Poj 1789 truck history (Minimum Spanning Tree)

Question link: http://poj.org/problem? Id = 1789

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 (role t for the first truck type which was not derived from any other type ). the quality of a derivation plan was then defined
1/Σ (to, TD) D (to, TD)
Where the sum goes over all pairs of types in the derivation plan such that to is the original type and TD the type derived from it and D (to, TD) 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 shocould 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 shocould output the text "the highest possible quality is 1/Q.", where 1/Q is the quality of the best derivation plan.

Sample Input

4aaaaaaabaaaaaaabaaaaaaabaaaa0

Sample output

The highest possible quality is 1/3.

Source

CTU open2003

Question:

N types of trucks are provided. Each type of truck consists of seven characters. One type of truck can be derived from another type of truck, the cost is the number of different characters of the two types of trucks. The minimum cost derived from the N types of trucks is obtained. One of the N types of vehicles is the original one, the other n-1 types are derived.

Ideas:

Minimum Spanning Tree.

The Code is as follows:

#include <cstdio>#include <cstring>#define INF 0x3f3f3f3fconst int MAXN = 2000+17;char s[MAXN][17];int m[MAXN][MAXN];int low[MAXN], visited[MAXN];int n;int Cont(int x, int y){     int c = 0;    for(int i = 0; i < 7; i++)    {        if(s[x][i] != s[y][i])            c++;    }    return c;}int prim(){    int i, j;    int pos, minn, result = 0;    memset(visited,0,sizeof(visited));    visited[0] = 1;    pos = 0;    for(i = 0; i < n; i++)    {        low[i] = m[pos][i];    }    for(i = 0; i < n-1; i++)    {        minn = INF;        pos = -1;        for(j = 0; j < n; j++)        {            if(!visited[j] && low[j] < minn)            {                minn = low[j];                pos = j;            }        }        result += minn;        visited[pos] = 1;        for(j = 0; j < n; j++)        {            if(!visited[j] && low[j]>m[pos][j])                low[j] = m[pos][j];        }    }    return result;}int main(){    while(scanf("%d",&n) && n)    {        getchar();        for(int i = 0; i < n; i++)        {            gets(s[i]);        }        memset(m,0,sizeof(m));        for(int i = 0; i < n-1; i++)        {            for(int j = i+1; j < n; j++)            {                m[i][j] = m[j][i] = Cont(i,j);            }        }        int ans = prim();        printf("The highest possible quality is 1/%d.\n",ans);    }    return 0;}