Bridge Tree

// Bridge Tree
// O(n)

struct NODE {
    int v, e;
};
vector <NODE> G[MAXN];
bool isBridge[MAXN],
     vis[MAXN];
int  timer,
     dis[MAXN],
     low[MAXN];

void FIND_BRIDGE(int u, int p = -1) {
    vis[u] = 1;
    dis[u] = low[u] = timer++;
    for (NODE E : G[u]) {
        int v = E.v;
        int e = E.e;
        if (v == p)
            continue;
        if (!vis[v]) {
            FIND_BRIDGE(v, u);
            low[u] = min(low[u], low[v]);
            if (dis[u] < low[v])
                isBridge[e] = 1;
        }
        else {
            low[u] = min(low[u], dis[v]);
        }
    }
}

int compo;
bool used[MAXN];
int compo_num[MAXN];
vector <int> TREE[MAXN];

void BRIDGE_TREE(int src) {
    used[src] = 1;
    int cur_compo = compo;
    compo_num[src] = cur_compo;
    queue <int> PQ; // for BFS
    PQ.push(src);
    while (!PQ.empty()) {
        int u = PQ.front();
                PQ.pop();
        for (NODE E : G[u]) {
            int v = E.v;
            int e = E.e;
            if (used[v])
                continue;



            if (isBridge[e]) {
                compo++;
                TREE[cur_compo].push_back(compo);
                TREE[compo].push_back(cur_compo);

                BRIDGE_TREE(v);
            }

            else {
                PQ.push(v);

                used[v] = 1;
                compo_num[v] = cur_compo; // v's component number
            }
        }
    }
}

int main() {
    // Take input
    for (int i = 0; i < tNode; i++) {  // 0 <= node_num < tNode
        if (!vis[i])
            FIND_BRIDGE(i);
    }
    for (int i = 0; i < tNode; i++) {
        if (!used[i]) {
            BRIDGE_TREE(i);
            compo++;
        }
    }
    // Output
}