Formatted question description: https://leetcode.ca/all/1952.html

1952. Three Divisors

Level

Easy

Description

Given an integer n, return true if n has exactly three positive divisors. Otherwise, return false.

An integer m is a divisor of n if there exists an integer k such that n = k * m.

Example 1:

Input: n = 2

Output: false

Explantion: 2 has only two divisors: 1 and 2.

Example 2:

Input: n = 4

Output: true

Explantion: 4 has three divisors: 1, 2, and 4.

Constraints:

  • 1 <= n <= 10^4

Solution

If n has three divisors, then n must be a perfect square number. Calculate the square root of n, and loop over all integers from 1 to the square root minus 1. For each i such that n is divisible by i, add 2 to the number of divisors. The final divisor is the square root of n. Return true if the number of divisors equals 3.

  • class Solution {
        public boolean isThree(int n) {
            int sqrt = (int) Math.sqrt(n);
            if (sqrt * sqrt != n)
                return false;
            int divisors = 1;
            for (int i = 1; i < sqrt; i++) {
                if (n % i == 0)
                    divisors += 2;
            }
            return divisors == 3;
        }
    }
    
  • // OJ: https://leetcode.com/problems/three-divisors/
    // Time: O(N)
    // Space: O(1)
    class Solution {
    public:
        bool isThree(int n) {
            int ans = 0;
            for (int i = 1; i <= n && ans <= 3; ++i) {
                if (n % i == 0) ++ans;
            }
            return ans == 3;
        }
    };
    
  • # 1952. Three Divisors
    # https://leetcode.com/problems/three-divisors/
    
    class Solution:
        def isThree(self, n: int) -> bool:
            res = 0
            
            for k in range(1, n + 1):
                if n % k == 0: res += 1
                
                if res > 3: return False
            
            return res == 3
    
    

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