bitwise_binary_search_cost.py

import math

for n in range(1, 65):
    valid = [
        (l, r)
        for l in range(10 + math.ceil(math.log2(n + 1)))
        for r in range(10 + math.ceil(math.log2(n + 1)))
        if 2**l - 1 <= n and 2**r - 1 <= n and 2**l + 2**r - 1 >= n
    ]
    
    cost = lambda l, r: 2**l * l + (n + 1 - 2**l) * r
    minimal = min(cost(l, r) for l, r in valid)
    for l, r in valid:
        if cost(l, r) == minimal:
            print(f"{n:2} {l:2} {r:2}")