Set CUT_VERTICES = {}

int dfsnum = 0
// define v.low to be the lowest dfs number
// of a non-outputted vertex reachable
// by using at most one-non tree edge.

foreach v in V
    if (v.dfsnum is not defined)
        findcut(v,null)


// parent is the vertex that called findcut
// if u is root, parent = null
void findcut(vertex v, vertex parent)
{
    // children here refer to children of v in the dfs tree
    // hence, children cannot be connected except thru v (in the tree)
    int children = 0

    v.dfsnum = dfsnum++
    v.low = v.dfsnum

    foreach (v,u) in E
    {

        if (u.dfsnum is not defined) {
            // u is a child of v
            // i.e. v is a parent of u
            children++
            findcut(u,v)
            v.low = min(v.low, u.low)

        }else if (u.dfsnum is defined && u != parent) {
            // i.e. u is not parent of v
            // u must be an ancestor
            v.low = min(v.low, u.dfsnum)
        }

       // v is not a root...
       if (parent != null && v.low >= parent.dfsnum) {
           // Since the low of parent's childrens are higher than
           // parent's low, there is no back edge to parent's ancestors
           // i.e. if parent is removed, there is no way children can be
           // connected to ancestors
           // so parent has to be a cut vertex
           CUT_VERTICES.add(parent)
       }
    }

    // v is a root (special case)
    if (parent == null && children >= 2) {
        CUT_VERTICES.add(v)
    }
}