Tarjan - Implementation

Here is Tarjan:

function tarjan(v):
    disc[v] = low[v] = timer
    timer = timer + 1
    st.push(v)
    onStack[v] = true

    for u in adj[v]:
        if disc[u] == -1:
            tarjan(u)
            low[v] = min(low[v], low[u])
        else if onStack[u]:
            low[v] = min(low[v], disc[u])

    if low[v] == disc[v]:
        while st.top() != v:
            scc[st.top()] = comp
            onStack[st.top()] = false
            st.pop()
        scc[v] = comp
        onStack[v] = false
        comp = comp + 1
        st.pop()

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