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)

Answer 1

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.