POJ 1789

最新推荐文章于 2017-08-17 16:36:54 发布

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本文介绍了一种使用Prim算法解决历史学家提出的高级货物运输公司卡车类型衍生计划的问题。该问题要求找到一种方法，使得从原始卡车类型到所有其他衍生类型的总距离最小，采用Prim算法可以在稠密图中高效地计算出最低总距离。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

这个题粗略读一遍题目，恩，没懂......

然后再看......

Kruskal算法之前都用的这个算法，但是这个题要用的是prim算法，这个算法用于稠密的图来计算最短路径

这个算法感觉用起来比Kruskal算法剪短一点没有用到之间的并查集的知识

Truck History

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 24278		Accepted: 9442

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_{(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.

#include <iostream>
using namespace std;
const int Max=2005;
const int inf=0xfffff;

int n,ans;
int map[Max][Max],dis[Max];

int min(int a,int b)
{
	return a<b?a:b;
}

void prim()
{
    int i, j, now, min_node, min_edge;
    for(i = 1; i <= n; i ++)
        dis[i] = inf;
    now = 1;
    ans = 0;
    for(i = 1; i < n; i ++)
	{
        dis[now] = -1;
        min_edge = inf;
        for(j = 1; j <= n; j ++)
            if(j != now && dis[j] >= 0)
			{
                dis[j] = min(dis[j], map[now][j]);
                if(dis[j] < min_edge)
				{
                    min_edge = dis[j];
                    min_node = j;
                }
            }
			now = min_node;
			ans += min_edge;
    }
}

int main()
{
	int i,j,k;
	char truck[Max][8];
	while (cin>>n&&n!=0)
	{
		for (i=1;i<=n;i++)
		{
			scanf("%s",&truck[i]);
			for (j=i-1;j>=1;j--)
			{
				int edge=0;
				for(k=0;k<7;k++)
					if(truck[i][k]!=truck[j][k])
						edge++;
					map[i][j]=map[j][i]=edge;<span style="white-space:pre">		</span>//搜索时候的i和j  j和i是一样的没有区别

			}
		}
		prim();
		printf("The highest possible quality is 1/%d.\n", ans);
	}
	return 0;
}