Find depth of a k-ary tree given a parent array : Solution 1

The problem statement is mentioned here.

Following is the first solution.

initialize maxDepth to 0
for each node i from 0 to N-1
    set parent to P[i]
    set depth to 1
    while parent is not -1
       set parent to P[parent]
       increment depth
    end while
    if maxDepth < depth
       set maxDepth = depth
    end if
end for

As can be seen, the time complexity of the algorithm is $O(N^2)$ where $N$ is the number of nodes. The space complexity is $O(1)$.