知识结构图

单元最短路

Dijkstra

代码实现

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 510;
int n, m, dist[N], g[N][N];
bool st[N];
int dijkstra()
{
    memset(dist, 0x3f, sizeof dist);
    dist[1] = 0;
    for (int i = 0; i < n - 1; i ++ )
    {
        int t = -1;
        for (int j = 1; j <= n; j ++ )
            if (!st[j] && (t == -1 || dist[t] > dist[j]))
                t = j;

        for (int j = 1; j <= n; j ++ )
            dist[j] = min(dist[j], dist[t] + g[t][j]);

        st[t] = true;
    }
    if(dist[n] == 0x3f3f3f3f) return -1;
    return dist[n];
}
int main()
{
    scanf("%d%d", &n, &m);
    memset(g, 0x3f, sizeof g);
    while (m -- )
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        g[a][b] = min(g[a][b], c);
    }
    printf("%d", dijkstra());
    return 0;
}

运用

AcWing 849. Dijkstra求最短路 I

堆优化版Dijkstra

#include <cstring>
#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
typedef pair<int, int> PII;
const int N = 1e6 + 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)
{
    e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx ++ ;
}
int dijkstra()
{
    memset(dist, 0x3f, sizeof dist);
    dist[1] = 0;
    priority_queue<PII, vector<PII>, greater<PII>> heap;
    heap.push({0, 1});
    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});
            }
        }
    }
    if (dist[n] == 0x3f3f3f3f) return -1;
    return dist[n];
}
int main()
{
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h);
    while (m -- )
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        add(a, b, c);
    }
    cout << dijkstra() << endl;
    return 0;
}

to be continued