题目连接：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 (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 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 should find the highest possible quality of a derivation plan.
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
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 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.
题目大意：
给一堆长度固定为7的只含小写英文字母的字符串，每两个字符串之间的距离定义为他们不同的字母个数，求最小生成树。
解题思路：
很直接的最小生成树，由题意这是一个完全图，所以选prim算法，有多组输入，注意一下初始化即可。
代码如下：
#include<iostream> #include<cstdio> #include<algorithm> #include<cstring> #define MAX 2005 #define INF 14005 using namespace std; int G[MAX][MAX]; int d[MAX]; bool vis[MAX]={0}; char a[MAX][MAX]; int n; int prim(int s) { vis[s]=1; for(int i=0;i<n;i++) d[i]=G[s][i]; int now,m; int res=0; for(int i=1;i<n;i++) { m=INF; for(int j=0;j<n;j++) { if(!vis[j]&&d[j]<m) { now=j; m=d[j]; } } vis[now]=1; res+=m; for(int j=0;j<n;j++) { if(!vis[j]&&d[j]>G[now][j]) d[j]=G[now][j]; } } return res; } void init() { memset(vis,0,sizeof(vis)); for(int i=0;i<n;i++) for(int j=0;j<n;j++) G[i][j]=INF; } int getdis(char * a,char * b) { int res=0; for(int i=0;i<7;i++) { if(a[i]!=b[i]) res++; } return res; } int main() { while(scanf("%d",&n)!=EOF) { if(n==0) return 0; init(); for(int i=0;i<n;i++) scanf("%s",a[i]); for(int i=0;i<n;i++) for(int j=0;j<n;j++) G[i][j]=getdis(a[i],a[j]); printf("The highest possible quality is 1/%d.\n",prim(0)); } }
