Augmenting Path Algorithm : 一般图最大匹配

算法原理详见 http://www.csie.ntnu.edu.tw/~u91029/Matching.html

orz 带花树很神奇，挖坑最大权匹配

#include <iostream>
#include <cstring>
#include <cstdio>
#include <deque>
using namespace std;
const int maxn = 50;
deque<int> p[maxn];  //树根到x的交错路径
bool adj[maxn][maxn];
int m[maxn]; //记录匹配情况
int d[maxn]; //记录奇点和偶点
int q[maxn], *qf, *qb; //记录可延伸的偶点
int n;

void label_one_side(int x, int y, int bi){
    for(int i = bi+1; i < p[x].size(); i++){
        int z = p[x][i];
        if(d[z] == 1){
            p[z] = p[y];
            p[z].insert(p[z].end(), p[x].rbegin(), p[x].rend()-i);
            d[z] = 0;
            *qb++ = z;
        }
    }
}

bool BFS(int r){
    for(int i = 0; i < n; i++) p[i].clear();
    p[r].push_back(r);
    for(int i = 0; i < n; i++) d[i] = -1;
    d[r] = 0;
    qf = qb = q;
    *qb++ = r;
    while(qf < qb){
        for(int x = *qf++, y = 0; y < n; y++){
            if(adj[x][y] && m[y] != y){
                if(d[y] == -1){
                    if(m[y] == -1){
                        for(int i = 0; i+1 < p[x].size(); i += 2){
                            m[p[x][i]] = p[x][i+1];
                            m[p[x][i+1]] = p[x][i];
                        }
                        m[x] = y; m[y] = x;
                        return true;
                    } else {
                        int z = m[y];
                        p[z] = p[x];
                        p[z].push_back(y);
                        p[z].push_back(z);
                        d[y] = 1; d[z] = 0;
                        *qb++ = z;
                    }
                } else if(d[y] == 0) {
                    int bi = 0;
                    while(bi < p[x].size() && bi < p[y].size() && p[x][bi] == p[y][bi]) bi++;
                    bi--;
                    label_one_side(x, y, bi);
                    label_one_side(y, x, bi);
                }
            }
        }
    }
    return false;
}

int match(){
    for(int i = 0; i < n; i++) m[i] = -1;
    int c = 0;
    for(int i = 0; i < n; i++){
        if(m[i] == -1)
            if(BFS(i)) c++;
            else m[i] = i;
    }
    return c;
}

int main(){
    cin>>n;
    int x, y;
    while(cin>>x>>y) adj[x][y] = adj[y][x] = true;
    match();
}

这个是缩点版本的

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
const int N = 50;
int n;
bool adj[N][N];
int p[N];
int m[N];
int d[N];
int c1[N], c2[N];
int q[N], *qf, *qb;

int pp[N];
int f(int x) { return x == pp[x] ? x : pp[x] = f(pp[x]); }
void u(int x, int y) { pp[x] = y; }
int v[N];

void path(int r, int x){
    if(r == x) return;
    if(d[x] == 0){
        path(r, p[p[x]]);
        int i = p[x], j = p[p[x]];
        m[i] = j; m[j] = i;
    } else if(d[x] == 1){
        path(m[x], c1[x]);
        path(r, c2[x]);
        int i = c1[x], j = c2[x];
        m[i] = j; m[j] = i;
    }
}

int lca(int x, int y, int r){
    int i = f(x), j = f(y);
    while(i != j && v[i] != 2 && v[j] != 1){
        v[i] = 1; v[j] = 2;
        if(i != r) i = f(p[i]);
        if(j != r) j = f(p[j]);
    }
    int b = i, z = j; if(v[j] == 1) swap(b, z);
    for(int i = b; i != z; i = f(p[i])) v[i] = -1;
    v[z] = -1;
    return b;
}

void contract_one_side(int x, int y, int b){
    for(int i = f(x); i != b; i = f(p[i])){
        u(i, b);
        if(d[i] == 1) c1[i] = x, c2[i] = y, *qb++ = i;
    }
}

bool BFS(int r){
    for(int i = 0; i < n; i++) pp[i] = i;
    for(int i = 0; i < n; i++) v[i] = d[i] = -1;
    d[r] = 0;
    qf = qb = q;
    *qb++ = r;
    while(qf < qb){
        for(int x = *qf++, y = 0; y < n; y++){
            if(!adj[x][y] || m[y] == y || f(x) == f(y)) continue;
            if(d[y] == -1){
                if(m[y] == -1){
                    path(r, x);
                    m[x] = y; m[y] = x;
                    return true;
                } else {
                    p[y] = x; p[m[y]] = y;
                    d[y] = 1; d[m[y]] = 0;
                    *qb++ = m[y];
                }
            } else if(d[f(y)] == 0){
                int b = lca(x, y, r);
                contract_one_side(x, y, b);
                contract_one_side(y, x, b);
            }
        }
    }
    return false;
}

int main(){

}