二分图匹配（匈牙利算法 BFS 实现）

二分图匹配（匈牙利算法 BFS 实现）

| INIT: g[][] 邻接矩阵 ;

| CALL: res = MaxMatch (); Nx, Ny 初始化！！！

| 优点：适用于稀疏二分图，边较少，增广路较短。

| 匈牙利算法的理论复杂度是 O(VE)

\*==================================================*/

const int MAXN = 1000;

int g[MAXN][MAXN], Mx[MAXN], My[MAXN], Nx, Ny;

int chk[MAXN], Q[MAXN], prev[MAXN];

int MaxMatch(void) {

int res = 0;

int qs, qe;

memset(Mx, -1, sizeof(Mx));

memset(My, -1, sizeof(My));

memset(chk, -1, sizeof(chk));

for (int i = 0; i < Nx; i++){

if (Mx[i] == -1){

qs = qe = 0;

Q[qe++] = i;

prev[i] = -1;

bool flag = 0;

while (qs < qe && !flag){

int u = Q[qs];

for (int v = 0; v < Ny && !flag; v++)

if (g[u][v] && chk[v] != i) {

chk[v] = i; Q[qe++] = My[v];

if (My[v] >= 0) prev[My[v]] = u;

else {

flag = 1;

int d = u, e = v;

while (d != -1) {

int t = Mx[d];

Mx[d] = e; My[e] = d;

d = prev[d]; e = t;

}

}

}

qs++;

}

if (Mx[i] != -1) res++;

}

}

return res;

}