anivarth

def pairwise(x, N = 1):
    """
    Pair wise summation algorithm
    is a summaiton algorithm
    used to get accurate summation
    of the given lists"""
    if len(x) == 0:
        return 0
    if len(x) <= N:
        s = x[0]

anivarth

def KahanSum(l):
    """
    This function will find the sum
    of a given list without compromising
    on the accuracy"""
    summation = 0.0
    c = 0.0
    for i in l:
        y = i - c
        t = summation + y

anivarth

def gcd(u, v):
    """
    A non recursive function
    while takes two integers as input
    and returns the GCD of the numbers
    """
    # if u is 0, return v
    if u == 0: return v
    # if v is 0, return u
    if v == 0: return u

anivarth

# import the function
from fractions import gcd

# use it directly
print gcd(500, 5) #5

anivarth

def gcd(u, v):
    """ This function will calcluate
    GCD of given two numbers.
    If the input is negative, both the
    numbers are converted to positive
    before the calculation
    """
    if u == v:
        return u
    elif u == 0:

anivarth

def heap(a):
"""
This program will take any iterable object
as input and will give a generator object
as output which can be used with for 
loop to get all the permutations
"""
    n = len(a)
    c = [0]*n
    A = list(a)

anivarth

def heap_string(a):
""" 
This function will find different permutations of
a given string.  It was first proposed by B. R. Heap in 1963.
https://en.wikipedia.org/wiki/Heap%27s_algorithm
"""
    n = len(a)
    c = [0]*n
    yield a
    i = 1

anivarth

# http://radiusofcircle.blogspot.com

# time module
import time

# time at the start of program execution
start = time.time()

# 4 digit triangular numbers
tria = [n*(n+1)/2 for n in xrange(45, 141)]

anivarth

#  http://radiusofcircle.blogspot.com

# time, random, math modules
import time, random, math

# start of program
start = time.time()

# Sieve of Erotosthenes
# One of the best algorithm to generate prime numbers

anivarth

# http://radiusofcircle.blogspot.com

# time module
import time

# time at the start of program execution
start = time.time()


def check_english(ascii1, ascii2):