Given a number n, we need to count square numbers smaller than or equal to n.
Input : n = 5 Output : Square Number : 2 Non-square numbers : 3 Explanation : Square numbers are 1 and 4. Non square numbers are 2, 3 and 5. Input : n = 10 Output : Square Number : 3 Non-square numbers : 7 Explanation : Square numbers are 1, 4 and 9. Non square numbers are 2, 3, 5, 6, 7, 8 and 10.
A simple solution is to traverse through all numbers from 1 to n and for every number check if n is perfect square or not.
An efficient solution is based on below formula.
Count of square numbers that are greater than 0 and smaller than or equal to n are floor(sqrt(n)) or ⌊√(n)⌋
Count of non-square numbers = n – ⌊√(n)⌋
Count of squares 3 Count of non-squares 7
- Count numbers upto N which are both perfect square and perfect cube
- Permutation of numbers such that sum of two consecutive numbers is a perfect square
- Sum of square of first n odd numbers
- Sum of square of first n even numbers
- Count of pairs in an array whose sum is a perfect square
- Sum of square-sums of first n natural numbers
- Program to print non square numbers
- Print n numbers such that their sum is a perfect square
- Find maximum N such that the sum of square of first N natural numbers is not more than X
- Count numbers < = N whose difference with the count of primes upto them is > = K
- Check if product of array containing prime numbers is a perfect square
- Count numbers which are divisible by all the numbers from 2 to 10
- Count numbers which can be constructed using two numbers
- Check if a number is perfect square without finding square root
- Count numbers that don't contain 3
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.