Networking 【poj-1287】 【最小生成树】

Networking

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 11900 Accepted: 6424

Description

You are assigned to design network connections between certain points in a wide area. You are given a set of points in the area, and a set of possible routes for the cables that may connect pairs of points. For each possible route between two points, you are given the length of the cable that is needed to connect the points over that route. Note that there may exist many possible routes between two given points. It is assumed that the given possible routes connect (directly or indirectly) each two points in the area. 
Your task is to design the network for the area, so that there is a connection (direct or indirect) between every two points (i.e., all the points are interconnected, but not necessarily by a direct cable), and that the total length of the used cable is minimal.

Input

The input file consists of a number of data sets. Each data set defines one required network. The first line of the set contains two integers: the first defines the number P of the given points, and the second the number R of given routes between the points. The following R lines define the given routes between the points, each giving three integer numbers: the first two numbers identify the points, and the third gives the length of the route. The numbers are separated with white spaces. A data set giving only one number P=0 denotes the end of the input. The data sets are separated with an empty line. 
The maximal number of points is 50. The maximal length of a given route is 100. The number of possible routes is unlimited. The nodes are identified with integers between 1 and P (inclusive). The routes between two points i and j may be given as i j or as j i. 

Output

For each data set, print one number on a separate line that gives the total length of the cable used for the entire designed network.

Sample Input

1 02 31 2 372 1 171 2 683 71 2 192 3 113 1 71 3 52 3 893 1 911 2 325 71 2 52 3 72 4 84 5 113 5 101 5 64 2 120

Sample Output

0171626

题意：给出n个节点，再有m条边，这m条边代表从a节点到b节点电缆的长度，现在要你将所有节点都连起来，并且使长度最小。

题解：最小生成树，不过输入有重边，要特别注意。两种算法，用Kruskal算法比较简单；用Prim算法需要考虑重边的情况。

代码如下：

《1》Kruskal

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespace std;const int maxn=105;int n,m;int par[maxn];int Rank[maxn];int ans;struct Edge{    int x;    int y;    int v;}e[maxn*maxn/2];void init(){    for(int i=0;i<=n;i++){        par[i]=i;        Rank[i]=0;    }}bool cmp(Edge e1,Edge e2){    return e1.v<e2.v;}int find(int p){    if(p!=par[p])        par[p]=find(par[p]);    return par[p];}void unite(int x,int y){      if(Rank[x]>Rank[y])         par[y]=x;      else{         if(Rank[x]==Rank[y])           Rank[y]++;        par[x] = y;      }      }  void Kruskal(){    init();    ans=0;    sort(e,e+m,cmp);    for(int i=0;i<m;i++){        int x=find(e[i].x);        int y=find(e[i].y);                if(x!=y){            ans+=e[i].v;            unite(x,y);        }    }    }int main(){    while(scanf("%d",&n)&&n){    scanf("%d",&m);                for(int i=0;i<m;i++){            scanf("%d%d%d",&e[i].x,&e[i].y,&e[i].v);        }        Kruskal();        printf("%d\n",ans);    }            return 0;}

《2》Prim

#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>using namespace std;const int maxn=105;const int INF=0x3f3f3f3f;int n,m;int cost[maxn][maxn];int vis[maxn][maxn];int mincost[maxn];bool used[maxn];int prim(){for(int i=1;i<=n;i++){mincost[i]=INF;used[i]=false;}mincost[1]=0;int res=0;while(true){int v=-1;for(int u=1;u<=n;u++){if(!used[u]&&(v==-1||mincost[u]<mincost[v]))v=u;}if(v==-1) break;used[v]=true;res+=mincost[v];for(int u=1;u<=n;u++){mincost[u]=min(mincost[u],cost[v][u]);}}return res;}int main(){while(scanf("%d",&n)&&n){scanf("%d",&m);int a,b,c;memset(vis,0,sizeof(vis));for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){cost[i][j]=INF;}}for(int i=0;i<m;i++){scanf("%d%d%d",&a,&b,&c);if(vis[a][b]==1&&cost[a][b]>c){cost[a][b]=c;vis[a][b]=1;}else if(vis[a][b]==0){cost[a][b]=c;vis[a][b]=1;}}for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){cost[i][j]=cost[j][i]=min(cost[i][j],cost[j][i]);}}int sum=prim();printf("%d\n",sum);}return 0;}