Given a number N, the task is to find distinct N numbers such that their product is a perfect cube.
Input: N = 3
Output: 1, 8, 27
Product of the output numbers = 1 * 8 * 27 = 216, which is the perfect cube of 6 (63 = 216)
Input: N = 2
Output: 1 8
Product of the output numbers = 1 * 8 = 8, which is the perfect cube of 2 (23 = 8)
Approach: The solution is based on the fact that
The product of the first ‘N’ Perfect Cube numbers is always a Perfect Cube.
So, the Perfect Cube of first N natural numbers will be printed as the output.
For N = 1 =>  Product is 1 and cube root of 1 is also 1 For N = 2 => [1, 8] Product is 8 and cube root of 8 is 2 For N = 3 => [1, 8, 27] Product is 216 and cube root of 216 is 6 and so on
Below is the implementation of the above approach:
1 8 27 64
- Time Complexity: As in the above approach, we are finding the Perfect Cube of N numbers, therefore it will take O(N) time.
- Auxiliary Space Complexity: As in the above approach, there are no extra space used; therefore the Auxiliary Space complexity will be O(1).
Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.