1111 Online Map (Dij/spfa)

link

 Dijkstra:

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <cstring>
# define LL long long
using namespace std;

int N;
int M;

int len[500][500];
int ti[500][500];
int S,T;
int dispre[500];
int mindis[500];
int needtime[500];

int fastest[500];
int needsection[500];
int fastpre[500];

struct comp{
    bool operator()(vector<int> p1, vector<int> p2){
        return p1[1]>p2[1];
    }
};

void shortestPath(){
    priority_queue<vector<int>, vector<vector<int>>, comp> pq;  // {site,dis}
    memset(mindis,127,sizeof(mindis));
    mindis[S]=0;
    needtime[S]=0;
    pq.push({S,0});
    vector<int> completed(N,0);
    while(!pq.empty()){
        auto cur=pq.top();
        pq.pop();
        int u=cur[0];
        if(u==T) break;
        if(completed[u]==1) continue;
        completed[u]=1;
        int d=cur[1];
        int t=needtime[u];
        for(int i=0;i<N;i++){
            if(len[u][i]==-1 || completed[i]==1) continue;
            if(d+len[u][i]<mindis[i]){
                mindis[i]=d+len[u][i];
                dispre[i]=u;
                needtime[i]=t+ti[u][i];
                pq.push({i,mindis[i]});
            }else if(d+len[u][i]==mindis[i]){
                if(t+ti[u][i]<needtime[i]){
                    dispre[i]=u;
                    needtime[i]=t+ti[u][i];
                }
            }
        }
    }
}

void fastestPath(){
    priority_queue<vector<int>, vector<vector<int>>, comp> pq;  // {site,time}
    memset(fastest,127,sizeof(fastest));
    fastest[S]=0;
    needsection[S]=0;
    pq.push({S,0});
    vector<int> completed(N,0);
    while(!pq.empty()){
        auto cur=pq.top();
        pq.pop();
        int u=cur[0];
        if(u==T) break;
        if(completed[u]==1) continue;
        completed[u]=1;
        int t=cur[1];
        int s=needsection[u];
        for(int i=0;i<N;i++){
            if(len[u][i]==-1 || completed[i]==1) continue;
            if(t+ti[u][i]<fastest[i]){
                fastest[i]=t+ti[u][i];
                fastpre[i]=u;
                needsection[i]=s+1;
                pq.push({i,fastest[i]});
            }else if(t+ti[u][i]==fastest[i]){
                if(s+1<needsection[i]){
                    fastpre[i]=u;
                    needsection[i]=1+s;
                }
            }
        }

    }
}

int main(){
    scanf("%d %d", &N, &M);
    memset(len,-1,sizeof(len));
    memset(ti,-1,sizeof(ti));
    memset(dispre,-1,sizeof(dispre));
    for(int i=0;i<M;i++){
        int a,b,c,d,e;
        scanf("%d%d%d%d%d", &a, &b, &c ,&d, &e);
        len[a][b]=d;
        ti[a][b]=e;
        if(c==0){
            len[b][a]=d;
            ti[b][a]=e;
        }
    }
    scanf("%d%d", &S, &T);
    shortestPath();
    vector<int> path;
    int v=T;
    path.push_back(v);
    while(true){
        v=dispre[v];
        path.push_back(v);
        if(v==S) break;
    }

    fastestPath();
    vector<int> fapath;
    v=T;
    fapath.push_back(v);
    while(true){
        v=fastpre[v];
        fapath.push_back(v);
        if(v==S) break;
    }

    int issame=1;
    if(path.size()!=fapath.size()){
        issame=0;
    }else{
        for(int i=0;i<path.size();i++){
            if(path[i]!=fapath[i]){
                issame=0;
                break;
            }
        }
    }
    if(issame==1){
        //Distance = 3; Time = 4: 3 -> 2 -> 5
        printf("Distance = %d; Time = %d: ", mindis[T], fastest[T]);
        for(int i=path.size()-1;i>=0;--i){
            if(i!=path.size()-1){
                printf(" -> ");
            }
            printf("%d", path[i]);
        }
        return 0;
    }
    //Distance = 6: 3 -> 4 -> 8 -> 5
    printf("Distance = %d: ", mindis[T]);
    for(int i=path.size()-1;i>=0;--i){
        if(i!=path.size()-1){
            printf(" -> ");
        }
        printf("%d", path[i]);
    }
    printf("
");
    printf("Time = %d: ", fastest[T]);
    for(int i=fapath.size()-1;i>=0;--i){
        if(i!=fapath.size()-1){
            printf(" -> ");
        }
        printf("%d", fapath[i]);
    }
    return 0;
}

另一种写法：

struct comp{
    bool operator()(vector<int> p1, vector<int> p2){
        if(p1[1]==p2[1]) return p1[2]>p2[2];
        return p1[1]>p2[1];
    }
};

void shortestPath(){
    priority_queue<vector<int>, vector<vector<int>>, comp> pq;  // {site,dis,time}
    memset(mindis,127,sizeof(mindis));
    mindis[S]=0;
    needtime[S]=0;
    pq.push({S,0,0});
    vector<int> completed(N,0);
    while(!pq.empty()){
        auto cur=pq.top();
        pq.pop();
        int u=cur[0];
        if(u==T) break;
        if(completed[u]==1) continue;
        completed[u]=1;
        int d=cur[1];
        int t=cur[2];
        for(int i=0;i<N;i++){
            if(len[u][i]==-1 || completed[i]==1) continue;
            if(d+len[u][i]<mindis[i]){
                mindis[i]=d+len[u][i];
                dispre[i]=u;
                needtime[i]=t+ti[u][i];
                pq.push({i,mindis[i],needtime[i]});
            }else if(d+len[u][i]==mindis[i]){
                if(t+ti[u][i]<needtime[i]){
                    dispre[i]=u;
                    needtime[i]=t+ti[u][i];
                    pq.push({i,mindis[i],needtime[i]});
                }
            }
        }
    }
}

SPFA:

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <cstring>
# define LL long long
using namespace std;

int N;
int M;

int len[500][500];
int ti[500][500];
int S,T;
int dispre[500];
int mindis[500];
int needtime[500];

int fastest[500];
int needsection[500];
int fastpre[500];

struct comp{
    bool operator()(vector<int> p1, vector<int> p2){
        return p1[1]>p2[1];
    }
};

void shortestPath(){
    queue<int> q;
    memset(mindis,127,sizeof(mindis));
    mindis[S]=0;
    needtime[S]=0;
    q.push(S);
    vector<int> inque(N,0);
    inque[S]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        inque[u]=0;
        for(int i=0;i<N;i++){
            if(len[u][i]==-1) continue;
            if(mindis[u]+len[u][i]<mindis[i]){
                mindis[i]=mindis[u]+len[u][i];
                dispre[i]=u;
                needtime[i]=needtime[u]+ti[u][i];
                if(inque[i]==0){
                    q.push(i);
                    inque[i]=1;
                }

            }else if(mindis[u]+len[u][i]==mindis[i]){
                if(needtime[u]+ti[u][i]<needtime[i]){
                    dispre[i]=u;
                    needtime[i]=needtime[u]+ti[u][i];
                    if(inque[i]==0){
                        q.push(i);
                        inque[i]=1;
                    }
                }
            }
        }
    }
}

void fastestPath(){
    queue<int> q;
    memset(fastest,127,sizeof(fastest));
    fastest[S]=0;
    needsection[S]=0;
    q.push(S);
    vector<int> inque(N,0);
    inque[S]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        inque[u]=0;
        for(int i=0;i<N;i++){
            if(len[u][i]==-1) continue;
            if(fastest[u]+ti[u][i]<fastest[i]){
                fastest[i]=fastest[u]+ti[u][i];
                fastpre[i]=u;
                needsection[i]=needsection[u]+1;
                if(inque[i]==0){
                    q.push(i);
                    inque[i]=1;
                }

            }else if(fastest[u]+ti[u][i]==fastest[i]){
                if(needsection[u]+1<needsection[i]){
                    fastpre[i]=u;
                    needsection[i]=needsection[u]+1;
                    if(inque[i]==0){
                        q.push(i);
                        inque[i]=1;
                    }
                }
            }
        }
    }
}

int main(){
    scanf("%d %d", &N, &M);
    memset(len,-1,sizeof(len));
    memset(ti,-1,sizeof(ti));
    memset(dispre,-1,sizeof(dispre));
    for(int i=0;i<M;i++){
        int a,b,c,d,e;
        scanf("%d%d%d%d%d", &a, &b, &c ,&d, &e);
        len[a][b]=d;
        ti[a][b]=e;
        if(c==0){
            len[b][a]=d;
            ti[b][a]=e;
        }
    }
    scanf("%d%d", &S, &T);
    shortestPath();
    vector<int> path;
    int v=T;
    path.push_back(v);
    while(true){
        v=dispre[v];
        path.push_back(v);
        if(v==S) break;
    }

    fastestPath();
    vector<int> fapath;
    v=T;
    fapath.push_back(v);
    while(true){
        v=fastpre[v];
        fapath.push_back(v);
        if(v==S) break;
    }

    int issame=1;
    if(path.size()!=fapath.size()){
        issame=0;
    }else{
        for(int i=0;i<path.size();i++){
            if(path[i]!=fapath[i]){
                issame=0;
                break;
            }
        }
    }
    if(issame==1){
        //Distance = 3; Time = 4: 3 -> 2 -> 5
        printf("Distance = %d; Time = %d: ", mindis[T], fastest[T]);
        for(int i=path.size()-1;i>=0;--i){
            if(i!=path.size()-1){
                printf(" -> ");
            }
            printf("%d", path[i]);
        }
        return 0;
    }
    //Distance = 6: 3 -> 4 -> 8 -> 5
    printf("Distance = %d: ", mindis[T]);
    for(int i=path.size()-1;i>=0;--i){
        if(i!=path.size()-1){
            printf(" -> ");
        }
        printf("%d", path[i]);
    }
    printf("
");
    printf("Time = %d: ", fastest[T]);
    for(int i=fapath.size()-1;i>=0;--i){
        if(i!=fapath.size()-1){
            printf(" -> ");
        }
        printf("%d", fapath[i]);
    }
    return 0;
}