| Time Limit: 2000MS | Memory Limit: 65536K | |
| Total Submissions: 26547 | Accepted: 10300 |
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.
Sample Input
4 aaaaaaa baaaaaa abaaaaa aabaaaa 0
Sample Output
The highest possible quality is 1/3.
Source
题意：
给你一个n；
n个长为7的字符串；
每个字符串表示一个节点，每个节点向其他所有点都有边，边长为两个节点字符串同一位置不同字符的数量；
需要你生成最短路的边权和。
代码实现（prim）：
1 #include<cstdio> 2 #include<cstring> 3 #include<iostream> 4 using namespace std; 5 const int maxn=2010; 6 const int inf=maxn*7; 7 int n; 8 int a[maxn],map[maxn][maxn]; 9 char ch[maxn][10]; 10 bool v[maxn]; 11 int bj(int x,int y){ 12 int ret=0; 13 for(int i=0;i<7;i++) 14 if(ch[x][i]!=ch[y][i]) ret++; 15 return ret; 16 } 17 void intn(){ 18 for(int i=1;i<=n;i++) scanf("%s",ch[i]); 19 for(int i=1;i<=n;i++) 20 for(int j=i+1;j<=n;j++) 21 map[j][i]=map[i][j]=bj(i,j); 22 } 23 int prim(){ 24 memset(v,0,sizeof(v)); 25 int ans=0,p,b; 26 v[1]=1; 27 for(int i=1;i<=n;i++) a[i]=map[1][i]; 28 for(int m=1;m<n;m++){ 29 p=inf; 30 for(int i=1;i<=n;i++) if(a[i]<p&&!v[i]){p=a[i];b=i;} 31 ans+=a[b];v[b]=1; 32 for(int i=1;i<=n;i++) a[i]=min(a[i],map[b][i]); 33 } 34 return ans; 35 } 36 int main(){ 37 while(scanf("%d",&n)){ 38 if(!n) break; 39 else intn(); 40 printf("The highest possible quality is 1/%d. ",prim()); 41 } 42 return 0; 43 }
之前的prim打的丑，poj一直给我TLE（只有TLE），果然poj逼格这么高的地方不适合我这样不会英语，又很娇弱的蒟蒻。
题目来源：POJ