Golomb Coding Parameter

Problem

For a geometric source P(k) = (1 - p) * p^k, the optimal Golomb modulus m is the smallest integer with p^m <= 1/2, that is m = ceil(-1 / log2(p)), never below 1. Return that parameter for 0 < p < 1, and 1 when p <= 0 or p >= 1.

Hint

Pick m so that the geometric probability at m is about one half.

Test cases

case 1

in: [0.5]

expected: 1

case 2

in: [0.9]

expected: 7

case 3

in: [0.25]

expected: 1

case 4

in: [0.1]

expected: 1

case 5

in: [0.7]

expected: 2

Starter codePython

import math
def golomb_parameter(p):
    # Your code here
    pass

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