J - Truck History

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.

题意：有n种卡车，每个卡车都有一个特殊的编号，有的卡车是由其他的卡车衍生上来的，定义q为第一代车到第d代车的距离之和，问1/q的最大值；

思路：其实就是求q的最小值，初始车到第d代车的距离为权值，这样就转化为了最小生成树。。。。而距离的求法就是看两个车的编码有几个字母不同。。。

下面附上代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#define N 2000005
using namespace std;
int pre[2010],zz[2010];
char s[2000][7];
struct node
{
	int u,v,w;
}p[N];
bool cmp(node a,node b)
{
	return a.w<b.w;
}
int dis(char a[],char b[])
{
	int r=0;
	for(int i=0;i<7;i++)
	{
		if(a[i]!=b[i])
				r++;
	}
	return r;
}
int find(int x)
{
	if(x==pre[x])
		return x;
	return pre[x]=find(pre[x]);
}
void merge(int x,int y)
{
	int fx=find(x),fy=find(y);
	if(fx==fy)
		return ;
	if(zz[fx]<zz[fy]) pre[fx]=fy;
	else
	{
		pre[fy]=fx;
		if(zz[fx]==zz[fy]) zz[fx]++;
	}
}
int main()
{
	int n;
	while(~scanf("%d",&n)&&n)
	{
		memset(s,0,sizeof(s));
		for(int i=1;i<=n;i++)
		{
			pre[i]=i;
			zz[i]=0;
		}
		for(int i=1;i<=n;i++)
			scanf("%s",s[i]);
		int l=1; 
		for(int i=1;i<=n;i++)
			for(int j=i+1;j<=n;j++)
			{
				p[l].u=i;
				p[l].v=j;
				p[l].w=dis(s[i],s[j]);
				l++;
			}
		sort(p+1,p+l+1,cmp);
		int sum=0;
		for(int i=1;i<=l;i++)
			if(find(p[i].u)!=find(p[i].v))
			{
				sum+=p[i].w;	
				merge(p[i].u,p[i].v);
			}
		printf("The highest possible quality is 1/%d.\n",sum);
	}
	return 0;
}