Truck History
| Time Limit: 2000MS | Memory Limit: 65536K | |
| Total Submissions: 18093 | Accepted: 6989 |
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.
Sample Input
4 aaaaaaa baaaaaa abaaaaa aabaaaa 0
Sample Output
The highest possible quality is 1/3.
算法分析：
构建map[][];
填充map元素，运用普里姆算法直接计算最小生成树即是最后的结果。
#include <stdio.h>
#include <string.h>
char s[2002][8];
int map[2002][2002];
int dis[2002];
int vt[2002];
int n, sum;
void prim()
{
int i, j;
int pos;
memset(vt, 0, sizeof(vt));
for(i=1; i<=n; i++)
{
dis[i] = map[1][i] ;
}
vt[1]=1;
int min=1000000;
for(i=1; i<n; i++)
{
min = 1000000;
for(j=1; j<=n; j++)
{
if(vt[j]==0 && dis[j]<min)
{
min = dis[j];
pos = j;
}
}
sum =sum + min;
vt[pos] = 1;
for(j=1; j<=n; j++)
{
if(vt[j]==0 && map[pos][j] < dis[j] )
{
dis[j] = map[pos][j] ;
}
}
}
printf("The highest possible quality is 1/%d.
", sum );
}
int main()
{
int i, j, e;
int cnt;
while(scanf("%d%*c", &n)!=EOF)
{
if(n==0)
break;
sum = 0;
for(i=1; i<=n; i++)
{
scanf("%s", s[i] );
}
for(i=1; i<=n; i++)
{
for(j=i; j<=n; j++)
{
cnt=0;
for(e=0; e<8; e++)
{
if(s[i][e]!=s[j][e] )
{
cnt++;
}
}
map[i][j] = cnt;
map[j][i] = cnt;
//printf("*%d* ", cnt );
}
}
prim();
}
return 0;
}