Given a number N. The task is to count total numbers under N which are both perfect square and cube of some integers.
Input: N = 100 Output: 2 They are 1 and 64. Input: N = 100000 Output: 6
Approach: For a given positive number N to be a perfect square, it must satisfy P2 = N Similarly, Q3 = N for a perfect cube where P and Q are some positive integers.
N = P2 = Q3
Thus, if N is a 6th power, then this would certainly work. Say N = A6 which can be written as (A3)2 or (A2)3.
So, pick 6th power of every positive integers which are less than equal to N.
Below is the implementation of the above approach:
- Count all triplets whose sum is equal to a perfect cube
- Count of pairs in an array whose sum is a perfect square
- Permutation of numbers such that sum of two consecutive numbers is a perfect square
- Perfect cube greater than a given number
- Largest perfect cube number in an Array
- Largest number in an array that is not a perfect cube
- Smallest perfect Cube divisible by all elements of an array
- Check if a number is perfect square without finding square root
- Perfect Square String
- Closest perfect square and its distance
- Largest number that is not a perfect square
- Check if given number is perfect square
- Largest factor of a given number which is a perfect square
- Find the Next perfect square greater than a given number
- Check perfect square using addition/subtraction
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