Find depth of a k-ary tree given a parent array : Solution 3

The problem statement is mentioned here. The first solution is here. The second solution is here.

While traversing up the tree from a leaf node, we can avoid the whole path till root if we can utilize the depth already found for nodes that were traversed earlier. This will reduce the problem to $ O(N) $ as below with extra space of $ O(N) $.

Let DEPTH be an array of length N
Initialize all elements of DEPTH to -1
FINDDEPTH(i)
    if DEPTH[i] == -1
        if P[i] == -1
            DEPTH[i] = 0
        else
            pDepth = FINDDEPTH(P[i])
           DEPTH[i] = pDepth + 1
    return DEPTH[i]

Let L be an array of length N
Initialize all elements of L to true
for each node i from 0 to N-1
   if P[i] is not -1
       set L[P[i]] to false
   end if
end for
initialize maxDepth to 0
for each node i from 0 to N-1
    if L[i] is false, continue next node
    depth = FINDDEPTH(i)
    if maxDepth < depth
       set maxDepth = depth
    end if
end for

As can be seen, the time complexity of the algorithm is $O(N)$ where $N$ is the number of nodes. The space complexity is $O(N)$. Thanks to my colleague Jignesh Parsana to help point to this solution.