[maxn];

int main()
{
    int len,n;
    while(cin>>len&&len)
    {
        cin>>n;
        for(int i=1;i<=n;i++)
            cin>>a[i];
        a[0]=0;
        a[++n]=len;//可用的长度
        memset(dp,0,sizeof(dp));
        for(int l=2;l<len;l++)//枚举长度
        {
            for(int i=0;i+l<=n;i++)
            {
                int j=i+l;
                dp[i][j]=INT_MAX;
                for(int k=i+1;k<j;k++)//枚举中间断点k
                    dp[i][j]=min(dp[i][k]+dp[k][j]+a[j]-a[i],dp[i][j]);
            }
        }
        cout<<"The minimum cutting is "<<dp[0][n]<<"."<<endl;
    }
    return 0;
}

UVA 10003 - Cutting Sticks,布布扣,bubuko.com

UVA 10003 - Cutting Sticks

标签：style   color   os   strong   io   for   cti   ar   

原文地址：http://blog.csdn.net/u013582254/article/details/38306149