一般图匹配

一般图最大匹配+输出方案

#include <bits/stdc++.h>
using namespace std;
namespace edmond {
    const int LEN = 4e4 + 5;
    int n, m, ans, tot, qh, qt, Time;
    int head[LEN], pre[LEN], fa[LEN], flag[LEN], nxt[LEN], q[LEN], vis[LEN];
    struct edge {
        int vet, next, len;
    } E[LEN * 2];
    void add(int u, int v) {
        E[++tot] = (edge){v, head[u]};
        head[u] = tot;
    }
    int getf(int x) {
        if (fa[x] != x) fa[x] = getf(fa[x]);
        return fa[x];
    }
    int lca(int x, int y) {
        ++Time;
        x = getf(x), y = getf(y);
        for (;;swap(x, y)) {
            if (x) {
                if (flag[x] == Time) return x;
                flag[x] = Time;
                x = getf(pre[nxt[x]]);
            }
        }
        return x;
    }
    void blossom(int x, int y, int z) {
        while (getf(x) != z) {
            pre[x] = y;
            y = nxt[x];
             if (vis[y] == 1) {
                 q[++qt] = y;
                 vis[y] = 0;
             }
             if (fa[x] == x) fa[x] = z;
             if (fa[y] == y) fa[y] = z;
             x = pre[y];
        }
    }
    int match(int s) {
        for (int i = 0; i <= n; i++) {
            fa[i] = i;
            vis[i] = -1;
        }
        qh = qt = 0;
        q[++qt] = s;
        vis[s] = 0;
        while (qh < qt) {
            int u = q[++qh];
            for (int e = head[u]; e != -1; e = E[e].next) {
                int v = E[e].vet;
                if (vis[v] == -1) {
                    pre[v] = u;
                    vis[v] = 1;
                    if (!nxt[v]) {
                        for (int x = v, y = u, last; y; x = last, y = pre[x]) {
                            last = nxt[y];
                            nxt[y] = x;
                            nxt[x] = y;
                            
                        }
                        return 1;
                    }
                    q[++qt] = nxt[v];
                    vis[nxt[v]] = 0;
                } else if (!vis[v] && getf(v) != getf(u)) {
                    int w = lca(v, u);
                    blossom(u, v, w);
                    blossom(v, u, w);
                }
            }
        }
        return 0;
    }
    void init() {
        Time = 0;
        tot = -1;
        for (int i = 1; i <= n; i++) {
            head[i] = -1;
            flag[i] = nxt[i] = pre[i] = 0;
        }
    }
}
using namespace edmond;
int main() {
    scanf("%d %d", &n, &m);
    init();
    for (int i = 1; i <= m; i++) {
        int x, y;
        scanf("%d %d", &x, &y);
        add(x, y);
        add(y, x);
    }
    for (int i = n; i >= 1; i--) {
        if (!nxt[i]) ans += match(i);
    }
    printf("%d
", ans);
    for (int i = 1; i < n; i++) printf("%d ", nxt[i]);
    printf("%d
", nxt[n]);
    return 0;
}