Basic Implementation

Start with a global timer at $0$. Run DFS from the root. When entering node $v$, set tin[v] = timer and increment. Recurse on children. When exiting, set tout[v] = timer without incrementing. Pseudocode:

timer := 0

function dfs(v, parent):
    tin[v] := timer
    timer := timer + 1
    for each child u of v:
        if u != parent then
            dfs(u, v)
    tout[v] := timer

After this DFS, you have entry and exit times for every node. All $tin$ values are unique ($0$ to $n-1$), while $tout$ values may repeat. All values stay within $n$. This is part of the Euler Tour framework for converting tree structures into arrays.

This runs in $O(n)$ time and uses $O(n)$ space.