D-ary Heap Height

Problem

A complete d-ary heap with n nodes has height h, the smallest integer such that 1 + d + ... + d^h >= n. Return the height in edges for n >= 0 and d >= 2; the height is 0 when n <= 1.

Hint

Level k of a complete d-ary tree holds d^k nodes, so add powers of d until the capacity reaches n.

Test cases

case 1

in: [10,2]

expected: 3

case 2

in: [9,3]

expected: 2

case 3

in: [1,2]

expected: 0

case 4

in: [0,5]

expected: 0

case 5

in: [8,2]

expected: 3

Starter codePython

def dary_heap_height(n, d):
    # Your code here
    pass

5 test cases · run your code against them in the editor