notebook/code/MaxBipartiteMatching_sqrt.cc

// O(sqrt(n)*E)
// Use : set G (adjacency list), set uN, then m = MaxMatch() and the result is in Mx and My
const int MAXN = 1000; const int INF = 0x3f3f3f3f; vector<int>G [MAXN];
int uN;
int Mx[MAXN],My[MAXN]; int dx[MAXN],dy[MAXN]; int dis;
bool used[MAXN];
bool SearchP() {
  queue<int>Q;
  dis = INF;
  memset(dx,-1,sizeof(dx)); memset(dy,-1,sizeof(dy));
  for(int i = 0 ; i < uN; 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;
    int sz = G[u].size();
    for(int i = 0;i < sz;i++) {
      int v = G[u][i];
      if(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) {
  int sz = G[u].size();
  for(int i = 0;i < sz;i++) {
    int v = G[u][i];
    if(!used[v] && dy[v] == dx[u] + 1) {
      used[v] = true;
      if(My[v] != -1 && dy[v] == dis) continue;
      if(My[v] == -1 || DFS(My[v])) {
        My[v] = u; Mx[u] = v; return true;
      }
    }
  }
  return false;
}
int MaxMatch() {
  int res = 0;
  memset(Mx,-1,sizeof(Mx)); memset(My,-1,sizeof(My));
  while(SearchP()) {
	  memset(used,false,sizeof(used));
    for(int i = 0;i < uN;i++)
		   if(Mx[i] == -1 && DFS(i)) res++;
	}
  return res;
}