Binomial Heap Tree Orders

Problem

Insert n nodes one at a time into a binomial heap. The heap contains one binomial tree for each set bit of n, whose order equals the bit position. Return [tree_count, orders] with orders listed from largest to smallest, or [0, []] for n = 0.

Hint

Merging equal-order trees is binary carry, so the tree orders are exactly the set bits of n.

Test cases

case 1

in: [13]

expected: [3,[3,2,0]]

case 2

in: [7]

expected: [3,[2,1,0]]

case 3

in: [1]

expected: [1,[0]]

case 4

in: [0]

expected: [0,[]]

case 5

in: [64]

expected: [1,[6]]

Starter codePython

def binomial_heap_orders(n):
    # Your code here
    pass

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