Skip to content
Related Articles

Related Articles

Improve Article

Iterated Logarithm log*(n)

  • Difficulty Level : Medium
  • Last Updated : 26 Apr, 2021

Iterated Logarithm or Log*(n) is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.
 

\log ^{*}n:={\begin{cases}0}n\leq 1;\\1+\log ^{*}(\log n)}n>1\end{cases}}}
 

Applications: It is used in analysis of algorithms (Refer Wiki for details)

 

C++




// Recursive CPP program to find value of
// Iterated Logarithm
#include <bits/stdc++.h>
using namespace std;
 
int _log(double x, double base)
{
    return (int)(log(x) / log(base));
}
 
double recursiveLogStar(double n, double b)
{
    if (n > 1.0)
        return 1.0 + recursiveLogStar(_log(n, b), b);
    else
        return 0;
}
 
// Driver code
int main()
{
    int n = 100, base = 5;
    cout << "Log*(" << n << ") = "
         << recursiveLogStar(n, base) << "\n";
    return 0;
}

Java




// Recursive Java program to
// find value of Iterated Logarithm
import java.io.*;
 
class GFG
{
static int _log(double x,
                double base)
{
    return (int)(Math.log(x) /
                 Math.log(base));
}
 
static double recursiveLogStar(double n,
                               double b)
{
    if (n > 1.0)
        return 1.0 +
               recursiveLogStar(_log(n,
                                 b), b);
    else
        return 0;
}
 
// Driver code
public static void main (String[] args)
{
    int n = 100, base = 5;
    System.out.println("Log*(" + n + ") = " +
                  recursiveLogStar(n, base));
}
}
 
// This code is contributed by jit_t

Python3




# Recursive Python3 program to find value of
# Iterated Logarithm
import math
 
def _log(x, base):
 
    return (int)(math.log(x) / math.log(base))
 
def recursiveLogStar(n, b):
 
    if(n > 1.0):
        return 1.0 + recursiveLogStar(_log(n, b), b)
    else:
        return 0
 
 
# Driver code
if __name__=='__main__':
    n = 100
    base = 5
    print("Log*(", n, ") = ", recursiveLogStar(n, base))
 
# This code is contributed by
# Sanjit_Prasad

C#




// Recursive C# program to
// find value of Iterated Logarithm
 
using System;
 
public class GFG{
static int _log(double x, double baset)
{
    return (int)(Math.Log(x) /
                Math.Log(baset));
}
 
static double recursiveLogStar(double n,
                            double b)
{
    if (n > 1.0)
        return 1.0 +
            recursiveLogStar(_log(n,
                                b), b);
    else
        return 0;
}
 
// Driver code
    static public void Main (){
     
    int n = 100, baset = 5;
    Console.WriteLine("Log*(" + n + ") = " +
                recursiveLogStar(n, baset));
}
}
 
// This code is contributed by ajit.

PHP




<?php
// Recursive PhP program to find
// value of Iterated Logarithm
 
function _log($x, $base)
{
    return (int)(log($x) / log($base));
}
 
function recursiveLogStar($n, $b)
{
    if ($n > 1.0)
        return 1.0 +
               recursiveLogStar(_log($n,
                               $b), $b);
    else
        return 0;
}
 
// Driver code
$n = 100; $base = 5;
echo "Log*(" , $n , ")"," = ",
recursiveLogStar($n, $base), "\n";
 
// This code is contributed by ajit
?>

Javascript




<script>
 
// Javascript program to
// find value of Iterated Logarithm
 
    function _log( x, base)
{
    return (Math.log(x) /
                 Math.log(base));
}
  
function recursiveLogStar(n, b)
{
    if (n > 1.0)
        return 1.0 +
               recursiveLogStar(_log(n,
                                 b), b);
    else
        return 0;
}
     
// Driver code
 
    let n = 100, base = 5;
    document.write("Log*(" + n + ") = " +
                  recursiveLogStar(n, base));
     
    // This code is contributed by sanjoy_62.
</script>

Output : 



Log*(100) = 2

Iterative Implementation : 

C++




// Iterative CPP function to find value of
// Iterated Logarithm
int iterativeLogStar(double n, double b)
{
    int count = 0;
    while (n >= 1) {
        n = _log(n, b);
        count++;
    }
    return count;
}

Java




// Iterative Java function to find value of
// Iterated Logarithm
public static int iterativeLogStar(double n, double b)
{
    int count = 0;
    while (n >= 1) {
        n = _log(n, b);
        count++;
    }
    return count;
}
 
// This code is contributed by pratham76

Python3




# Iterative Python function to find value of
# Iterated Logarithm
 
 
def iterativeLogStar(n, b):
 
    count = 0
    while(n >= 1):
        n = _log(n, b)
        count = count + 1
 
    return count
 
# This code is contributed by
# Sanjit_Prasad

C#




// Iterative C# function to find value of
// Iterated Logarithm
static int iterativeLogStar(double n, double b)
{
    int count = 0;
    while (n >= 1)
    {
        n = _log(n, b);
        count++;
    }
    return count;
}
 
// This code is contributed by rutvik_56

This article is contributed by Abhishek rajput. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :