Ice_cream’s world III

本文介绍了一个关于构建最小成本路径网络的问题,通过Prim算法解决了一个包含N个城市和M条道路的王国如何以最低成本确保每个城市都能通过某些路径连接到首都的问题。该文提供了一个完整的C语言实现代码示例。

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Ice_cream’s world III

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1212    Accepted Submission(s): 401


Problem Description
ice_cream’s world becomes stronger and stronger; every road is built as undirected. The queen enjoys traveling around her world; the queen’s requirement is like II problem, beautifies the roads, by which there are some ways from every city to the capital. The project’s cost should be as less as better.
 

Input
Every case have two integers N and M (N<=1000, M<=10000) meaning N cities and M roads, the cities numbered 0…N-1, following N lines, each line contain three integers S, T and C, meaning S connected with T have a road will cost C.
 

Output
If Wiskey can’t satisfy the queen’s requirement, you must be output “impossible”, otherwise, print the minimum cost in this project. After every case print one blank.
 

Sample Input
2 1 0 1 10 4 0
 

Sample Output
10 impossible
 
 
#include<stdio.h>
#include<string.h>
#include<math.h>
#define mx 0x3f3f3f
int n,m;
int g[1100][1100];
void prim()
{
	int i,j,k,v,min,sum=0;
	int dis[1100],vis[1100];
	memset(vis,0,sizeof(vis));
	for(i=0;i<n;i++)
	{
		dis[i]=g[0][i];
	}
	dis[0]=0;
	vis[0]=1;
	for(v=1;v<n;v++)
	{
		min=mx;
		k=0;
		for(i=1;i<n;i++)
		{
			if(!vis[i]&&dis[i]<min)
			{
				min=dis[i];
				k=i;
			}
		}
		vis[k]=1;
		if(min==mx)
		{
			printf("impossible\n");
			return ;
		}
		sum+=min;
		for(i=0;i<n;i++)
		{
			if(!vis[i]&&dis[i]>g[k][i])
			dis[i]=g[k][i];
		}
	}
	printf("%d\n",sum);
}
int main(){
	int i,j,l,x,y;
	while(scanf("%d%d",&n,&m)!=EOF)
	{
		for(x=0;x<n;x++)//初始化g,不然会错 
		{
			for(y=0;y<n;y++)
			{
				if(x==y)
					g[x][y]=0;
				else
					g[x][y]=mx;
			}
		}
		while(m--)
		{
			scanf("%d%d%d",&i,&j,&l);
			if(g[i][j]>l)
				g[i][j]=g[j][i]=l;
		}
		prim();
		printf("\n");
	}
	return 0;
}


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