Given a positive integer n(1 <= n <= 1018). Check whether a number has exactly three distinct factors or not. Print “Yes” if it has otherwise “No“.
Input : 9 Output: Yes Explanation Number 9 has exactly three factors: 1, 3, 9, hence answer is 'Yes' Input : 10 Output : No
Simple approach is to count factors by generating all divisors of a number by using this approach, after that check whether the count of all factors are equal to ‘3’ or not. Time complexity of this approach is O(sqrt(n)).
Better approach is to use Number theory. According to property of perfect square, “Every perfect square(x2) always have only odd numbers of factors“.
If the square root of given number(say x2) is prime(after conforming that number is perfect square) then it must have exactly three distinct factors i.e.,
- A number 1 of course.
- Square root of a number i.e., x(prime number).
- Number itself i.e., x2.
Below is the implementation of above approach:
Yes No No
Time complexity : O(n1/4)
Auxiliary space: O(1)
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