圖論基本算法(一)

#include<bits/stdc++.h>
#define int long long
using namespace std;

int n,m,s,t,ans;
struct path{
	int a;
	int b;
	int w;
};
bool operator<(path a,path b){
	return a.w>b.w;
}
vector<path> mapa[1000010];
int dist[1000010];
priority_queue<path> Q;
signed main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	int a,b,w;
	memset(dist,-1,sizeof(dist));
	cin>>n>>m;
	for (int i=0;i<m;i++){
		cin>>a>>b>>w;
		mapa[a].push_back(path{a,b,w});
		mapa[b].push_back(path{b,a,w});
	}
	cin>>s>>t;
	Q.push(path{0,s,0});
	path from;
	while (Q.size()){
		from=Q.top();Q.pop();
		if (dist[from.b]==-1){
			dist[from.b]=from.w;
			for (path x:mapa[from.b]){
				if (dist[x.b]==-1){
					Q.push(path{x.a,x.b,x.w+from.w});
				}
			}
		}
	}
	cout<<dist[t]<<'\n';
	return 0;
}

#include<bits/stdc++.h>
#define int long long
using namespace std;

int n,m,MST;
struct edge{
	int a;
	int b;
	int w;
	int id;
};
bool operator<(edge a,edge b){
	return a.w<b.w;
}
edge edges[200010];

int DSU_parent[200010];
int DSU_sizset[200010];
int get_parent(int x){
	if (DSU_parent[x]!=x){
		DSU_parent[x]=get_parent(DSU_parent[x]);
	}
	return DSU_parent[x];
}

signed main(){
	cin>>n>>m;
	for (int i=0;i<m;i++){
		cin>>edges[i].a>>edges[i].b>>edges[i].w;
		edges[i].id=i;
	}
	sort(edges,edges+m);
	for (int i=1;i<=n;i++){
		DSU_parent[i]=i;
		DSU_sizset[i]=1;
	}
	int pa,pb;
	for (int i=0;i<m;i++){
		pa=get_parent(edges[i].a);
		pb=get_parent(edges[i].b);
		if (pa!=pb){
			if (DSU_sizset[pa]<DSU_sizset[pb]){
				DSU_parent[pa]=pb;
				DSU_sizset[pb]+=DSU_sizset[pa];
			}else {
				DSU_parent[pb]=pa;
				DSU_sizset[pa]+=DSU_sizset[pb];
			}
			MST+=edges[i].w;
		}
	}
	cout<<MST;
	return 0;
}

#include <bits/stdc++.h>
using namespace std;

int n;
double ans=0;
struct node{
	int x;
	int y;
}test[5010];
double dist(node a,node b){
	int dx=a.x-b.x;
	int dy=a.y-b.y;
	return sqrt(dx*dx+dy*dy);
}
double distfromtree[5010];
int main()
{
	cin>>n;
	for (int i=0;i<n;i++){
		cin>>test[i].x>>test[i].y;
	}
	for (int i=0;i<n;i++){
		distfromtree[i]=dist(test[0],test[i]);
	}
	for (int i=1;i<n;i++){
		int nowit;
		double nowdist=1e9;
		for (int i=0;i<n;i++){
			if (distfromtree[i]!=0&&distfromtree[i]<nowdist){
				nowit=i;
				nowdist=distfromtree[i];
			}
		}
		ans+=nowdist;
		for (int i=0;i<n;i++){
			distfromtree[i]=min(distfromtree[i],dist(test[nowit],test[i]));
		}
	}
	cout<<ans;
   	return 0;
}