Question

I’m trying to write code that returns the depth of the deepest leaf in a tree with arbitrary number of children per nodes, in Python, using DFS rather than BFS. It seeems I’m close, but the following code still has some bug that I can’t figure out (i.e. the returned depth is not correct). Any help?

A test tree would be simply: [[1,2,3],[4,5],[6],[7],[8],[],[],[],[]]

def max_depth_dfs(tree): # DOESN'T WORK

    max_depth, curr_depth, Q = 0,0, [0]
    visited = set()

    while Q != []:
        n = Q[0]
        more = [v for v in tree[n] if v not in visited]
        if not more:
            visited.add(n)
            curr_depth -= 1
            Q = Q[1:]
        else:
            curr_depth += 1

        max_depth = max(max_depth, curr_depth)
        Q = more + Q

    return max_depth

Answer 1

I found the bug!

if not more:
    visited.add(n)
    curr_depth -= 1
    Q = Q[1:]

When you visit the node 4, curr_depth is equal to 2. Node 4 has no children, so you decrease the curr_depth and curr_depth is equal to 1 now. However, the next node you will visit is node 5 and the depth of node 5 is 2 instead of 1. Therefore, curr_depth doesn’t record the correct depth of the node in the tree.

The following solution may be helpful.

def max_depth_dfs(tree):

    max_depth, curr_depth, Q = 0, 0, [0]
    visited = set()

    while Q != []:
        n = Q[0]

        max_depth = max(max_depth, curr_depth)

        if n in visited:
            curr_depth -= 1
            Q = Q[1:]
            continue

        #print n, curr_depth     #show the node and its depth in the tree

        visited.add(n)
        more = [v for v in tree[n]]
        if not more:
            Q = Q[1:]
        else:
            curr_depth += 1
            Q = more + Q

    return max_depth