dij、floyed与spfa

无优化spfa

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<sstream>
#include<queue>
#include<map>
#include<vector>
#include<set>
#include<deque>
#include<cstdlib>
#include<ctime>
#define dd double
#define ll long long
#define ull unsigned long long
#define N 500010
#define M number
using namespace std; 

const ll INF=2147483647;
int n,m,s;

struct edge{
	int to,w,next;
	
	inline void readin(int to,int w,int next)
	{
		this->to=to;this->w=w;this->next=next;
	}
};

edge li[N];
int tail,head[N];
ll d[N];bool vis[N];

inline void add(int from,int to,int w)
{
	li[++tail].readin(to,w,head[from]);
	head[from]=tail;
}

struct node{
	int i;ll d;
	node(int i,int d): i(i),d(d) {}
	node() {}
};
queue<node> q;

inline void spfa(int s)
{
	d[s]=0;
	q.push(node(s,d[s]));
	vis[s]=1;
	while(!q.empty())
	{
		node now=q.front();q.pop();
		vis[now.i]=0;
		for(int k=head[now.i];k;k=li[k].next)
		{
			if(d[li[k].to]>d[now.i]+li[k].w)
			{
				d[li[k].to]=d[now.i]+li[k].w;
				if(!vis[li[k].to]) vis[li[k].to]=1,q.push(node(li[k].to,d[li[k].to]));
			}
		}
	}
}

int main()
{
	scanf("%d%d%d",&n,&m,&s);
	for(int i=1;i<=m;i++)
	{
		int from,to,w;
		scanf("%d%d%d",&from,&to,&w);
		add(from,to,w);
	}
	
	for(int i=1;i<=n;i++) d[i]=INF;
	spfa(s);
	for(int i=1;i<=n;i++) printf("%lld ",d[i]);
}

堆优化dij

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
#include<cstring>
#include<sstream>
#include<queue>
#include<map>
#include<vector>
#include<set>
#include<deque>
#include<cstdlib>
#include<ctime>
#define dd double
#define ll long long
#define ull unsigned long long
#define N 300000
using namespace std;

const ll INF=0x3f3f3f3f;

struct edge{
	int to,w,next;
	
	inline void readin(int a,int b,int c)
	{
		to=a;w=b;next=c;
	}
};
edge li[N];int head[N],tail;

inline void add(int from,int to,int w)
{
	li[++tail].readin(to,w,head[from]);
	head[from]=tail;
}

struct node{
	int d,sum;
	node() {}
	node(int d,int sum): d(d),sum(sum) {}
};
node a[N/2+10];

struct cmp{
	inline bool operator () (node a,node b)
	{
		return a.d>b.d;
	}
};
priority_queue<node,vector<node>,cmp> q;

int n,m,s;
bool vis[N/2+10];

inline void dij(int s)
{
	q.push(node(0,s));
	while(!q.empty())
	{
		node now=q.top();q.pop();
		if(vis[now.sum]) continue;
		vis[now.sum]=1;
		for(int k=head[now.sum];k;k=li[k].next)
		{
			int to=li[k].to;
			if(a[to].d>a[now.sum].d+li[k].w)
			{
				a[to].d=a[now.sum].d+li[k].w;
				q.push(a[to]);
			}
		}
	}
}

int main()
{
	scanf("%d%d%d",&n,&m,&s);
	for(int i=1;i<=m;i++)
	{
		int from,to,w;
		scanf("%d%d%d",&from,&to,&w);
		add(from,to,w);
	}
	for(int i=1;i<=n;i++) a[i].d=INF,a[i].sum=i;
	a[s].d=0;
	dij(s);
	for(int i=1;i<=n;i++) printf("%d ",a[i].d);
}

floyed

int d[N][N];

int main(){
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			for(int q=1;q<=n;q++)
				if(d[j][p]>d[j][i]+d[i][q])
					d[j][p]=d[j][i]+d[i][q];
}

其中 floyed作为多源最短路算法，可以用来传递闭包，或者是解决无向图最小环问题。