1492. The kth Factor of n

1492. The kth Factor of n (Medium)

Given two positive integers n and k.

A factor of an integer n is defined as an integer i where n % i == 0.

Consider a list of all factors of n sorted in ascending order, return the kth factor in this list or return -1 if n has less than k factors.

 

Example 1:

Input: n = 12, k = 3
Output: 3
Explanation: Factors list is [1, 2, 3, 4, 6, 12], the 3rd factor is 3.

Example 2:

Input: n = 7, k = 2
Output: 7
Explanation: Factors list is [1, 7], the 2nd factor is 7.

Example 3:

Input: n = 4, k = 4
Output: -1
Explanation: Factors list is [1, 2, 4], there is only 3 factors. We should return -1.

Example 4:

Input: n = 1, k = 1
Output: 1
Explanation: Factors list is [1], the 1st factor is 1.

Example 5:

Input: n = 1000, k = 3
Output: 4
Explanation: Factors list is [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000].

 

Constraints:

• 1 <= k <= n <= 1000

Related Topics:
Math

Solution 1.

// OJ: https://leetcode.com/problems/the-kth-factor-of-n/
// Author: github.com/lzl124631x
// Time: O(sqrt(N))
// Space: O(1)
class Solution {
public:
    int kthFactor(int n, int k) {
        int i = 1;
        for (; i * i <= n; ++i) {
            if (n % i) continue;
            if (--k == 0) return i;
        }
        --i;
        if (i * i == n) --i;
        for (; i >= 1; --i) {
            if (n % i) continue;
            if (--k == 0) return n / i;
        }
        return -1;
    }
};