最短路算法包

ACM 最短路

#include<iostream>
#include<string>
#include<string.h>
#include<algorithm>
#include<iomanip>
#include<cstdio>
#include<queue>
#include<stack> 
#include<vector>
#include<functional>  
#define INF 99999
using namespace std;
typedef pair<int, int> P;
struct edge {
    int from, to, cost;
};
int n, m;           //n为顶点数，m为边数
int a[100][100];
void warshall()
{
    int b[100][100] = { 0 };
    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= n; j++)
            b[i][j] = a[i][j];
    cout << "Floyd-warshall: \n";
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            for (int k = 1; k <= n; k++)
            {
                if (b[j][k] > b[j][i] + b[i][k])
                {
                    b[j][k] = b[j][i] + b[i][k];
                }
            }
        }
    }
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            cout << b[i][j] << " ";
        }
        cout << endl;
    }
}
void Dijkstra()
{
    int dis[100] = { 0 };
    bool book[100] = { 0 };
    int b[100][100] = { 0 };
    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= n; j++)
            b[i][j] = a[i][j];
    for (int i = 1; i <= n; i++)
    {
        dis[i] = a[1][i];
    }
    book[1] = 1;
    for (int i = 1; i <= n - 1; i++)
    {
        int minv = INF, min = 0;
        for (int i = 1; i <= n; i++)
        {
            if (!book[i] && minv > dis[i])
            {
                minv = dis[i];                   //在取最小值的过程中可以用堆优化
                min = i;
            }
        }
        book[min] = 1;
        for (int j = 1; j <= n; j++)
        {
            if (dis[j] > dis[min] + a[min][j])
            {
                dis[j] = dis[min] + a[min][j];    //用最短的边对其他所有点进行优化
            }
        }
    }
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << " ";
    }
    cout << endl;
}
void Bellman()
{
    int dis[100] = { 0 };
    int b[100][100] = { 0 };
    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= n; j++)
            b[i][j] = a[i][j];
    for (int i = 1; i <= n; i++)
        dis[i] = INF;
    dis[1] = 0;
    /*for (int i = 1; i <= n; i++)
    {
        dis[i] = a[1][i];
    }*/
    for (int i = 1; i <= n - 1; i++)
    {
        for (int j = 1; j <= n; j++)
        {
            for (int k = 1; k <= n; k++)
            {
                if (dis[k] > dis[j] + a[j][k])
                {
                    dis[k] = dis[j] + a[j][k];
                }
            }
        }
    }
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << " ";
    }
    cout << endl;
}
void BellmanQueue()
{
    int dis[100] = { 0 };
    int b[100][100] = { 0 };
    for (int i = 0; i <= n; i++)
        for (int j = 0; j <= n; j++)
            b[i][j] = a[i][j];
    for (int i = 1; i <= n; i++)
        dis[i] = INF;
    dis[1] = 0;
    queue<int> que;
    bool book[100] = { 0 };
    que.push(1);
    book[1] = 1;
    while (que.size())
    {
        int k = que.front();
        que.pop();
        for (int i = 1; i <= n; i++)
        {
            if (dis[i] > dis[k] + b[k][i])
            {
                dis[i] = dis[k] + b[k][i];
                if (!book[i])
                {
                    que.push(i);
                    book[i] = 1;
                }
            }
        }
        book[k] = 0;
    }
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << " ";
    }
    cout << endl;
}
void warshall2()
{
    vector<edge> G[100];
    int n, m;
    cin >> n >> m;
    for (int i = 0; i < m; i++)
    {
        int p;
        edge q;
        cin >> p >> q.to >> q.cost;
        G[p].push_back(q);
    }
    for (int i = 1; i <= n; i++)
    {
        for (int k = 1; k <= n; k++)
        {
            for (int j = 0; j < G[k].size(); j++)
            {
                edge e = G[k][j];
            }
        }
    }
    cout << "不会\n";
}
void Dijkstra2()
{
    vector<edge> G[100];
    int n, m;
    cin >> n >> m;
    int dis[100] = { 0 };
    fill(dis, dis + 100, INF);
    dis[1] = 0;
    for (int i = 0; i < m; i++)
    {
        int p;
        edge q;
        cin >> p >> q.to >> q.cost;
        G[p].push_back(q);
    }
    priority_queue<P, vector<P>, greater<P> >que;
    que.push(P(0, 1));
    while (que.size())
    {
        P p= que.top(); que.pop();
        for (int i = 0; i < G[p.second].size(); i++)
        {
            edge e = G[p.second][i];
            if (dis[e.to] > dis[p.second] + e.cost)
            {
                dis[e.to] = dis[p.second] + e.cost;
                que.push(P(dis[e.to], e.to));
            }
        }
    }
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << " ";
    }
    cout << endl;
}
void Bellman2()
{
    edge G[100];
    int n, m;
    cin >> n >> m;
    int dis[100] = { 0 };
    fill(dis, dis + 100, INF);
    dis[1] = 0;
    for (int i = 0; i < m; i++)
    {
        cin >> G[i].from >> G[i].to >> G[i].cost;
    }
    for (int i = 1; i <= n - 1; i++)
    {
        for (int j = 0; j < m; j++)
        {
            dis[G[j].to] = min(dis[G[j].to], dis[G[j].from] + G[j].cost);
        }
    }
    for (int i = 1; i <= n; i++)
    {
        cout << dis[i] << " ";
    }
    cout << endl;
}
int main()
{
    cin >> n >> m;
    for(int i=0;i<=n;i++)
        for (int j = 0; j <= n; j++)
        {
            if (i == j) a[i][j] = 0;
            else a[i][j] = INF;
        }
    for (int i = 1; i <= m; i++)
    {
        int p, q, t;
        cin >> p >> q >> t;
        a[p][q] = t;
    }
    cout << "邻接矩阵:\n";
    cout << "1:Floyd-warshall    2:Dijkstra    3:Bellman-Ford    4:Bellman队列优化(SPFA)\n";
    cout << "邻接表\n";
    cout << "5:Floyd-warshall    6:Dijkstra(堆优化)   7：Bellman-Ford\n";
    int t;
    while (cin >> t)
    {
        if (t == 1)
        {
            warshall();
        }
        else if (t == 2)
        {
            cout << "Dijkstra:\n";
            Dijkstra();
        }
        else if (t == 3)
        {
            cout << "Bellman-Ford:\n";
            Bellman();
        }
        else if (t == 4)
        {
            cout << "Bellman队列优化:\n";
            BellmanQueue();
        }
        else if (t == 5)
        {
            cout << "Floyd-warshall（邻接表）:\n";
            warshall2();
        }
        else if (t == 6)
        {
            cout << "Dijkstra(堆优化) \n";
            Dijkstra2();
        }
        else if (t == 7)
        {
            cout << "Bellman-Ford:\n";
            Bellman2();
        }
    }
}