Truck History

Truck History

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 27617		Accepted: 10736

Description

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(t_o,t_d)
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.

Source

CTU Open 2003

【解析】

首先说一下题意。

输入几个7个字符的字符串。两个字符串之间的距离为对应位置上不同的个数。

并且字符串之前是互相衍生出来的，求最小的衍生距离。

就是求一棵最小生成树。每个点就是一串字符，两点间的距离就是字符串之间的距离。

【mtl代码】因为是稠密图所以用prim比kruskal更好。。可是我懒得写~

#include<iostream>
#include<cstdio>
#include<algorithm>
using namespace std;
#define N 2009
char name[N][N];
int n,sum;
int far[N];
struct Edge
{
    int x,y,v;
}edge[N<<1];
bool cmp(Edge a,Edge b)
{
    return a.v<b.v;
}
int l(char a[],char b[])
{
    int num=0;
    for(int i=0;i<7;i++)
    {
        if(a[i]!=b[i])
        num++;
    }
    return num;
}
int f(int x)
{
    return far[x]==x?x:far[x]=f(far[x]);
}
int main()
{
    while(scanf("%d",&n)&&n)
    {
        int ans=0;
        for(int i=0;i<n;i++)
        scanf("%s",name[i]);
        for(int i=0;i<n;i++)
        {
            for(int j=i+1;j<n;j++)
            {
                edge[++sum].v=l(name[i],name[j]);
                edge[sum].x=i;
                edge[sum].y=j;
            }
        }
        sort(edge+1,edge+sum+1,cmp);
        for(int i=0;i<n;i++)far[i]=i;
        for(int i=1;i<=sum;i++)
        {
            if(f(edge[i].x)!=f(edge[i].y))
            {
                far[f(edge[i].x)]=f(edge[i].y);
                ans+=edge[i].v;
            }
        }
        printf("The highest possible quality is 1/%d.
",ans);
    }
    return 0;
}