Problem p03205 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 10;
const int INF = 1e9;

struct Edge {
  int u, v, cap, flow;
};

namespace Max_flow {

vector<Edge> E;
vector<int> G[N];

int S, T, n, d[N];

void init(int _n, int _s, int _t) {
  n = _n, S = _s, T = _t;
  for (int i = 0; i <= n; i++)
    G[i].clear();
  E.clear();
}

void addedge(int u, int v, int cap) {
  E.push_back((Edge){u, v, cap, 0});
  E.push_back((Edge){v, u, 0, 0});
  int m = E.size();
  G[u].push_back(m - 2);
  G[v].push_back(m - 1);
}

bool bfs() {
  for (int i = 0; i <= n; i++)
    d[i] = 0;
  d[S] = 1;
  queue<int> q;
  q.push(S);
  while (q.size()) {
    int u = q.front();
    q.pop();
    for (int i : G[u]) {
      if (E[i].cap > E[i].flow && !d[E[i].v]) {
        d[E[i].v] = d[u] + 1;
        q.push(E[i].v);
      }
    }
  }
  return d[T];
}

int dfs(int u, int a) {
  if (!a || u == T)
    return a;
  int flow = 0;
  for (int i : G[u]) {
    if (d[E[i].v] != d[u] + 1)
      continue;
    int f = dfs(E[i].v, min(E[i].cap - E[i].flow, a));
    flow += f;
    a -= f;
    E[i].flow += f;
    E[i ^ 1].flow -= f;
  }
  if (!flow)
    d[u] = 0;
  return flow;
}

int max_flow() {
  int flow = 0;
  while (bfs()) {
    flow += dfs(S, INF);
  }
  return flow;
}

} // namespace Max_flow

int n, c[N], p[N], q[N], vis[N];
vector<int> g[N], bel[N];

int main() {
  scanf("%d", &n);
  Max_flow::init(2 * n + 1, 0, 2 * n + 1);
  for (int i = 1; i < n; i++) {
    scanf("%d", &c[i]);
    g[i].resize(c[i]);
    Max_flow::addedge(0, i, 1);
    for (int j = 0; j < c[i]; j++) {
      scanf("%d", &g[i][j]);
      bel[g[i][j]].push_back(i);
      Max_flow::addedge(i, g[i][j] + n, 1);
    }
  }
  for (int i = 1; i <= n; i++) {
    Max_flow::addedge(i + n, 2 * n + 1, 1);
  }
  if (Max_flow::max_flow() != n - 1) {
    puts("-1");
    return 0;
  }
  for (Edge e : Max_flow::E) {
    if (e.u <= n && e.v > n && e.cap == e.flow) {
      p[e.u] = e.v - n;
      vis[e.v - n] = 1;
    }
  }
  queue<int> tmp;
  for (int i = 1; i <= n; i++) {
    if (!vis[i])
      tmp.push(i);
    vis[i] = 0;
  }
  int cnt = 0;
  while (tmp.size()) {
    cnt++;
    int u = tmp.front();
    tmp.pop();
    for (int i : bel[u])
      if (!vis[i]) {
        vis[i] = 1;
        q[i] = u;
        tmp.push(p[i]);
      }
  }
  if (cnt != n) {
    puts("-1");
    return 0;
  }
  for (int i = 1; i < n; i++) {
    printf("%d %d\n", p[i], q[i]);
  }
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>

using namespace std;

const int N = 3e5 + 10;
const int INF = 1e9;

struct Edge {
  int u, v, cap, flow;
};

namespace Max_flow {

vector<Edge> E;
vector<int> G[N];

int S, T, n, d[N];

void init(int _n, int _s, int _t) {
  n = _n, S = _s, T = _t;
  for (int i = 0; i <= n; i++)
    G[i].clear();
  E.clear();
}

void addedge(int u, int v, int cap) {
  E.push_back((Edge){u, v, cap, 0});
  E.push_back((Edge){v, u, 0, 0});
  int m = E.size();
  G[u].push_back(m - 2);
  G[v].push_back(m - 1);
}

bool bfs() {
  for (int i = 0; i <= n; i++)
    d[i] = 0;
  d[S] = 1;
  queue<int> q;
  q.push(S);
  while (q.size()) {
    int u = q.front();
    q.pop();
    for (int i : G[u]) {
      if (E[i].cap > E[i].flow && !d[E[i].v]) {
        d[E[i].v] = d[u] + 1;
        q.push(E[i].v);
      }
    }
  }
  return d[T];
}

int dfs(int u, int a) {
  if (!a || u == T)
    return a;
  int flow = 0;
  for (int i : G[u]) {
    if (d[E[i].v] != d[u] + 1)
      continue;
    int f = dfs(E[i].v, min(E[i].cap - E[i].flow, a));
    flow += f;
    a -= f;
    E[i].flow += f;
    E[i ^ 1].flow -= f;
  }
  if (!flow)
    d[u] = 0;
  return flow;
}

int max_flow() {
  int flow = 0;
  while (bfs()) {
    flow += dfs(S, INF);
  }
  return flow;
}

} // namespace Max_flow

int n, c[N], p[N], q[N], vis[N];
vector<int> g[N], bel[N];

int main() {
  scanf("%d", &n);
  Max_flow::init(2 * n + 1, 0, 2 * n + 1);
  for (int i = 1; i < n; i++) {
    scanf("%d", &c[i]);
    g[i].resize(c[i]);
    Max_flow::addedge(0, i, 1);
    for (int j = 0; j < c[i]; j++) {
      scanf("%d", &g[i][j]);
      bel[g[i][j]].push_back(i);
      Max_flow::addedge(i, g[i][j] + n, 1);
    }
  }
  for (int i = 1; i <= n; i++) {
    Max_flow::addedge(i + n, 2 * n + 1, 1);
  }
  if (Max_flow::max_flow() != n - 1) {
    puts("-1");
    return 0;
  }
  for (Edge e : Max_flow::E) {
    if (e.u <= n && e.v > n && e.cap == e.flow) {
      p[e.u] = e.v - n;
      vis[e.v - n] = 1;
    }
  }
  queue<int> tmp;
  for (int i = 1; i <= n; i++) {
    if (!vis[i])
      tmp.push(i);
    vis[i] = 0;
  }
  int cnt = 0;
  while (tmp.size()) {
    cnt++;
    int u = tmp.front();
    tmp.pop();
    for (int i : bel[u])
      if (!vis[i]) {
        vis[i] = 1;
        q[i] = u;
        tmp.push(p[i]);
      }
  }
  if (cnt != n) {
    puts("-1");
    return 0;
  }
  for (int i = 1; i < n; i++) {
    printf("%d %d\n", p[i], q[i]);
  }
  return 0;
}