Given a range [n, m], the task is to find the number of elements that have even number of factors in the given range (n and m inclusive).
Examples :
Input: n = 5, m = 20 Output: 14 The numbers with even factors are 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20. Input: n = 5, m = 100 Output: 88
A Simple Solution is to loop through all numbers starting from n. For every number, check if it has an even number of factors. If it has an even number of factors then increment count of such numbers and finally print the number of such elements. To find all divisors of a natural number efficiently, refer All divisors of a natural number
An Efficient Solution is to find the numbers with odd number of factors i.e only the perfect squares have odd number of factors, so all numbers other than perfect squares will have even number of factors. So, find the count of perfect squares in the range and subtract from the total numbers i.e. m-n+1 .
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach#include <bits/stdc++.h>using namespace std;// Function to count the perfect squaresint countOddSquares(int n, int m){ return (int)pow(m, 0.5) - (int)pow(n - 1, 0.5);}// Driver codeint main(){ int n = 5, m = 100; cout << "Count is " << (m - n + 1) - countOddSquares(n, m); return 0;} |
Java
// Java implementation of the above approachimport java.io.*;class GFG { // Function to count the perfect squaresstatic int countOddSquares(int n, int m){ return (int)Math.pow(m, 0.5) - (int)Math.pow(n - 1, 0.5);}// Driver codepublic static void main (String[] args){ int n = 5, m = 100; System.out.println("Count is " + ((m - n + 1) - countOddSquares(n, m)));}}// This code is contributed by ajit.. |
Python 3
# Python3 implementation of the# above approach # Function to count the perfect squares def countOddSquares(n, m) : return (int(pow(m, 0.5)) - int(pow(n - 1, 0.5))) # Driver code if __name__ == "__main__" : n = 5 ; m = 100; print("Count is", (m - n + 1) - countOddSquares(n, m)) # This code is contributed by Ryuga |
C#
// C# implementation of the above approachusing System;class GFG{ // Function to count the perfect squaresstatic int countOddSquares(int n, int m){ return (int)Math.Pow(m, 0.5) - (int)Math.Pow(n - 1, 0.5);}// Driver codestatic public void Main (){ int n = 5, m = 100; Console.WriteLine("Count is " + ((m - n + 1) - countOddSquares(n, m)));}}// This Code is contributed by akt_mit. |
PHP
<?php// PHP implementation of the // above approach// Function to count the perfect squaresfunction countOddSquares($n, $m){ return (int)pow($m, 0.5) - (int)pow($n - 1, 0.5);}// Driver code$n = 5;$m = 100;echo "Count is ", ($m - $n + 1) - countOddSquares($n, $m); // This code is contributed by ajit?> |
Javascript
<script>// Javascript implementation of the above approach// Function to count the perfect squaresfunction countOddSquares(n, m){ return Math.pow(m,0.5) - Math.pow(n - 1, 0.5);}// Driver codevar n = 5, m = 100;document.write( "Count is " + ((m - n + 1) - countOddSquares(n, m)));</script> |
Count is 88
Time Complexity: O(1)
Auxiliary Space: O(1)
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