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utiles.py
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utiles.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Mar 9 10:50:20 2017
@author: Refaia
"""
import time
import math
import itertools
def continuedFractionListLen(num) :
R = math.floor(math.sqrt(num))
if R * R == num :
return 0
a = R
P = 0
Q = 1
P = a * Q - P
Q = (num - P * P) // Q
a = (R + P) // Q
counter = 1
while Q != 1 :
P = a * Q - P
Q = (num - P * P) // Q
a = (R + P) // Q
counter += 1
return counter
def continuedFractionList (num) :
R = math.floor(math.sqrt(num))
L = [R, []]
if R * R == num :
return L
a = R
P = 0
Q = 1
P = a * Q - P
Q = (num - P * P) // Q
a = (R + P) // Q
L[1].append(a)
while Q != 1 :
P = a * Q - P
Q = (num - P * P) // Q
a = (R + P) // Q
L[1].append(a)
return L
def pythagoreanTriplets(limitP) :
delta = time.time()
a, b, c = 0, 0, 0
m = 2
L = []
for m in range(2, math.floor(math.sqrt(limitP))):
for n in range(1, m) :
if (math.gcd(n, m) == 1) and (n % 2 == 0 or m % 2 == 0) :
a = (m * m - n * n)
b = (2 * m * n)
c = (m * m + n * n)
if a + b + c > limitP :
break
L.append((a, b, c))
delta = time.time() - delta
return L, delta
def gcdBinary(u, v):
if u == 0: return v
if v == 0: return u
u = abs(u)
v = abs(v)
k = 1
while u & 1 == 0 and v & 1 == 0:
k <<= 1
u >>= 1
v >>= 1
while u & 1 == 0:
u >>= 1
while v & 1 == 0:
v >>= 1
while v != 0:
if u > v:
u, v = v, u
v = v - u
return u*k
def gcd(a, b):
while b != 0 :
a, b = b, a % b
return a
def powExp(x, n) :
result = 1
while n >= 1 :
if n % 2 != 0 :
result *= x
x *= x
n //= 2
return result
def isPrime(n) :
if n <= 1 :
return False
if n <= 3 :
return True
if n % 2 == 0 or n % 3 == 0 :
return False
i = 5
while i * i <= n :
if n % i == 0 or n % (i + 2) == 0 :
return False
i += 6
return True
def primeBelow(n):
if n < 2:
return 0
primeList = []
listNum = [2] + [i for i in range(3, n + 1, 2)]
for i in range(1, int(math.sqrt(n)) + 1, 1):
if listNum[i] :
for j in range(i + listNum[i], len(listNum), listNum[i]):
listNum[j] = 0
for prime in listNum :
if prime :
primeList.append(prime)
return primeList
def primeFactors(n):
i = 2
factors = set()
if isPrime(n) :
factors.add(n)
else :
while i * i <= n:
if n % i != 0:
i += 1
else:
n //= i
factors.add(i)
if n > 1:
factors.add(n)
return factors
def eulerTotient(n) :
result = n
for prime in primeFactors(n) :
result *= (1 - (1 / prime))
return int(result)
def triangle(n):
return (n**2 + n) // 2
def pentagonal(n) :
return (3 * n**2 - n) // 2
def hexagonal(n) :
return (2 * n**2) - n
def binarySearch(n, L) :
upperBound = len(L) - 1
lowerBound = 0
found = False
if n > L[upperBound] or n < L[lowerBound] :
return False
while not found and upperBound >= lowerBound :
valueMid = L[(upperBound + lowerBound) // 2]
if n == valueMid :
found = True
elif n > valueMid :
lowerBound = ((upperBound + lowerBound) // 2) + 1
else :
upperBound = ((upperBound + lowerBound) // 2) - 1
return found