最短路算法汇总

优先队列优化的Dijkstra：

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 5e5 + 5, inf = 0x3f3f3f3f;

struct point {
    int id, dis;
};

struct cmp {
    bool operator ()(const point &x, const point &y) {
        return x.dis > y.dis;
    }
};

struct edge {
    int to, nxt, val;
} edges[MAXN];

priority_queue <point, vector<point>, cmp> heap;
int head[MAXN], dist[MAXN], cnt = 0;
bool vis[MAXN];

void addEdge(int from, int to, int val) {
    edges[cnt].to = to; edges[cnt].nxt = head[from]; edges[cnt].val = val;
    head[from] = cnt++;
}

void dijkstra(int s) {
    memset(dist, 0x3f, sizeof(dist));
    dist[s] = 0;
    point tmp;
    tmp.id = s; tmp.dis = 0;
    heap.push(tmp);
    while(!heap.empty()) {
        while(!heap.empty() && vis[heap.top().id]) heap.pop();
        if(heap.empty()) break;
        tmp = heap.top(); heap.pop();
        vis[tmp.id] = true;
        for(int i = head[tmp.id]; i != -1; i = edges[i].nxt)
            if(dist[tmp.id] + edges[i].val < dist[edges[i].to]) {
                dist[edges[i].to] = dist[tmp.id] + edges[i].val;
                point ntmp;
                ntmp.id = edges[i].to; ntmp.dis = dist[edges[i].to];
                heap.push(ntmp);
            }
    }
}


int main() {
    ios::sync_with_stdio(false);
    memset(head, 0xff, sizeof(head));
    int n, m, u, v, w, s;
    cin >> n >> m >> s;
    for(int i = 0; i < m; i++) {
        cin >> u >> v >> w;
        addEdge(u, v, w);
    }
    dijkstra(s);
    for(int i = 1; i <= n; i++)
        cout << (dist[i] == inf ? 0x7fffffff : dist[i]) << " ";
    cout << endl;
    return 0;
}

线段树优化的Dijkstra：

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 1e5 + 5, inf = 0x3f3f3f3f;

int st[MAXN << 3], head[MAXN], dist[MAXN], ans[MAXN], n, m, cnt = 0;
bool vis[MAXN];

struct edge {
    int to, nxt, val;
} edges[MAXN << 1];

void addedge(int from, int to, int val) {
    edges[cnt].to = to, edges[cnt].val = val;
    edges[cnt].nxt = head[from]; head[from] = cnt++;
}

void pushup(int x) {
    st[x] = dist[st[x << 1]] < dist[st[x << 1 | 1]] ? st[x << 1] : st[x << 1 | 1];
}

void build(int x, int l, int r) {
    if(l < r) {
        int mid = (l + r) >> 1;
        build(x << 1, l, mid);
        build(x << 1 | 1, mid + 1, r);
        pushup(x);
    } else st[x] = l;
}

void updata(int x, int l, int r, int q) {
    if(l != r) {
        int mid = (l + r) >> 1;
        if(q <= mid) updata(x << 1, l, mid, q);
        else updata(x << 1 | 1, mid + 1, r, q);
        pushup(x);
    }
}

void dijkstra(int s) {
    ans[s] = dist[s] = 0;
    build(1, 1, n);
    while(dist[st[1]] < inf) {
        int v = st[1]; vis[v] = 1;
        for(int i = head[v]; i != -1; i = edges[i].nxt) if(!vis[edges[i].to]) {
            dist[edges[i].to] = min(dist[edges[i].to], dist[v] + edges[i].val);
            updata(1, 1, n, edges[i].to);
        }
        ans[v] = dist[v]; dist[v] = inf;
        updata(1, 1, n, v);
    }
}

int main() {
    ios::sync_with_stdio(false);
    memset(dist, 0x3f, sizeof(dist));
    memset(head, 0xff, sizeof(head));
    memset(ans, 0x3f, sizeof(ans));
    int u, v, w, s;
    cin >> n >> m >> s;
    for(int i = 0; i < m; i++) {
        cin >> u >> v >> w;
        addedge(u, v, w);
    }
    dijkstra(s);
    for(int i = 1; i <= n; i++) cout << ans[i] << " ";
    cout << endl;
    return 0;
}