Calculate the max difference between nodes in a binary tree

Question

Is there a way to calculate the max difference between node values without storing in a list? I was hoping to do it in 1 pass, but it doesn't seem possible. This was from a codility interview question to calculate the amplitude of the binary tree defined as the max absolute difference of the nodes.

        def max_diff(nodes):
            return abs(max(nodes) - min(nodes))

        def amplitude(T):
            nodes = []
            def calc_amplitude(T, nodes):

                if not isinstance(T, tuple):
                    if not isinstance(T, int):
                        return 0
                    nodes.append(T)
                    return T
                else:
                    [calc_amplitude(t, nodes) for t in T]
                    return max_diff(nodes)
            return calc_amplitude(T, nodes)

        tree = (5, (8, (12, None, None), (2, None, None)),(9, (7, (1, None, None), None), (4, (3, None, None), None)))

        print amplitude(tree)

Is the amplitude the maximum difference between all nodes in the tree or maximum difference between two nodes on any path from root to leaf? See http://siyang2notleetcode.blogspot.my/2015/02/amplitude-of-tree.html for explanation — niemmi, May 08 '16 at 11:36
thx - I guess that shows the approach - I also see that I am not respecting the node path validity. It's funny that the codesays solution was requested to be removed from codility. — Michael T, May 08 '16 at 11:45

niemmi · Accepted Answer · 2016-05-08T12:18:16.953

In case that you want to know the maximum difference between two nodes on any path from root to leaf you can use following code:

def amplitude(tree, cur_min=None, cur_max=None):
    if tree is None:
        if cur_min is None:
            return 0
        else:
            return cur_max - cur_min

    if cur_min is None:
        cur_min = cur_max = tree[0]
    else:
        cur_min = min(cur_min, tree[0])
        cur_max = max(cur_max, tree[0])

    return max(amplitude(tree[1], cur_min, cur_max),
               amplitude(tree[2], cur_min, cur_max))

It will track minimum and maximum value on each path. Once it reaches the leaf it will simply return the difference between those two thus stopping the recursion. For non-leaf nodes it will first update minimum and maximum value. Then it recurses to both children and returns the maximum value between the two results.

Calculate the max difference between nodes in a binary tree

1 Answers1