vector神教实现最短路模版

${\LARGE \mathcal{SPFA} } $

#include <bits/stdc++.h>
#define otto auto

using namespace std;

struct edge
{
    int v, w;
    // v --> to, w --> value
};

const int maxn = 1e5 + 5; // 点数

vector<edge> e[maxn];
int dis[maxn], cnt[maxn], vis[maxn];
queue<int> q;

bool spfa(int n, int s)
{
    memset(dis, 0x3f, sizeof(dis));
    dis[s] = 0, vis[s] = 1;
    q.push(s);
    while (!q.empty())
    {
        int u = q.front();
        q.pop(), vis[u] = 0;
        for (otto ed : e[u])
        {
            int v = ed.v, w = ed.w;
            if (dis[v] > dis[u] + w)
            {
                dis[v] = dis[u] + w;
                cnt[v] = cnt[u] + 1; // 记录最短路经过的边数
                if (cnt[v] >= n)
                    return false;
                // 在不经过负环的情况下，最短路至多经过 n - 1 条边
                // 因此如果经过了多于 n 条边，一定说明经过了负环
                if (!vis[v])
                    q.push(v), vis[v] = 1;
            }
        }
    }
    return true;
}

int main()
{
    int n, m, s;
    cin >> n >> m >> s;

    for (int i = 1; i <= m; i++)
    {
        int u, v, w;
        cin >> u >> v >> w;
        edge inp;
        inp.v = v;
        inp.w = w;
        e[u].push_back(inp);
    }
    spfa(n, s);

    for (int i = 1; i <= n; i++)
    {
        if (i == s)
            cout << 0 << ' ';
        else
        {
            if(dis[i] == 0x3f3f3f3f)
                cout << 2147483647 <<' '; //若不能到达
            else
                cout << dis[i] << ' ';
        }
    }
}

${\LARGE \mathcal{Dijkstra} } $

#include <bits/stdc++.h>

using namespace std;

struct Edge
{
    int v, w;
    // v --> to, w --> value
    friend bool operator<(const Edge &x, const Edge &y)
    {
        return x.w > y.w; //NOTICE!!!!
    }
};

const int maxn = 1e5 + 5;

vector<Edge> e[maxn];
priority_queue<Edge> q;
int dis[maxn], vis[maxn], n, m, s;

void dijkstra()
{
    dis[s] = 0;
    q.push({s, 0});
    while (!q.empty())
    {
        Edge inp = q.top();
        q.pop();
        int p = inp.v;
        int tot = e[p].size();
        if (vis[p])
            continue;

        vis[p] = 1;
        for (int j = 0; j < tot; j++)
        {
            int v = e[p][j].v;
            if (dis[v] > dis[p] + e[p][j].w)
            {
                dis[v] = dis[p] + e[p][j].w;
                if (!vis[v])
                {
                    q.push(Edge{v, dis[v]});
                }
            }
        }
    }
    return;
}

int main()
{
    cin >> n >> m >> s;
    for (int i = 1; i <= n; i++)
        dis[i] = 2147483647;
    for (int i = 1; i <= m; i++)
    {
        int x, y, w;
        cin >> x >> y >> w;
        Edge inp;
        inp.v = y, inp.w = w;
        e[x].push_back(inp);
    }

    dijkstra();
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << ' ';
    }

    return 0;
}

${\LARGE \mathcal{Dijkstra} } $

按照开始点到点n的顺序输出，如果倒序输出则删掉stack处理部分。

#include <bits/stdc++.h>

using namespace std;

struct Edge
{
    int v, w;
    // v --> to, w --> value
    friend bool operator<(const Edge &x, const Edge &y)
    {
        return x.w > y.w; 
    }
};

const int maxn = 1e5 + 5;

vector<Edge> e[maxn];

//NEW
stack<int> out;
int pre[maxn];
//NEW

priority_queue<Edge> q;
int dis[maxn], vis[maxn], n, m, s;

void dijkstra()
{
    dis[s] = 0;
    q.push({s, 0});
    while (!q.empty())
    {
        Edge inp = q.top();
        q.pop();
        int p = inp.v;
        int tot = e[p].size();
        if (vis[p])
            continue;

        vis[p] = 1;
        for (int j = 0; j < tot; j++)
        {
            int v = e[p][j].v;
            if (dis[v] > dis[p] + e[p][j].w)
            {
                dis[v] = dis[p] + e[p][j].w;
                if (!vis[v])
                {
                    q.push(Edge{v, dis[v]});

                    //NEW
                    pre[v] = p;
                    //NEW

                }
            }
        }
    }
    return;
}

int main()
{
    cin >> n >> m;
    s = 1;
    for (int i = 1; i <= n; i++)
    {
        dis[i] = 2147483647;

        //NEW
        pre[i] = -1;
        //NEW

    }

    for (int i = 1; i <= m; i++)
    {
        int x, y, w;
        cin >> x >> y >> w;
        Edge inp;
        inp.v = y, inp.w = w;
        e[x].push_back({y, w});
        e[y].push_back({x, w});
    }

    dijkstra();


    //NEW
    for (int i = n; i != -1; i = pre[i])
    {
        out.push(i);
    }

    int flag = 0;
    while (!out.empty())
    {
        cout << out.top() << ' ';
        out.pop();
        flag = 1;
    }
    if(flag == 0)
        cout << -1 << ' ';
    //NEW

    return 0;
}