Bridges & Articulation Points

function findBridgesAndCuts(n, edges) {
    const adj = Array.from({length: n}, () => []);
    for (const [u, v, id] of edges) {
        adj[u].push([v, id]);
        adj[v].push([u, id]);
    }

    const disc = new Array(n).fill(-1);
    const low = new Array(n).fill(0);
    const bridges = [], cuts = [];
    let timer = 0;

    function dfs(u, parentEdgeId) {
        disc[u] = low[u] = timer++;
        let children = 0;

        for (const [v, eid] of adj[u]) {
            if (disc[v] === -1) {
                children++;
                dfs(v, eid);
                low[u] = Math.min(low[u], low[v]);

                // Bridge check: v's subtree can't reach u or above
                if (low[v] > disc[u]) bridges.push(eid);

                // Articulation point: non-root with low[v] >= disc[u]
                if (parentEdgeId !== -1 && low[v] >= disc[u]) cuts.push(u);
            } else if (eid !== parentEdgeId) {
                // Back edge (not parent): update low
                low[u] = Math.min(low[u], disc[v]);
            }
        }

        // Root is articulation point iff it has >= 2 DFS children
        if (parentEdgeId === -1 && children >= 2) cuts.push(u);
    }

    for (let i = 0; i < n; i++) if (disc[i] === -1) dfs(i, -1);
    return { bridges: [...new Set(bridges)], cuts: [...new Set(cuts)] };
}