Closest Divisors — LeetCode 1362 Python Solution

The problem

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

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.

Python solution

class Solution:
    def closestDivisors(self, num: int) -> List[int]:
        def f(x):
            for i in range(int(sqrt(x)), 0, -1):
                if x % i == 0:
                    return [i, x // i]

        a = f(num + 1)
        b = f(num + 2)
        return a if abs(a[0] - a[1]) < abs(b[0] - b[1]) else b

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1362. Closest Divisors is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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