Question

I have a tree with n elements that store something like |id|parent_id|. I need to find the maximum depth of this tree. I need to do this in Ruby, but pseudo code can help me too.

Answer 1

Assuming that {id, parent_id} pairs are in a dictionary/map, you can find max depth using memoization technique:

Main function (pseudocode):

Map tree; // <<=== This is your tree; id is the key; parent_id is the value
Map depth; // This map is used for memoization
int max = -1;
foreach pair in tree
    max = Max(memoized_depth(id, tree, depth), max)

Recursive depth function:

int memoized_depth(id, tree, depth)
    if (depth.containsKey(id)) return depth[id];
    if (!tree.contains(id)) return 0; // no parent means it's a root
    int res = memoized_depth(tree[id] // parent, tree, depth) + 1;
    depth[id] = res;
    return res;