What is the time and space complexity of Find the Smallest Divisor Given a Threshold?

Time complexity: O(n log m) where m is max(nums). Space complexity: O(1).

Find the Smallest Divisor Given a Threshold

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Solution Guide: Find the Smallest Divisor Given a Threshold

Approach

For each candidate divisor, compute required sum of hours (ceil division). If the sum fits threshold, search smaller divisors; otherwise search larger.

Complexity Analysis

Time: O(n log m) where m is max(nums)
Space: O(1)

Pattern

Binary Search on Answer

Why It Works

If a divisor d is valid (sum <= threshold), every larger divisor is also valid. Monotonic feasibility allows binary search for the minimum valid d.

Updated Feb 2026