Articulation Points - Algorithm

$1.$ Build adjacency list.

$2.$ Initialize disc[v] = -1, low[v] = 0, $timer = 0$, $result = set()$.

$3.$ For each unvisited vertex, run DFS with $isRoot = true$:

• Set disc[v] = low[v] = timer, $timer{+}{+}$, $children = 0$
• For each neighbor $w$: if unvisited, recurse, $children{+}{+}$, update low[v], check low[w] >= disc[v]; if visited (not parent), update low[v]
• If $isRoot$ and $children \geq 2$, add $v$ to result

$4.$ Return result.

This runs in $O(V + E)$ time and uses $O(V)$ space.