I - Truck History

题目：

Advanced Cargo Movement, Ltd. uses trucks of different types. Some trucks are used for vegetable delivery, other for furniture, or for bricks. The company has its own code describing each type of a truck. The code is simply a string of exactly seven lowercase letters (each letter on each position has a very special meaning but that is unimportant for this task). At the beginning of company's history, just a single truck type was used but later other types were derived from it, then from the new types another types were derived, and so on. 

Today, ACM is rich enough to pay historians to study its history. One thing historians tried to find out is so called derivation plan -- i.e. how the truck types were derived. They defined the distance of truck types as the number of positions with different letters in truck type codes. They also assumed that each truck type was derived from exactly one other truck type (except for the first truck type which was not derived from any other type). The quality of a derivation plan was then defined as 

1/Σ(to,td)d(to,td)

where the sum goes over all pairs of types in the derivation plan such that t o is the original type and t d the type derived from it and d(t o,t d) is the distance of the types. 
Since historians failed, you are to write a program to help them. Given the codes of truck types, your program should find the highest possible quality of a derivation plan. 

Input

The input consists of several test cases. Each test case begins with a line containing the number of truck types, N, 2 <= N <= 2 000. Each of the following N lines of input contains one truck type code (a string of seven lowercase letters). You may assume that the codes uniquely describe the trucks, i.e., no two of these N lines are the same. The input is terminated with zero at the place of number of truck types.

Output

For each test case, your program should output the text "The highest possible quality is 1/Q.", where 1/Q is the quality of the best derivation plan.

Sample Input

4
aaaaaaa
baaaaaa
abaaaaa
aabaaaa
0

Sample Output

The highest possible quality is 1/3.

题意：

给你一个数字n,代表有n辆车子，每一辆车子都有一个长度为7编号，每辆车子的编号都不相同，同时每一个编号都是由另外一个编号衍生出来的，衍生的代价是两辆车子编号字符不同的个数，第一辆车除外；

思路：

这道题是一个最小生成树问题，难点在于我们如何建图，构成每辆车子之间的联系，然后用最小生成树进行计算就可以了；

代码如下：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;

const int N=2010;
const int inf=0x3f3f3f3f;

int n;
char a[N][8];
int map[N][N];
int dis[N];
int book[N];

int qq(int i,int j)//计算衍生代价；
{
    int c=0;
    for(int k=0;k<7;k++)
    {
        if(a[i][k]!=a[j][k])
            c++;
    }
    return c;
}

int ww()//最小生成树；
{
    int i,j;
    memset(book,0,sizeof book);
    book[1]=1;
    int count=1,minn,sum=0,k;
    while(count<n)
    {
        minn=inf;
        for(i=1;i<=n;i++)
        {
            if(book[i]==0&&dis[i]<minn)
            {
                minn=dis[i];
                k=i;
            }
        }
        book[k]=1;
        count++;
        sum+=dis[k];
        for(i=1;i<=n;i++)
        {
            if(book[i]==0)
            {
                if(dis[i]>map[k][i])
                    dis[i]=map[k][i];
            }
        }
    }
    return sum;
}

int main()
{
    while(~scanf("%d",&n)&&n)
    {
        int i,j;
        for(i=1;i<=n;i++)
        {
            scanf("%s",a[i]);
        }
        memset(map,0,sizeof map);
        for(i=1;i<=n;i++)
        {
            for(j=1;j<=n;j++)
            {
                map[i][j]=map[j][i]=qq(i,j);//建图；
            }
        }
        /*for(i=1;i<=n;i++)//建出来的关系图；
        {
            for(j=1;j<=n;j++)
            {
                printf("%d ",map[i][j]);
            }
            printf("\n");
        }*/
        for(i=1;i<=n;i++)
        {
            dis[i]=map[1][i];//距离初始化；
        }
        int kk=ww();
        printf("The highest possible quality is 1/%d.\n",kk);
    }
    return 0;
}