Power Under a Maximum | Dataford Interview Questions

Your question is Power Under a Maximum. Start with the requirements on the right.

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Problem

A Veeam Backup & Replication policy may need to determine the largest growth exponent that keeps a calculated value within a configured limit. Given positive integers maxVal and a, return the largest non-negative integer b such that a^b <= maxVal.

Use integer arithmetic only. Do not rely on floating-point logarithms, because rounding can produce an incorrect exponent near an exact power.

Formal Specification

Implement biggest_power_exponent(maxVal, a):

Input: integers maxVal and a
Output: the largest integer b >= 0 satisfying a^b <= maxVal
The input guarantees a >= 2 and maxVal >= 1

You should avoid computing unnecessarily large powers. A suitable solution first finds an upper bound for b, then uses binary search with overflow-safe, capped exponentiation.

Constraints

1 <= maxVal <= 10^18
2 <= a <= 10^9
The returned exponent must be a non-negative integer
Use integer arithmetic, not floating-point logarithms

Function Signature

def biggest_power_exponent(maxVal, a):