Related Articles

Related Articles

Elias Gamma Encoding in Python
  • Last Updated : 26 Mar, 2020

The Elias gamma code is a universal code that is used to encode a sequence of positive integers. It is developed by Peter Elias. It is most useful when the upper-bound of integers cannot be determined beforehand.

Steps in Encoding:

To encode a number X,

  • Find the largest N, with
    2^{N}\leq X(greater power of 2).

  • Encode N using Unary coding(i.e N zeroes followed by a one).
  • Append the integer (X-2^{N}) using N digits in Binary.

Example: Let’s consider an example whwre we want to encode 10,
We can represent 10 as:
10=2^{3} + 2.
Step1: Here, largest N = 3
Step2: N(=3) in Unary followed by a one = 0001
Step3: Now Representation of 2 in Binary using N(=3) digits = 010
So, Elias gamma encoding of 10 = 0001010

Below is the implementation of the above approach.



filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation
from math import log
  
log2 = lambda x: log(x, 2)
  
def Unary(x):
    return (x-1)*'0'+'1'
  
def Binary(x, l = 1):
    s = '{0:0%db}' % l
    return s.format(x)
      
def Elias_Gamma(x):
    if(x == 0): 
        return '0'
  
    n = 1 + int(log2(x))
    b = x - 2**(int(log2(x)))
  
    l = int(log2(x))
  
    return Unary(n) + Binary(b, l)
      
print(Elias_Gamma(10))

chevron_right


Output:

0001010

Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course.

My Personal Notes arrow_drop_up
Recommended Articles
Page :