Find the smallest divisor given a threshold

Array Binary Search

65.5% acceptance

Feb 25, 2026

3557

225

Given an array of integers nums and an integer threshold, we will choose a positive integer divisor, divide all the array by it, and sum the division's result. Find the smallest divisor such that the result mentioned above is less than or equal to threshold. Each result of the division is rounded to the nearest integer greater than or equal to that element. (For example: 7/3 = 3 and 10/2 = 5). The test cases are generated so that there will be an answer.

Solution

Rust

Time O(n log n)

Space O(1)

LeetCode

solution.rs

impl Solution {
  pub fn smallest_divisor(nums: Vec<i32>, threshold: i32) -> i32 {
    let mut lo = 1i32;
    let mut hi = *nums.iter().max().unwrap();
    while lo < hi {
      let mid = (lo + hi) / 2;
      let sum: i32 = nums.iter().map(|&x| (x + mid - 1) / mid).sum();
      if sum <= threshold {
        hi = mid;
      } else {
        lo = mid + 1;
      }
    }
    lo
  }
}