Count square and non-square numbers before n

Given a number n, we need to count square numbers smaller than or equal to n.

Examples :

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)⌋

C++

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// CPP program to count squares and
// non-squares before a number.
#include <bits/stdc++.h>
using namespace std;
  
void countSquaresNonSquares(int n)
{
    int sc = floor(sqrt(n));
    cout << "Count of squares " 
         << sc << endl;
    cout << "Count of non-squares " 
         << n - sc << endl;
}
  
// Driver Code
int main()
{
    int n = 10;
    countSquaresNonSquares(n);
    return 0;
}

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Java

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// Java program to count squares and
// non-squares before a number.
import java.io.*;
import java.math.*;
  
class GFG 
{
    static void countSquaresNonSquares(int n)
    {
        int sc = (int)(Math.floor(Math.sqrt(n)));
        System.out.println("Count of"
                     " squares " + sc);
        System.out.println("Count of"
                      " non-squares "
                            (n - sc) );
    }
  
    // Driver code
    public static void main(String args[])
    {
        int n = 10;
        countSquaresNonSquares(n);
    }
}
  
// This code is contributed 
// by Nikita Tiwari.

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Python3

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# Python 3 program to count 
# squares and non-squares
# before a number.
import math
  
def countSquaresNonSquares(n) :
    sc = (math.floor(math.sqrt(n)))
    print("Count of squares ", sc)
    print("Count of non-squares ", (n - sc) )
      
      
# Driver code
n = 10
countSquaresNonSquares(n)
  
# This code is contributed
# by Nikita Tiwari.

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C#

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// C# program to count squares and
// non-squares before a number.
using System;
  
class GFG
{
static void countSquaresNonSquares(int n)
{
    int sc = (int)Math.Sqrt(n);
    Console.WriteLine( "Count of "
                        "squares "
                               sc) ;
    Console.WriteLine("Count of "
                   "non-squares " +
                         (n - sc));
}
  
    // Driver Code
    static public void Main ()
    {
    int n = 10;
    countSquaresNonSquares(n);
    }
}
  
// This code is contributed by anuj_67.

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PHP

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<?php
// PHP program to count 
// squares and non-squares
// before a number.
  
// function to count squares
// and non-squares before a 
// number
function countSquaresNonSquares($n)
{
    $sc = floor(sqrt($n));
    echo("Count of squares "
                  $sc . "\n");
    echo("Count of non-squares "
                      ($n - $sc));
}
  
// Driver code
$n = 10;
countSquaresNonSquares($n);
  
// This code is contributed by Ajit.
?>

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Output :

Count of squares 3
Count of non-squares 7


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