poj-1789--Truck History-最小生成数

最新推荐文章于 2021-06-05 10:52:23 发布

原创最新推荐文章于 2021-06-05 10:52:23 发布 · 618 阅读

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本文探讨了在给定的车辆类型代码集合中，如何通过最小生成树算法来构建最优的衍生计划，以量化每种车辆类型间的演化关系。通过分析不同代码之间的差异，我们能够计算出每对车辆类型的距离，并最终找到最高质量的衍生计划。

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_{(t_o,t_d)}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

4
aaaaaaa
baaaaaa
abaaaaa
aabaaaa
0

Sample Output

The highest possible quality is 1/3.

题意，是什么衍生啥的，不懂，可以转化为最小生成树，两个字符串之间的不同字母的个数，就是两个的权值，然后用prim，就A了

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#define  MAX 0x3f3f3f
char ls[2001][8];
int n;
int map[2001][2001];
int dis[2001];
bool bj[2001];
void prim()
{
    int pos = 0,i,j;
    for(i = 0; i < n; i++)
        bj[i] = true;
     for(i = 1; i < n; i++)
            dis[i] = map[pos][i];
     int ans = 0;
     bj[pos] = false;
     for(i = 1; i < n; i++)
     {
         int min = MAX;
         for(j = 0; j < n; j++)
         {
             if(min > dis[j] && bj[j])
                    min = dis[pos = j];
         }
         ans += min;
         bj[pos] = false;
         for(j = 0; j < n; j++)
         {
             if(map[pos][j] < dis[j] && bj[j])
                dis[j] = map[pos][j];
         }
     }
     printf("The highest possible quality is 1/%d.\n",ans);

}
int main()
{

    while(~scanf("%d",&n)&&n)
    {
        int i,j;
        for(i = 0; i < n; i++)
        {
            scanf("%s",ls[i]);
        }
        for(i = 0; i < n; i++)
            for(j = 0; j < n; j++)
                  if(i != j)
                     map[i][j] = MAX;
        int str = strlen(ls[0]);
        int c = 0;
        for(i = 0; i < n; i++)
        {
            for(j = i+1; j < n; j++)
            {
                c = 0;
                for(int k = 0; k < str; k++)
                {
                    if(ls[i][k] != ls[j][k])
                        c++;
                }
                map[i][j] = c;
                map[j][i] = c;
            }
        }
        prim();
    }
    return 0;
}