1030 Travel Plan (30分)

法一：Dijkstra

#include<iostream>
#include<cstring>
#include<algorithm>
#define mm(a,x) memset(a,x,sizeof(a))
#define inf 0x3f3f3f3f
const int maxn =510;

using namespace std;

int n,m,s,d;
int map[maxn][maxn];
int dist[maxn];
int cost[maxn][maxn];
int dicost[maxn];
int path[maxn];
int vis[maxn];

void dijkstra(){
   
	mm(dist,inf);mm(dicost,inf);
	for(int i=0;i<n;i++) path[i]=i;
	dist[s]=0;
	dicost[s]=0;
	for(int i=0;i<n;i++){
   
		int u=-1,minn=inf;
		for(int j=0;j<n;j++){
   
			if(!vis[j]&&dist[j]<minn){
   
				u=j;minn=dist[j];
			}
		}
		if(u==-1) return ;
		vis[u]=1;
		for(int v=0;v<n;v++){
   
			if(!vis[v]&&map[u][v]!=inf){
   
				if(dist[u]+map[u][v]<dist[v]){
   
					dist[v]=dist[u]+map[u][v];
					dicost[v]=dicost[u]+cost[u][v];
					path[v]=u;
				}else if(dist[u]+map[u][v]==dist[v]){
   
					if(dicost[u]+cost[u][v]<dicost[v])
					{
   
					dicost[v]=dicost[u]+cost[u][v];
					path[v]=u;
					}
				}
			}
		}
	}
}

void dfs(int v){
   
	if(v==s){
   
		cout<<v<<" ";
		return ;
	}
	dfs(path[v]);
	cout<<v<<" ";
}
int main(){
   
	cin>>n>>m>>s>>d;
	mm(map,inf);
	for(int i=0;i<m;i++){
   
		int t1,t2,t3,t4;cin>>t1>>t2>>t3>>t4;
		map[t1][t2]=map[t2][t1]=t3;
		cost[t1][t2]=cost[t2][t1]=t4;
	}
	dijkstra();
	dfs(d);
	cout<<dist[d]<<" "<<dicost[d];
	return 0;
}

法二：Dijkstra+DFS

#include<iostream>
#include<cstring>
#include<vector>
#include<algorithm>
#define mm(a,x) memset(a,x,sizeof(a))
#define inf 0x3f3f3f3f
const int maxn =510;

using namespace std;

int n,m,s,d;
int map[maxn][maxn],cost[maxn][maxn];
int dist[maxn],minCost=inf;
int vis[maxn];
vector<int > pre[maxn];//前驱 
vector<int > tempPath,path;//临时路径、最优路径 

void dijkstra(){
   
	mm(dist,inf);
	dist[s]=0;
	for(int i=0;i<n;i++){
   
		int u=-1,minn=inf;
		for(int j=0;j<n;j++){
   
			if(!vis[j]&&dist[j]<minn){
   
				u=j;minn=dist[j];
			}
		}
		if(u==-1) return ;
		vis[u]=1;
		for(int v=0;v<n;v++){
   
			if(!vis[v]&&map[u][v]!=inf){
   
				if(dist[u]+map[u][v]<dist[v]){
   
					dist[v]=dist[u]+map[u][v];
					pre[v].clear();
					pre[v].push_back(u);
				}else if(dist[u]+map[u][v]==dist[v]){
   
					pre[v].push_back(u);
				}
			}
		}
	}
}

void dfs(int v){
   //v为当前结点 
	if(v==s){
   //递归边界，到达叶子结点（路径起点） 
		tempPath.push_back(v);
		int tempCost=0;	//记录当前路径的花费之和 
		for(int i=tempPath.size()-1;i>0;i--){
    //倒着访问
		//当前结点id和下一个结点idNext 
			int id=tempPath[i],idNext=tempPath[i-1];
			tempCost+=cost[id][idNext];
		}
		if(tempCost<minCost){
    //如果当前路径的边权之和更小 
			minCost=tempCost;//更新minCost 
			path=tempPath;//更新path 
		}
		tempPath.pop_back();
		return ;
	}
	tempPath.push_back(v);
	for(int i=0;i<pre[v].size();i++){
   
		dfs(pre[v][i]);
	}
	tempPath.pop_back();
}
int main(){
   
	cin>>n>>m>>s>>d;
	mm(map,inf);
	for(int i=0;i<m;i++){
   
		int t1,t2,t3,t4;cin>>t1>>t2>>t3>>t4;
		map[t1][t2]=map[t2][t1]=t3;
		cost[t1][t2]=cost[t2][t1]=t4;
	}
	dijkstra();
	dfs(d);
	for(int i=path.size()-1;i>=0;i--){
   
		cout<<path[i]<<" ";//倒着输出路径上的结点 
	}
	cout<<dist[d]<<" "<<minCost;
	return 0;
}