def prime_partitions(num):
"""Calculate a list of all prime partitions of num"""
parts = {}
parts[0] = set([()])
parts[1] = set([])
primes = sieve(num+1)
for n in range(2, num + 1):
parts[n] = set()
for p in itertools.takewhile(lambda x: x <= n, primes):
for pa in parts[n - p]:
parts[n].add(tuple(sorted(pa + (p,))))
return sorted(parts[num])
def test_corner_cases(self):
self.assertEqual(sieve(-1), [])
self.assertEqual(sieve(0), [])
self.assertEqual(sieve(1), [])
self.assertEqual(sieve(2), [2])
def test_some_primes(self):
primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97]
self.assertEqual(sieve(100), primes)
def test_programming_praxis(self):
magic_number = 15485863
self.assertEqual(len(sieve(magic_number)), 1000000)
array = [] dec_to_base_recursive.change_base(number=10, base=2, callback=array) """ NUMERIC OPTIMISATION """ gcd_iterative.gcd(a=5, b=10) gcd_recursive.gcd(a=5, b=10) lcm_iterative.lcm(a=5, b=10) lcm_recursive.lcm(a=5, b=10) prime_factorisation.factorise(number=100) change_making.change(amount=6) exponentiation_by_squaring.exponentiate(base=2, power=10) """ SEQUENCES """ fibonacci_iterative.fibonacci(count=5) fibonacci_recursive.fibonacci(count=5) sieve_of_eratosthenes.sieve(limit=13) """ NUMBER THEORY """ prime_number.is_prime(number=13) perfect_number.is_perfect(number=6)
