第k短路

C++14(g++5.4) 解法, 执行用时: 25ms, 内存消耗: 9140K, 提交时间: 2019-11-24 16:00:55

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int maxn=1005;
int n,m,s,t,k,dist[maxn],vis[maxn];
vector<pair<int,int> > G[maxn],_G[maxn];
void Dijkstra(int s)
{
	memset(vis,0,sizeof(vis));
	memset(dist,0x3F,sizeof(dist));
	priority_queue<pair<int,int> > q;
	q.push(make_pair(0,s));
	dist[s]=0;
	while(!q.empty())
	{
		int u=q.top().second;
		q.pop();
		if(vis[u]) continue;
		vis[u]=1;
		for(int i=0;i<(int)_G[u].size();i++)
		{
			int v=_G[u][i].first,w=_G[u][i].second;
			if(dist[v]>dist[u]+w)
			{
				dist[v]=dist[u]+w;
				q.push(make_pair(-dist[v],v));
			}
		}
	}
}
int A_Sharp(int s,int t,int k)
{
	if(s==t) k++;
	memset(vis,0,sizeof(vis));
	priority_queue<pair<int,int> > q;
	q.push(make_pair(-dist[s],s));
	while(!q.empty())
	{
		int u=q.top().second,tmp=q.top().first+dist[u];
		q.pop();
		vis[u]++;
		//printf("%d %d %d\n",u,vis[u],-tmp);
		if(u==t&&vis[u]==k) return -tmp;
		for(int i=0;i<(int)G[u].size();i++)
		{
			int v=G[u][i].first,w=-G[u][i].second;
			q.push(make_pair(tmp+w-dist[v],v));
		}
	}
	return -1;
}
signed main()
{
	scanf("%lld%lld",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int a,b,t;
		scanf("%lld%lld%lld",&a,&b,&t);
		G[a].push_back(make_pair(b,t));
		_G[b].push_back(make_pair(a,t));
	}
	scanf("%lld%lld%lld",&s,&t,&k);
	Dijkstra(t);
	printf("%lld\n",A_Sharp(s,t,k));
	return 0;
}

C++(g++ 7.5.0) 解法, 执行用时: 27ms, 内存消耗: 4928K, 提交时间: 2022-12-09 10:21:29

#include <iostream> 
#include <cstdio> 
#include <fstream> 
#include <algorithm> 
#include <cmath> 
#include <deque> 
#include <vector> 
#include <queue> 
#include <string> 
#include <cstring> 
#include <map> 
#include <stack> 
#include <set> 
#include <time.h>
#include <sstream>
#define pii pair<int,int>
#define mp make_pair
using namespace std;
int n,m,s,t,k,x,y,z,dis[2000],vis[2000],ans,cnt;
vector<pii>ed[2000],e[2000];
priority_queue<pii,vector<pii>,greater<pii>>q;
int main(){
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		cin>>x>>y>>z;
		ed[x].push_back(mp(y,z));
		e[y].push_back(mp(x,z));
	}
	cin>>s>>t>>k;
	memset(dis,0x3f,sizeof(dis));
	dis[t]=0;
	q.push(mp(0,t));
	while(!q.empty()){
		int p=q.top().second;
		q.pop();
		if(vis[p])continue;
		vis[p]=1;
		for(int i=0;i<e[p].size();i++){
			pii a=e[p][i];
			if(dis[a.first]>dis[p]+a.second){
				dis[a.first]=dis[p]+a.second;
				q.push(mp(dis[a.first],a.first));
			}
		}
	}
	if(dis[s]>1e9){
		cout<<-1<<endl;
		return 0;
	}
	q.push(mp(dis[s],s));
	while(!q.empty()){
		pii p=q.top();
		q.pop();
		if(p.second==t&&p.first)cnt++;
		if(cnt==k){
			cout<<p.first<<endl;
			return 0;
		}
		for(int i=0;i<ed[p.second].size();i++){
			pii a=ed[p.second][i];
			q.push(mp(p.first-dis[p.second]+a.second+dis[a.first],a.first));
		}
	}
	cout<<-1<<endl; 
}

C++ 解法, 执行用时: 15ms, 内存消耗: 4860K, 提交时间: 2021-09-13 15:32:41

#include<bits/stdc++.h>
using namespace std;
const int N=1e3+5;
int n,m,s,t,k,x,y,z,f[N],c[N];
bool v[N];
vector<pair<int,int> >e[N],re[N];
priority_queue<pair<int,int> >q;
void dij(){
	memset(f,0x3f,sizeof(f));
	f[t]=0,q.push(make_pair(0,t));
	while(q.size()){
		int x=q.top().second;q.pop();
		if(v[x]) continue;
		v[x]=1;
		for(pair<int,int> i:re[x]){
			int y=i.first,z=i.second;
			if(f[y]>f[x]+z) f[y]=f[x]+z,q.push(make_pair(-f[y],y));
		}
	}
}
int A_star(){
	if(s==t) k++;
	q.push(make_pair(-f[s],s));
	while(q.size()){
		int x=q.top().second,dis=-q.top().first-f[x];
		c[x]++,q.pop();
		if(x==t&&c[x]==k) return dis;
		for(pair<int,int> i:e[x]){
			int y=i.first,z=i.second;
			if(c[y]<k) q.push(make_pair(-dis-z-f[y],y));
		} 
	}
	return -1;
}
signed main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		scanf("%d%d%d",&x,&y,&z);
		e[x].push_back(make_pair(y,z));
		re[y].push_back(make_pair(x,z));
	}
	scanf("%d%d%d",&s,&t,&k);
	dij(),printf("%d\n",A_star());
	return 0;
}

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