123 lines
2.3 KiB
Python
123 lines
2.3 KiB
Python
#!/usr/bin/python3
|
|
|
|
from math import sqrt, floor, gcd
|
|
|
|
from numpy import ndarray, zeros
|
|
|
|
def is_prime(num):
|
|
if num < 4:
|
|
return num == 2 or num == 3
|
|
|
|
if num % 2 == 0 or num % 3 == 0:
|
|
return False
|
|
|
|
limit = floor(sqrt(num)) + 1
|
|
|
|
for i in range(5, limit, 6):
|
|
if num % i == 0 or num % (i + 2) == 0:
|
|
return False
|
|
|
|
return True
|
|
|
|
def is_palindrome(num, base):
|
|
reverse = 0
|
|
|
|
tmp = num
|
|
|
|
while tmp > 0:
|
|
reverse = reverse * base
|
|
reverse = reverse + tmp % base
|
|
tmp = tmp // base
|
|
|
|
if num == reverse:
|
|
return True
|
|
|
|
return False
|
|
|
|
def lcm(a, b):
|
|
return a * b // gcd(a, b)
|
|
|
|
def lcmm(values, n):
|
|
if n == 2:
|
|
return lcm(values[0], values[1])
|
|
|
|
value = values[0]
|
|
|
|
for i in range(1, n):
|
|
return lcm(value, lcmm(values[i:], n-1))
|
|
|
|
def sieve(n):
|
|
primes = ndarray((n,), int)
|
|
|
|
primes[0] = 0
|
|
primes[1] = 0
|
|
primes[2] = 1
|
|
primes[3] = 1
|
|
|
|
for i in range(4, n -1, 2):
|
|
primes[i] = 0
|
|
primes[i+1] = 1
|
|
|
|
limit = floor(sqrt(n))
|
|
|
|
for i in range(3, limit, 2):
|
|
if primes[i] == 1:
|
|
for j in range(i * i, n, 2 * i):
|
|
primes[j] = 0
|
|
|
|
return primes
|
|
|
|
def count_divisors(n):
|
|
count = 0
|
|
limit = floor(sqrt(n))
|
|
|
|
for i in range(1, limit):
|
|
if n % i == 0:
|
|
count = count + 2
|
|
|
|
if n == limit * limit:
|
|
count = count - 1
|
|
|
|
return count
|
|
|
|
def find_max_path(triang, n):
|
|
for i in range(n-2, -1, -1):
|
|
for j in range(0, i+1):
|
|
if triang[i+1][j] > triang[i+1][j+1]:
|
|
triang[i][j] = triang[i][j] + triang[i+1][j]
|
|
else:
|
|
triang[i][j] = triang[i][j] + triang[i+1][j+1]
|
|
|
|
return triang[0][0]
|
|
|
|
def is_pandigital(value, n):
|
|
i = 0
|
|
digits = zeros(n + 1, int)
|
|
|
|
while i < n and value > 0:
|
|
digit = value % 10
|
|
if digit > n:
|
|
return False
|
|
digits[digit] = digits[digit] + 1
|
|
value = value // 10
|
|
i = i + 1
|
|
|
|
if i < n or value > 0:
|
|
return False
|
|
|
|
if digits[0] != 0:
|
|
return False
|
|
|
|
for i in range(1, n+1):
|
|
if digits[i] != 1:
|
|
return False
|
|
i = i + 1
|
|
|
|
return True
|
|
|
|
def is_pentagonal(n):
|
|
i = (sqrt(24*n+1) + 1) / 6
|
|
|
|
return i.is_integer()
|
|
|