Kuhn's Algorithm — Simple Bipartite Matching

boolean tryKuhn(int v, boolean[] used, int[] match, List[] adj) {
  for (int to : adj[v]) {
    if (used[to]) continue;
    used[to] = true;
    if (match[to] == -1 || tryKuhn(match[to], used, match, adj)) {
      match[to] = v;
      return true;
    }
  }
  return false;
}
int maxMatching(int leftN, List[] adj) {
  int[] match = new int[rightN];
  Arrays.fill(match, -1);
  int result = 0;
  for (int v = 0; v < leftN; v++) {
    boolean[] used = new boolean[rightN];
    if (tryKuhn(v, used, match, adj)) result++;
  }
  return result;
}