D - Constructing Roads(最小生成树Prim算法和Kruskal算法)

There are N villages, which are numbered from 1 to N, and you should build some roads such that every two villages can connect to each other. We say two village A and B are connected, if and only if there is a road between A and B, or there exists a village C such that there is a road between A and C, and C and B are connected.

We know that there are already some roads between some villages and your job is the build some roads such that all the villages are connect and the length of all the roads built is minimum.

Input

The first line is an integer N (3 <= N <= 100), which is the number of villages. Then come N lines, the i-th of which contains N integers, and the j-th of these N integers is the distance (the distance should be an integer within [1, 1000]) between village i and village j.

Then there is an integer Q (0 <= Q <= N * (N + 1) / 2). Then come Q lines, each line contains two integers a and b (1 <= a < b <= N), which means the road between village a and village b has been built.

Output

You should output a line contains an integer, which is the length of all the roads to be built such that all the villages are connected, and this value is minimum.

Sample Input

3
0 990 692
990 0 179
692 179 0
1
1 2

Sample Output

179
题意很好理解，就是给你一个图的权值，然后其中一部分的道路已经有了路，然后求最小生成树。

Prim代码实现

#include
#include
#define INF 0x3f3f3f
using namespace std;
int n;
int G[105][105];
void Prim()
{
	int mst[105],dis[105];
	for(int i=2;i<=n;i++){
		dis[i]=G[1][i];
		mst[i]=1;
	}
	mst[1]=0;
	dis[1]=0;
	int res=0;
	for(int i=1;i<=n-1;i++){
		int minid,minn=INF;
		for(int j = 1;j<=n;j++)
		    if(minn>dis[j]&&mst[j]!=0)
		        minn=dis[minid=j];
		mst[minid]=0;
		dis[minid]=0;
		res+=minn;
		for(int j = 1;j<=n;j++){
			if(dis[j]>dis[minid]+G[minid][j])
			{
				dis[j]=dis[minid]+G[minid][j];
				mst[j]=minid;
			}
		}
	}
	printf("%d\n",res);
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	    for(int j=1;j<=n;j++)
	       G[i][j]=G[j][i]=(i==j)?0:INF;
	for(int i = 1;i<=n;i++)
	    for(int j = 1;j<=n;j++)
	        scanf("%d",&G[i][j]);
	int q;
	scanf("%d",&q);
	while(q--)
	{
		int a,b;
		scanf("%d%d",&a,&b);
		G[a][b]=G[b][a]=0;
	} 
	Prim();
	return 0;
 } 

Kruskal算法实现

#include
#include
#include
using namespace std;
struct edge{
	int from,to,cost;
}es[10005];
int p[10005];
int cnt,n;
bool cmp(edge x,edge y)
{
	return x.cost