Closest Divisors

Description

Given an integer num, find the closest two integers in absolute difference whose product equals num + 1 or num + 2.

Return the two integers in any order.

 

Example 1:

Input: num = 8
Output: [3,3]
Explanation: For num + 1 = 9, the closest divisors are 3 & 3, for num + 2 = 10, the closest divisors are 2 & 5, hence 3 & 3 is chosen.

Example 2:

Input: num = 123
Output: [5,25]

Example 3:

Input: num = 999
Output: [40,25]

 

Constraints:

• 1 <= num <= 10^9

Solution(javascript)

/**
 * @param {number} num
 * @return {number[]}
 */
const closestDivisors = function (num) {
  const diff = (x) => {
    let right = Math.floor(Math.sqrt(x))
    while (right >= 1) {
      const divisor = Math.floor(x / right)
      if (right * divisor === x) {
        return [divisor, right]
      }
      right--
    }
    return [1, x]
  }
  const [a, b] = diff(num + 1)
  const [c, d] = diff(num + 2)
  return Math.abs(b - a) <= Math.abs(c - d) ? [a, b] : [c, d]
}