Program to compute Log n

Write a one line C function that calculates and returns \log_2 n. For example, if n = 64, then your function should return 6, and if n = 129, then your function should return 7.

Using Recursion




C

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// C program to find log(n) using Recursion
#include <stdio.h>
  
unsigned int Log2n(unsigned int n)
{
    return (n > 1) ? 1 + Log2n(n / 2) : 0;
}
  
int main()
{
    unsigned int n = 32;
    printf("%u", Log2n(n));
    getchar();
    return 0;
}

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Java

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// Java program to find log(n)
// using Recursion
class Gfg1 
{
  
    static int Log2n(int n)
    {
        return (n > 1) ? 1 + Log2n(n / 2) : 0;
    }
      
    // Driver Code
    public static void main(String args[])
    {
        int n = 32;
        System.out.println(Log2n(n));
    }
}
  
// This code is contributed by Niraj_Pandey

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Python3

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# Python 3 program to
# find log(n) using Recursion
  
def Log2n(n):
  
    return 1 + Log2n(n / 2) if (n > 1) else 0
  
# Driver code
n = 32
print(Log2n(n))
  
# This code is contributed by
# Smitha Dinesh Semwal

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C#

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// C# program to find log(n)
// using Recursion
using System;
  
class GFG {
  
    static int Log2n(int n)
    {
        return (n > 1) ? 1 + 
            Log2n(n / 2) : 0;
    }
      
    // Driver Code
    public static void Main()
    {
        int n = 32;
          
        Console.Write(Log2n(n));
    }
}
  
// This code is contributed by
// nitin mittal.

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Output :

5

Time complexity: O(log n)
Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1)

Using inbuilt log function


We can use the inbuilt function of standard library which is available in library.

C

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// C program to find log(n) using Inbuilt
// function of <math.h> library
#include <math.h>
#include <stdio.h>
int main()
{
    unsigned int n = 32;
    printf("%d", (int)log2(n));
    return 0;
}

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Java

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// Java program to find log(n) using Inbuilt
// function of java.util.Math library
import java.util.*;
  
class Gfg2 
{
    public static void main(String args[])
    {
        int n = 32;
        System.out.println((int)(Math.log(n) / Math.log(2)));
    }
}
  
// This code is contributed by Niraj_Pandey

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Output :

5

Time complexity: O(1)
Auxiliary space: O(1)

Let us try an extended version of the problem.

Write a one line function Logn(n, r) which returns \lfloor\log_r n\rfloor.



Using Recursion


C

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// C program to find log(n) on arbitrary base using Recursion
#include <stdio.h>
  
unsigned int Logn(unsigned int n, unsigned int r)
{
    return (n > r - 1) ? 1 + Logn(n / r, r) : 0;
}
  
int main()
{
    unsigned int n = 256;
    unsigned int r = 3;
    printf("%u", Logn(n, r));
    return 0;
}

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Java

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// Java program to find log(n) on
// arbitrary base using Recursion
class Gfg3 
{
    static int Logn(int n, int r)
    {
        return (n > r - 1) ? 1 + Logn(n / r, r) : 0;
    }
      
    // Driver Code
    public static void main(String args[])
    {
        int n = 256;
        int r = 3;
        System.out.println(Logn(n, r));
    }
}
  
// This code is contributed by Niraj_Pandey

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Output :

5

Time complexity: O(log n)
Auxiliary space: O(log n) if the stack size is considered during recursion otherwise O(1)

Using inbuilt log function


We only need to use logarithm property to find the value of log(n) on arbitrary base r. i.e., \log_r n = \dfrac{log_k (n)}{\log_k (r)} where k can be any anything, which for standard log functions are either e or 10

C

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// C program to find log(n) on arbitrary base
// using log() function of maths library
#include <math.h>
#include <stdio.h>
  
unsigned int Logn(unsigned int n, unsigned int r)
{
    return log(n) / log(r);
}
  
int main()
{
    unsigned int n = 256;
    unsigned int r = 3;
    printf("%u", Logn(n, r));
  
    return 0;
}

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Java

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// Java program to find log(n) on arbitrary base
// using log() function of java.util.Math library
import java.util.*;
  
class Gfg4 {
  
    public static void main(String args[])
    {
        int n = 256;
        int r = 3;
        System.out.println((int)(Math.log(n) / Math.log(r)));
    }
}
  
// This code is contributed by Niraj_Pandey

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Output :

5

Time complexity: O(1)
Auxiliary space: O(1)
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Improved By : Niraj_Pandey, nitin mittal

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