二分图匹配（Hopcroft－Carp 的算法）

二分图匹配（ Hopcroft － Carp 的算法）

| INIT: g[][] 邻接矩阵 ;

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

| 时间复杂度为 O （ V^0.5 E ）

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

const int MAXN = 3001;

const int INF = 1 << 28;

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

int dx[MAXN], dy[MAXN], dis;

bool vst[MAXN];

bool searchP(void){

queue<int> Q;

dis = INF;

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

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

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

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

Q.push(i); dx[i] = 0;

}

while (!Q.empty()) {

int u = Q.front(); Q.pop();

if (dx[u] > dis) break;

for (int v = 0; v < Ny; v++)

if (g[u][v] && dy[v] == -1) {

dy[v] = dx[u]+1;

if (My[v] == -1) dis = dy[v];

else{

dx[My[v]] = dy[v]+1;

Q.push(My[v]);

}

}

}

return dis != INF;

}

bool DFS(int u){

for (int v = 0; v < Ny; v++)

if (!vst[v] && g[u][v] && dy[v] == dx[u]+1) {

vst[v] = 1;

if (My[v] != -1 && dy[v] == dis) continue;

if (My[v] == -1 || DFS(My[v])) {

My[v] = u; Mx[u] = v;

return 1;

}

}

return 0;

}

int MaxMatch(void){

int res = 0;

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

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

while (searchP()) {

memset(vst, 0, sizeof(vst));

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

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

}

return res;

}