[kuangbin带你飞]专题六 最小生成树

A - Jungle Roads 题目链接

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=30;bool vis[MAXN];int lowc[MAXN];int cost[MAXN][MAXN];int Prim(int n){int ans=0;memset(vis,false,sizeof(vis));memset(lowc,0,sizeof(lowc));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int main(){int n,m,a;char s[10],ss[10];while(scanf("%d",&n)==1){if(n==0)break;init(n);for(int i=1;i<n;i++){scanf("%s%d ",&s,&m);for(int j=0;j<m;j++){scanf("%s%d ",&ss,&a);cost[s[0]-'A'][ss[0]-'A']=cost[ss[0]-'A'][s[0]-'A']=a;}}printf("%d\n",Prim(n));}    return 0;}

B - Networking题目链接

#include <stdio.h>#include <string.h>#include <set>#include <map>#include <algorithm>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=59;bool vis[MAXN];int lowc[MAXN];int cost[109][109];int Prim(int n){int ans=0;memset(vis,false,sizeof(vis));vis[1]=true;for(int i=2;i<=n;i++)lowc[i]=cost[1][i];for(int i=2;i<=n;i++){int minc=INF;int p=-1;for(int j=1;j<=n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=1;j<=n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)cost[i][j]=cost[j][i]=INF;}int main(){int n,m;while(scanf("%d",&n)==1){if(n==0)break;scanf("%d",&m);init(n);while(m--){int a,b,time;scanf("%d%d%d",&a,&b,&time);if(cost[a][b]>time){cost[a][b]=cost[b][a]=time;}}/*for(int i=1;i<n;i++)for(int j=1;j<=n;j++)printf("%d ",cost[i][j]);*/printf("%d\n",Prim(n));}    return 0;}

C - Building a Space Station题目链接

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>#include <stdlib.h>using namespace std;const double INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];double lowc[MAXN];double cost[MAXN][MAXN];double Prim(int n){double ans=0;memset(vis,false,sizeof(vis));memset(lowc,0,sizeof(lowc));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){double minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int main(){int n;while(scanf("%d",&n)==1){if(n==0)break;init(n);for(int i=0;i<n;i++){double a[109],b[109],c[109],r[109];scanf("%lf%lf%lf%lf",&a[i],&b[i],&c[i],&r[i]);for(int j=0;j<i;j++){double dist=sqrt((a[i]-a[j])*(a[i]-a[j])+(b[i]-b[j])*(b[i]-b[j])+(c[i]-c[j])*(c[i]-c[j]));if(dist<=r[i]+r[j])cost[i][j]=cost[j][i]=0;elsecost[i][j]=cost[j][i]=dist-(r[i]+r[j]);}}printf("%.3lf\n",Prim(n));}return 0;}

D - Constructing Roads题目链接

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>#include <stdlib.h>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];int lowc[MAXN];int cost[MAXN][MAXN];int Prim(int n){int ans=0;memset(vis,false,sizeof(vis));memset(lowc,0,sizeof(lowc));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int main(){int n;scanf("%d",&n);for(int i=0;i<n;i++)for(int j=0;j<n;j++){int a;scanf("%d",&a);cost[i][j]=a;}int m;scanf("%d",&m);while(m--){int a,b;scanf("%d%d",&a,&b);cost[a-1][b-1]=cost[b-1][a-1]=0;}printf("%d\n",Prim(n));return 0;}

E - QS Network题目链接

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>#include <stdlib.h>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=1009;bool vis[MAXN];int lowc[MAXN];int pre[MAXN];int Max[MAXN][MAXN];bool used[MAXN][MAXN];int prim(int cost[][MAXN],int n){int ans=0;memset(vis,false,sizeof(vis));memset(Max,0,sizeof(Max));memset(used,false,sizeof(used));vis[0]=true;pre[0]=-1;for(int i=1;i<n;i++){lowc[i]=cost[0][i];pre[i]=0;}lowc[0]=0;for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;used[p][pre[p]]=used[pre[p]][p]=true;for(int j=0;j<n;j++){if(vis[j])Max[j][p]=Max[p][j]=max(Max[j][pre[p]],lowc[p]);if(!vis[j]&&lowc[j]>cost[p][j]){lowc[j]=cost[p][j];pre[j]=p;}}}return ans;}int Prim(int cost[][MAXN],int n){double ans=0;memset(vis,false,sizeof(vis));memset(lowc,0,sizeof(lowc));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int cost[][MAXN],int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int ans;int smst(int cost[][MAXN],int n){int Min=INF;for(int i=0;i<n;i++)for(int j=i+1;j<n;j++){if(cost[i][j]!=INF&&!used[i][j]){Min=min(Min,ans+cost[i][j]-Max[i][j]);}}if(Min==INF)return -1;return Min;}int cost[MAXN][MAXN];int main(){//freopen("in.txt","r",stdin);//freopen("out.txt","w",stdout);int T,s[MAXN];scanf("%d",&T);while(T--){int n;scanf("%d",&n);init(cost,n);for(int i=0;i<n;i++)scanf("%d",&s[i]);for(int i=0;i<n;i++)for(int j=0;j<n;j++){int a;scanf("%d",&a);cost[i][j]=a+s[i]+s[j];}printf("%d\n",Prim(cost,n));}return 0;}

I - Agri-Net题目链接

#include <stdio.h>#include <string.h>#include <iostream>#include <algorithm>#include <vector>#include <queue>#include <set>#include <map>#include <string>#include <math.h>#include <stdlib.h>#include <time.h>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];int lowc[MAXN];int cost[MAXN][MAXN];int n;int Prim(){int ans=0;memset(vis,0,sizeof(vis));vis[1]=true;for(int i=2;i<=n;i++){lowc[i]=cost[1][i];}for(int i=2;i<=n;i++){int minc=INF;int p=-1;for(int j=1;j<=n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=1;j<=n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);while(scanf("%d",&n)==1){for(int i=1;i<=n;i++)lowc[i]=i;for(int i=1;i<=n;i++)for(int j=1;j<=n;j++){scanf("%d",&cost[i][j]);}printf("%d\n",Prim());}    return 0;}

K - The Unique MST题目链接

此题错了5次。。

#include <stdio.h>#include <string.h>#include <math.h>#include <iostream>#include <stdlib.h>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];int lowc[MAXN];int pre[MAXN];int Max[MAXN][MAXN];bool used[MAXN][MAXN];int prim(int cost[][MAXN],int n){int ans=0;memset(vis,false,sizeof(vis));memset(Max,0,sizeof(Max));memset(used,false,sizeof(used));vis[0]=true;pre[0]=-1;for(int i=1;i<n;i++){lowc[i]=cost[0][i];pre[i]=0;}lowc[0]=0;for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;used[p][pre[p]]=used[pre[p]][p]=true;for(int j=0;j<n;j++){if(vis[j])Max[j][p]=Max[p][j]=max(Max[j][pre[p]],lowc[p]);if(!vis[j]&&lowc[j]>cost[p][j]){lowc[j]=cost[p][j];pre[j]=p;}}}return ans;}int Prim(int cost[][MAXN],int n){double ans=0;memset(vis,false,sizeof(vis));memset(lowc,0,sizeof(lowc));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int cost[][MAXN],int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int ans;int smst(int cost[][MAXN],int n){int Min=INF;for(int i=0;i<n;i++)for(int j=i+1;j<n;j++){if(cost[i][j]!=INF&&!used[i][j]){Min=min(Min,ans+cost[i][j]-Max[i][j]);}}if(Min==INF)return -1;return Min;}int cost[MAXN][MAXN];int main(){//freopen("in.txt","r",stdin);//freopen("out.txt","w",stdout);int T;scanf("%d",&T);while(T--){int n,m;scanf("%d%d",&n,&m);init(cost,n);while(m--){int a,b,c;scanf("%d%d%d",&a,&b,&c);cost[a-1][b-1]=cost[b-1][a-1]=c;}ans=prim(cost,n);if(ans==-1){printf("Not Unique!\n");continue;}if(ans==smst(cost,n)){printf("Not Unique!\n");}else{printf("%d\n",ans);}}return 0;}

L - 还是畅通工程题目链接

#include <stdio.h>#include <string.h>#include <iostream>#include <algorithm>#include <vector>#include <queue>#include <set>#include <map>#include <string>#include <math.h>#include <stdlib.h>#include <time.h>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];int lowc[MAXN];int cost[MAXN][MAXN];int n;int Prim(){int ans=0;memset(vis,0,sizeof(vis));vis[1]=true;for(int i=2;i<=n;i++){lowc[i]=cost[1][i];}for(int i=2;i<=n;i++){int minc=INF;int p=-1;for(int j=1;j<=n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=1;j<=n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;//printf("%d\n",ans);}int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);while(scanf("%d",&n)==1){if(n==0)break;for(int i=1;i<=n;i++)for(int j=1;j<=n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=INF;}for(int i=0;i<n*(n-1)/2;i++){int a,b,time;scanf("%d%d%d",&a,&b,&time);if(cost[a][b]>time)cost[a][b]=cost[b][a]=time;}printf("%d\n",Prim());}    return 0;}

M - Jungle Roads题目链接

#include <stdio.h>#include <string.h>#include <set>#include <map>#include <algorithm>#include <math.h>#include <iostream>using namespace std;const int INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];int lowc[MAXN];int cost[109][109];int Prim(int n){int ans=0;memset(vis,0,sizeof(vis));vis[0]=true;for(int i=1;i<n;i++)lowc[i]=cost[0][i];for(int i=1;i<n;i++){int minc=INF;int p=-1;for(int j=0;j<n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;ans+=minc;vis[p]=true;for(int j=0;j<n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=0;i<n;i++)for(int j=0;j<n;j++){if(i==j)cost[i][j]=0;elsecost[i][j]=cost[j][i]=INF;}}int main(){int n,m,a;char c,d;while(scanf("%d",&n)==1){if(n==0)break;getchar();init(n);for(int i=0;i<n-1;i++){scanf("%c %d",&c,&m);if(m!=0)getchar();while(m--){if(m==0)scanf("%c %d",&d,&a);elsescanf("%c %d ",&d,&a);cost[c-'A'][d-'A']=cost[d-'A'][c-'A']=a;//printf("%d %d \n",c-'A',d-'A');}getchar();}/*for(int i=0;i<n;i++){for(int j=0;j<n;j++){printf("%d ",cost[i][j]);}printf("\n");}*/printf("%d\n",Prim(n));}    return 0;}

N - 畅通工程再续题目链接

#include <stdio.h>#include <string.h>#include <set>#include <map>#include <algorithm>#include <math.h>#include <iostream>using namespace std;const double INF=0x3f3f3f3f;const int MAXN=109;bool vis[MAXN];double lowc[MAXN];double cost[109][109];struct node{double x,y;}s[109];double Prim(int n){double ans=0;memset(vis,false,sizeof(vis));vis[1]=true;for(int i=2;i<=n;i++)lowc[i]=cost[1][i];for(int i=2;i<=n;i++){double minc=INF;int p=-1;for(int j=1;j<=n;j++){if(!vis[j]&&minc>lowc[j]){minc=lowc[j];p=j;}}if(minc==INF)return -1;if(minc>1000||minc<10){return -1;}ans+=minc;vis[p]=true;for(int j=1;j<=n;j++){if(!vis[j]&&lowc[j]>cost[p][j])lowc[j]=cost[p][j];}}return ans;}void init(int n){for(int i=1;i<=n;i++)for(int j=1;j<=n;j++)cost[i][j]=cost[j][i]=INF;}int main(){int T;scanf("%d",&T);while(T--){int n;scanf("%d",&n);for(int i=1;i<=n;i++){scanf("%lf%lf",&s[i].x,&s[i].y);}init(n);int k=0;for(int i=1;i<=n;i++){for(int j=i+1;j<=n;j++){double time=sqrt((s[i].x-s[j].x)*(s[i].x-s[j].x)+(s[i].y-s[j].y)*(s[i].y-s[j].y));if(cost[i][j]>time&&time<=1000&&time>=10)cost[i][j]=cost[j][i]=time;}}if(Prim(n)==-1)printf("oh!\n");else{printf("%.1lf\n",Prim(n)*100.0);}}    return 0;}