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factorial3ArrayBase.py
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factorial3ArrayBase.py
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from math import log2
from sys import setrecursionlimit
from time import time
from matplotlib import pyplot as plt
def movingaverage(arr,win):
b = []
for k in range(int(win/2)): b.append(arr[k])
for k in range(int(win/2),len(arr)-int(win/2)):
s = 0
for l in range(k-int(win/2),k+int(win/2)):
s = s + arr[l]
b.append(s/win)
for k in range(len(arr)-int(win/2),len(arr)): b.append(arr[k])
return b
def karatsuba_Algo(a,b):
n1 = int(log2(a)+1) if a!=0 else 1
n2 = int(log2(b)+1) if b!=0 else 1
n = n1 if n1>n2 else n2
if n == 1: return a*b
m = int(n/2)
x0, x1 = int(a/(2**m)), a%(2**m)
y0, y1 = int(b/(2**m)), b%(2**m)
z0 = karatsuba_Algo(x0,y0)
z1temp = karatsuba_Algo(x0+x1,y0+y1)
z2 = karatsuba_Algo(x1,y1)
z1 = z1temp - z0 - z2
return z0*(2**(2*m))+z1*(2**m)+z2
def fact(n):
if n == 0: return 1
else: return n*fact(n-1)
def modifiedFactorial(n):
if n == 0: return 1
else: return karatsuba_Algo(n,modifiedFactorial(n-1))
#setrecursionlimit(998)
N = 60
A = [0 for i in range(60)]
B = [0 for i in range(60)]
for k in range(len(A)):
start = time()
fact(k)
end = time()
A[k] = end-start
print("Number",k,"actual fact done")
start = time()
modifiedFactorial(k)
end = time()
B[k] = end-start
print("Number",k,"modified fact done")
A = movingaverage(A,int(N/3))
B = movingaverage(B,int(N/3))
plt.plot(A,'b')
plt.plot(B,'r')
plt.show()