图论 —— dijkstra

https://www.acwing.com/problem/content/852/

 

https://www.luogu.com.cn/problem/P3371

 

https://www.luogu.com.cn/problem/P4779

 

#include <cstring>
#include <iostream>
#include <algorithm>
#include <queue>
#include <cmath>
using namespace std;

typedef pair<int, int> PII;

const int N = 1e7 + 10;

int n, m;
int h[N], w[N], e[N], ne[N], idx;
int dist[N];
bool st[N];

void add(int a, int b, int c)
{
    w[idx] = c, e[idx] = b, ne[idx] = h[a], h[a] = idx ++ ;
}

void dijkstra(int u)
{
    memset(dist, 0x3f, sizeof dist);
    dist[u] = 0;
    priority_queue<PII, vector<PII>, greater<PII>> heap;
    heap.push({0, u});

    while (heap.size())
    {
        auto t = heap.top();
        heap.pop();

        int ver = t.second, distance = t.first;

        if (st[ver]) continue;
        st[ver] = true;

        for (int i = h[ver]; i != -1; i = ne[i])
        {
            int j = e[i];
            if (dist[j] > dist[ver] + w[i])
            {
                dist[j] = dist[ver] + w[i];
                heap.push({dist[j], j});
            }
        }
    }
    for(int i = 1; i <= n; i ++ )
    {
        if (dist[i] == 0x3f3f3f3f) dist[i] = pow(2, 31) - 1;
    }
    
}

int main()
{
    int u;
    scanf("%d%d%d", &n, &m, &u);

    memset(h, -1, sizeof h);
    while (m -- )
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        add(a, b, c);
    }
    dijkstra(u);
    for(int i = 1; i <= n; i ++ )
        cout << dist[i] << ' ';

    return 0;
}

 

知道图中任意两点间距离

要求所有点到一个确定的点的最短距离（可能到不了）

输出