POJ1789 Truck History(prim最小生成树)

Truck History

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 19866 Accepted: 7676

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

4aaaaaaabaaaaaaabaaaaaaabaaaa0

Sample Output

The highest possible quality is 1/3.

题目大意:

有m个位数为7的串，两个编号之间的距离就是字母不同的个数，一个编号只能由另一个编号派生出来，派生的代价为他们彼此的距离，求总代价最小，本题不难想到最小生成树，因为是稠密图所以选择了prim。

解题思路:

用vector<string>来存每一个串，然后相互求得他们之间的距离，然后运用prim算法即可求解。

代码如下:

#include<iostream>#include<vector>#include<cstring>#include<cstdio>#include<string>using namespace std;const int maxn = 2002;int m;int map[maxn][maxn];bool vis[maxn];int dis[maxn];#define inf 10000000int prim(){    int i,j;    int ans;    memset(vis,0,sizeof(vis));    for(i=0;i<m;i++)    {        dis[i] = inf;    }    ans = 0;    dis[0] = 0;    for(i=0;i<m;i++)    {        int tmp = inf,k = 0;        for(j=0;j<m;j++)        {            if(!vis[j] && dis[j] <tmp)            {                tmp = dis[j];                k = j;            }        }        if(tmp == inf) return 0;        vis[k] = true;        ans += tmp;        for(j=0;j<m;j++)        {            if(!vis[j] && dis[j] > map[k][j])            {                dis[j] = map[k][j];            }        }    }    return ans;}int main(){    int i,j,k;    string str;    int cnt;    //freopen("111","r",stdin);    while(cin>>m && m)    {        vector<string> s;        for(i=1; i<=m; i++)        {            cin>>str;            s.push_back(str);        }        for(i=0; i<m-1; i++)        {            for(j=i+1; j<m; j++)            {                cnt = 0;                for(k=0; k<7; k++)                {                    if(s[i][k] != s[j][k])                    {                        cnt++;                    }                }                map[i][j] = map[j][i] = cnt;            }        }        /*for(i=0;i<m;i++)        {            for(j=0;j<m;j++)            {                cout<<i<<","<<j<<" "<<dist[i][j]<<endl;            }        }*/        cout<<"The highest possible quality is "<<"1/"<<prim()<<"."<<endl;    }    return 0;}