Truck History
Time Limit: 2000MS | | Memory Limit: 65536K |
Total Submissions: 37428 | | Accepted: 14338 |
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.
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
CTU Open 2003
最短路模板题，只不过看着公式，看着英语，心中不免有一丝丝的胆怯。
cin，cout 超时 必须换成scanf 才能卡过
总结经验：写图论的题，输入输出最好用 scanf printf 来写。
好了最小生成树专题模块的题补完了 溜了
/*
T0是原始的类型 Td是由T0派生出来的类型 d(T0，Td)是两种类型的距离
最高质量的派生计划， 那么就要找 d（T0，Td）和最小
They defined the distance of truck types as the number of positions with different letters in truck type codes.
*/
#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <stack>
#include <queue>
#include <cstdio>
#include <vector>
#include <set>
#define Max 2222
#define inf 0x3f3f3f3f
using namespace std;
int n;
int vis[Max],dis[Max],edge[Max][Max];
char code[Max][Max];
int len (char a[],char b[]){
int cnt = 0;
for(int i = 0; i < strlen(a); i++) {
if(a[i] != b[i]) cnt++;
}
return cnt;
}
int prim(){
memset(vis, 0, sizeof(vis));
memset(dis, inf, sizeof(dis));
for(int i = 0; i < n; i++) {
dis[i] = edge[0][i];
}
dis[0] = 0;
vis[0] = 1;
int ans = 0;
for(int i = 1; i < n; i++){
int minn = inf, k = -1;
for(int j = 0; j < n; j++){
if(!vis[j] && dis[j] < minn) {
minn = dis[j];
k = j;
}
}
vis[k] = 1;
ans += minn;
for(int v = 0; v < n; v++) {
if(!vis[v] && dis[v] > edge[k][v]) {
dis[v] = edge[k][v];
}
}
}
return ans;
}
int main() {
// ios::sync_with_stdio(false);
// cin.tie(0);cout.tie(0);
while(scanf("%d", &n)) {
if(n == 0) break;
for(int i = 0; i < n; i++)
// cin >> code[i];
scanf("%s", code[i]);
for(int i = 0; i < n; i++) {
for(int j = i + 1; j < n; j++) {
edge[i][j] = edge[j][i] = len(code[i], code[j]);
}
}
int ans = prim();
// cout << "The highest possible quality is 1/" << ans << "." << endl;
printf("The highest possible quality is 1/%d.\n",ans);
}
return 0;
}
