Prime/Kruskal算法的伪代码描述

合集 - 图论(6)

1.深度优先遍历（模板）2024-07-292.深度优先遍历2024-07-313.DFS2024-07-284.BFS2024-07-295.BFS和Dijkstra结合2024-11-28

6.Prime/Kruskal算法的伪代码描述2024-12-17

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https://wenku.csdn.net/answer/950d58e43a8340899c2ccf14ae4c494b

Prime:添加点，基于邻接矩阵

// Luogu P3366 【模板】最小生成树
#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#define inf 1e9
using namespace std;

int n,m,a,b,c,ans,cnt;
const int N=5010;
struct edge{int v,w;};
vector<edge> e[N];
int d[N], vis[N];

bool prim(int s){
  for(int i=0;i<=n;i++)d[i]=inf;
  d[s]=0;
  for(int i=1;i<=n;i++){
    int u=0;
    for(int j=1;j<=n;j++)
      if(!vis[j]&&d[j]<d[u]) u=j;
    vis[u]=1; //标记u已出圈
    ans+=d[u];
    if(d[u]!=inf) cnt++;
    for(auto ed : e[u]){
      int v=ed.v, w=ed.w;
      if(d[v]>w) d[v]=w;
    }
  }
  return cnt==n;
}
int main(){
  cin>>n>>m;
  for(int i=0; i<m; i++){
    cin>>a>>b>>c;
    e[a].push_back({b,c});
    e[b].push_back({a,c});
  }
  if(!prim(1))puts("orz");
  else printf("%d\n",ans); 
  return 0;
}

///////////////////Heap-Prim 
#include <cstring>
#include <iostream>
#include <algorithm>
#include <queue>
#define inf 1e9
using namespace std;

const int N=5010;
int n,m,a,b,c,ans,cnt;
struct edge{int v,w;};
vector<edge> e[N];
int d[N], vis[N];
priority_queue<pair<int,int>> q;
        
bool prim(int s){
  for(int i=0;i<=n;i++) d[i]=inf;
  d[s]=0; q.push({0,s});
  while(q.size()){
    int u=q.top().second; q.pop();
    if(vis[u])continue;//再出队跳过
    vis[u]=1;//标记u已出队
    ans+=d[u]; cnt++;
    for(auto ed : e[u]){
      int v=ed.v, w=ed.w;
      if(d[v]>w){
        d[v]=w;
        q.push({-d[v],v});//大根堆
      }
    }
  }
  return cnt==n;
}
int main(){
  cin>>n>>m;
  for(int i=0; i<m; i++){
    cin>>a>>b>>c;
    e[a].push_back({b,c});
    e[b].push_back({a,c});
  }
  if(!prim(1))puts("orz");
  else printf("%d\n",ans); 
  return 0;
}

Kruskal:添加边，基于并查集

// Luogu P3366 【模板】最小生成树
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N=200006;
int n, m;
struct edge{
  int u,v,w;
  bool operator<(const edge &t)const
  {return w < t.w;}   
}e[N];
int fa[N],ans,cnt;

int find(int x){
  if(fa[x]==x) return x;
  return fa[x]=find(fa[x]);
}
bool kruskal(){
  sort(e,e+m);
  for(int i=1;i<=n;i++)fa[i]=i;
  for(int i=0; i<m; i++){
    int x=find(e[i].u);
    int y=find(e[i].v);
    if(x!=y){
      fa[x]=y;
      ans+=e[i].w;
      cnt++;
    }
  } 
  return cnt==n-1;
}
int main(){
  cin>>n>>m;
  for(int i=0; i<m; i++)
    cin>>e[i].u>>e[i].v>>e[i].w;
  if(!kruskal()) puts("orz");
  else printf("%d\n",ans);
  return 0;
}