Problem
Repeatedly divide n by 2, dropping any remainder (integer division), until it becomes 1. Count how many divisions that takes.
Implement halve_until_one(n).
Input
n: A positive integer.
Output
Return the number of divisions.
Constraints
1 ≤ n ≤ 1,000,000,000,000
Examples
Example 1
Input:
n = 20
Expected output:
expected = 4Input:
long long n = 20;
Expected output:
long long expected = 4;Input:
long n = 20;
Expected output:
long expected = 4;Explanation
20 → 10 → 5 → 2 → 1 takes 4 divisions.
Example 2
Input:
n = 1
Expected output:
expected = 0Input:
long long n = 1;
Expected output:
long long expected = 0;Input:
long n = 1;
Expected output:
long expected = 0;Explanation
n is already 1, so no divisions are needed.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Count how many times you can shrink the number by dividing by two before it becomes one.
Hint 2
Repeated integer division is enough here; no need to track the discarded remainders.
Hint 3
Make sure you stop exactly when the value reaches one, not when it becomes zero.
Expected complexity
O(log n) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.