Given an integer N, the task is to find the integer part of the geometric mean of the divisors of N. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers), and so on.
Examples:
Input: N = 4
Output: 2
Divisors of 4 are 1, 2 and 4
Geometric mean = (1 * 2 * 4)(1/3) = 8(1/3) = 2
Input: N = 16
Output: 8
Divisors of 16 are 1, 2, 4, 8 and 16
Geometric mean = (1 * 2 * 4 * 8 * 16)(1/5) = 1024(1/5) = 4
Approach: It can be observed that a series will be formed for the values of N as 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, ….. whose Nth term is ??n?.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to return the integer// part of the geometric mean// of the divisors of nint geometricMean(int n){ return sqrt(n);}// Driver codeint main(){ int n = 16; cout << geometricMean(n); return 0;} |
Java
// Java implementation of the approachclass GFG {// Function to return the integer// part of the geometric mean// of the divisors of nstatic int geometricMean(int n){ return (int) Math.sqrt(n);}// Driver codepublic static void main(String []args){ int n = 16; System.out.println(geometricMean(n));}}// This code is contributed by Rajput-Ji |
Python3
# Python3 implementation of the approach from math import sqrt# Function to return the integer # part of the geometric mean # of the divisors of n def geometricMean(n) : return int(sqrt(n)); # Driver code if __name__ == "__main__" : n = 16; print(geometricMean(n)); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approachusing System; class GFG { // Function to return the integer// part of the geometric mean// of the divisors of nstatic int geometricMean(int n){ return (int) Math.Sqrt(n);} // Driver codepublic static void Main(String []args){ int n = 16; Console.WriteLine(geometricMean(n));}}// This code is contributed by PrinciRaj1992 |
Javascript
<script>// Javascript implementation of the approach// Function to return the integer// part of the geometric mean// of the divisors of nfunction geometricMean(n){ return Math.sqrt(n);}// Driver codevar n = 16;document.write(geometricMean(n));</script> |
4
Time Complexity: O(logn) because using inbuilt sqrt function
Auxiliary Space: O(1)
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