图论之最短路问题

此种题型最为经典，可以有多种变化形式，但最终所需的模板总是万变不离其宗，这里复习一下模板，并有所改变。

Dijsktra:

#include<cstdio>
#include<algorithm>
#include<queue>
#include<cstring>
#include<vector>
#define INF 0x7f7f7f7f
#define maxn 100000
using namespace std;
int n,m;
struct Edge{
	int from,to,dist;
};
struct HeapNode{
	int d,u;
	bool operator < (HeapNode rhs)const{
		return d>rhs.d;
	}
};
struct Dijkstra{
	int n,m;
	vector<Edge> edges;
	vector<int> G[maxn];
	bool done[maxn];
	int d[maxn];
	int p[maxn];
	void init (int n){
		this->n=n;
		for (int i=0;i<n;i++) G[i].clear();
		edges.clear();
	}
	void addedge(int from,int to,int dist){
		edges.push_back((Edge){from,to,dist});
		m=edges.size();
		G[from].push_back(m-1);
	}
	void dijkstra(int s){
		priority_queue<HeapNode> Q;
		for (int i=0;i<n;i++) d[i]=INF;
		d[s]=0;
		memset(done,0,sizeof(done));
		Q.push((HeapNode){0,s});
		while (!Q.empty()){
			HeapNode x=Q.top();Q.pop();
			int u=x.u;
			if (done[u])continue;
			done[u]=true;
			for (int i=0;i<G[u].size();i++){
				Edge e=edges[G[u][i]];
				if (d[e.to]>d[u]+e.dist){
					d[e.to]=d[u]+e.dist;
					p[e.to]=G[u][i];
					Q.push((HeapNode){d[e.to],e.to});
				}
			}
	    }
	}
}dis;
int v[maxn],w[maxn],u[maxn];
int main(){
	freopen("input.in","r",stdin);
	freopen("output.out","w",stdout);
	scanf("%d %d",&n,&m);
	dis.init(n);
	for (int i=0;i<m;i++){
		scanf("%d %d %d",&u[i],&v[i],&w[i]);
		u[i]--;v[i]--;
		dis.addedge(u[i],v[i],w[i]);
		dis.addedge(v[i],u[i],w[i]);
	}
	dis.dijkstra(0);
	for (int i=0;i<n;i++)
		printf("%d ",dis.d[i]);
	return 0;
}

Spfa:

#include<cstdio>
#include<algorithm>
#include<queue>
#include<cstring>
#include<vector>
#define maxn 100000
#define INF 0x7f7f7f7f
using namespace std;
int n,m;
struct Edge{
	int to,dist;
};
struct Spfa{
	int n,m;
	bool inq[maxn];
	int d[maxn];
	vector<Edge> G[maxn];
	void init(int n){
		this->n=n;
		for (int i=0;i<n;i++)G[i].clear();
	}
	void addedge(int u,int v,int w){
		G[u].push_back((Edge){v,w});
		G[v].push_back((Edge){u,w});
	}
	void spfa(int s){
		queue<int> Q;
		memset(inq,0,sizeof(inq));
		for (int i=0;i<n;i++)d[i]=INF;
		d[s]=0;
		Q.push(s);inq[s]=true;
		while (!Q.empty()){
			int u=Q.front();Q.pop();
			inq[u]=false;
			for (int i=0;i<G[u].size();i++){
				Edge e=G[u][i];
				if (d[e.to]>d[u]+e.dist){
					d[e.to]=d[u]+e.dist;
					if (!inq[e.to]){
						Q.push(e.to);
						inq[e.to]=true;
					}
				}
			}
		}
	}
}dis;
int u[maxn],v[maxn],w[maxn];
int main(){
	freopen("input.in","r",stdin);
	freopen("output.out","w",stdout);
	scanf("%d %d",&n,&m);
	dis.init(n);
	for (int i=0;i<m;i++){
		scanf("%d %d %d",&u[i],&v[i],&w[i]);
		u[i]--;v[i]--;
		dis.addedge(u[i],v[i],w[i]);
		dis.addedge(v[i],u[i],w[i]);
	}
	dis.spfa(0);
	for (int i=0;i<n;i++)
		printf("%d ",dis.d[i]);
	return 0;
}