Moved solutions till 35 to Python.

python/e024.py

@@ -1,29 +1,26 @@
-from itertools import permutations
+from lib_misc import permutations
 
 
 def euler_024_library():
+    from itertools import permutations
     return int("".join(list(permutations("0123456789"))[1000000 - 1]))
 
 
-def permutations_(iterable):
-    if not iterable:
-        yield iterable
-    for i in range(len(iterable)):
-        elem = iterable[i:i + 1]
-        rest = iterable[:i] + iterable[i + 1:]
-        for ps in permutations_(rest):
-            yield elem + ps
-
-
-def n_th(generator, n):
+def nth(generator, n):
     for i in range(n):
         next(generator)
     return next(generator)
 
 
+def nth_permutation(iterable, n):
+    """ Returns the nth permutation of the iterable. """
+    #  XXX: Implement this!
+    return 0
+
+
 def euler_024():
-    g = permutations_("0123456789")
-    return int(n_th(g, 1000000 - 1))
+    g = permutations("0123456789")
+    return int(nth(g, 1000000 - 1))
 
 
 if __name__ == "__main__":

python/e027.py

@@ -1,56 +1,27 @@
-def get_primes_till(n):
-    square = lambda n: n * n
-    candiates = range(2, n + 1)
-    primes = []
-    while candiates:
-        prime = candiates[0]
-        primes.append(prime)
-        candiates = [c for c in candiates if c % prime != 0]
-    return primes
+from lib_prime import primes, is_prime
 
 
-def get_coprime(n):
-    primes = get_primes_till(n)
-    for p in primes:
-        if n % p != 0:
-            return p
-    raise Exception("No coprime found for {}.".format(n))
-
-def is_prime_fermat(n):
-    if n == 2:
-        return True
-    a = get_coprime(n)
-    if (a ** (n - 1) % n) != 1:
-        return False
-    else:
-        return True
-
-def is_prime_deterministic(n):
-    pass
-
-def is_prime(n):
-    if n == 2:
-        return True
-    if n < 2:
-        return False
-    if not is_prime_fermat(n):
-        return False
-    else:
-        return True
-        return is_prime_deterministic(n)
-
-def get_length(a, b):
+def number_consecutive_primes(a, b):
     def formula(n):
-        return n*n + a*n + b
-    for n in range(99999):
+        return n * n + a * n + b
+    n = 0
+    while True:
         if not is_prime(formula(n)):
             return n
+        n += 1
 
-def bruteforce():
-    solution = None
-    options = [(get_length(a, b), a, b)
-               for a in get_primes_till(1000)
-               for b in get_primes_till(1000)]
-    print(max(options))
 
-bruteforce()
+def euler_027():
+    n_max, a_max, b_max = 0, 0, 0
+    for b in primes(1000):
+        for a in range(-999, 1000):
+            a = -1 * a
+            n = number_consecutive_primes(a, b)
+            if n > n_max:
+                n_max, a_max, b_max = n, a, b
+    return a_max * b_max
+
+
+if __name__ == "__main__":
+    print("e027.py: {}".format(euler_027()))
+    assert(euler_027() == -59231)

python/e028.py

@@ -0,0 +1,12 @@
+def euler_028():
+    total = 1
+    current_corner = 3
+    for n in range(3, 1002, 2):
+        total += 4 * current_corner + 6 * (n - 1)
+        current_corner += 4 * n - 2
+    return total
+
+
+if __name__ == "__main__":
+    print("e028.py: {}".format(euler_028()))
+    assert(euler_028() == 669171001)

python/e029.py

@@ -0,0 +1,7 @@
+def euler_029():
+    return len(set([a**b for a in range(2, 101) for b in range(2, 101)]))
+
+
+if __name__ == "__main__":
+    print("e029.py: {}".format(euler_029()))
+    assert(euler_029() == 9183)

python/e030.py

@@ -0,0 +1,13 @@
+def euler_030():
+    fifth_power_lookup = {str(i): i**5 for i in range(0, 10)}
+
+    def is_number_sum_of_fiths_powers_of_digits(n):
+        return n == sum([fifth_power_lookup[d] for d in str(n)])
+
+    return sum([i for i in range(2, 1000000)
+                if is_number_sum_of_fiths_powers_of_digits(i)])
+
+
+if __name__ == "__main__":
+    print("e030.py: {}".format(euler_030()))
+    assert(euler_030() == 443839)

python/e031.py

@@ -0,0 +1,23 @@
+def count_change(change, coins):
+    from math import ceil
+    count = 0
+    coin, coins = coins[0], coins[1:]
+
+    if change % coin == 0:
+        count += 1
+
+    if not coins:
+        return count
+
+    for i in range(ceil(change / coin)):
+        count += count_change(change - i * coin, coins)
+    return count
+
+
+def euler_031():
+    return count_change(200, [200, 100, 50, 20, 10, 5, 2, 1])
+
+
+if __name__ == "__main__":
+    print("e031.py: {}".format(euler_031()))
+    assert(euler_031() == 73682)

python/e032.py

@@ -0,0 +1,23 @@
+from lib_misc import permutations
+
+
+def is_solution(s):
+    a, b, c = int(s[0:2]), int(s[2:5]), int(s[5:])
+    if a * b == c:
+        return c
+    a, b, c = int(s[0:1]), int(s[1:5]), int(s[5:])
+    if a * b == c:
+        return c
+    return 0
+
+
+def euler_032():
+    return sum(set([is_solution("".join(p))
+                    for p in permutations("123456789")]))
+
+
+if __name__ == "__main__":
+    assert(is_solution("391867254") == 7254)
+    assert(is_solution("391867245") == 0)
+    print("e032.py: {}".format(euler_032()))
+    assert(euler_032() == 45228)

python/e033.py

@@ -0,0 +1,38 @@
+from lib_misc import gcd
+
+
+def is_curious(n, d):
+    assert(len(str(n)) == 2 and len(str(d)) == 2)
+    if n == d:
+        return False
+    for i in range(1, 10):
+        if str(i) in str(n) and str(i) in str(d):
+            try:
+                n_ = int(str(n).replace(str(i), ""))
+                d_ = int(str(d).replace(str(i), ""))
+            except ValueError:
+                return False
+            try:
+                if n_ / d_ == n / d:
+                    return True
+            except ZeroDivisionError:
+                return False
+    return False
+
+
+def euler_033():
+    fs = [(n, d) for n in range(10, 100)
+          for d in range(n, 100) if is_curious(n, d)]
+    n = 1
+    d = 1
+    for n_, d_ in fs:
+        n *= n_
+        d *= d_
+    return d // gcd(n, d)
+
+
+if __name__ == "__main__":
+    assert(is_curious(49, 98) is True)
+    assert(is_curious(30, 50) is False)
+    print("e033.py: {}".format(euler_033()))
+    assert(euler_033() == 100)

python/e034.py

@@ -0,0 +1,26 @@
+from lib_misc import factorial
+
+
+def is_curious(n):
+    s = sum([factorial(int(d)) for d in str(n)])
+    return n == s
+
+
+def is_curious_faster(n):
+    """ Potentially faster solution. """
+    s = 0
+    for d in str(n):
+        s += factorial(int(d))
+        if s > n:
+            return False
+    return n == s
+
+
+def euler_034():
+    return sum([n for n in range(3, 10**5) if is_curious(n)])
+
+
+if __name__ == "__main__":
+    assert(is_curious(145))
+    print("e034.py: {}".format(euler_034()))
+    assert(euler_034() == 40730)

python/e035.py

@@ -0,0 +1,25 @@
+from lib_prime import primes
+
+
+def cyles(xs):
+    if len(xs) <= 1:
+        return xs
+    return [xs[i:] + xs[:i] for i in range(len(xs))]
+
+
+def is_circular(p, prime_set):
+    cs = cyles(str(p))
+    for c in cs:
+        if not int("".join(c)) in prime_set:
+            return False
+    return True
+
+
+def euler_035():
+    ps = set(primes(1000000))
+    return len([p for p in ps if is_circular(p, ps)])
+
+
+if __name__ == "__main__":
+    print("e035.py: {}".format(euler_035()))
+    assert(euler_035() == 55)

python/lib_misc.py

@@ -136,9 +136,10 @@ def collatz_sequence_length(n):
 
 @lru_cache(maxsize=10000)
 def factorial(n):
-    if n == 1:
-        return 1
-    return n * factorial(n - 1)
+    p = 1
+    for i in range(1, n + 1):
+        p *= i
+    return p
 
 
 def proper_divisors(n):
@@ -177,3 +178,25 @@ def sum_proper_divisors(n):
                 s += q
         d += 1
     return s
+
+
+def permutations(iterable):
+    """
+    Generator that returns all permutations for the iterable.
+
+    Generates equivalent result to itertools.permutations.
+    """
+    if not iterable:
+        yield iterable
+    for i in range(len(iterable)):
+        elem = iterable[i:i + 1]
+        rest = iterable[:i] + iterable[i + 1:]
+        for ps in permutations(rest):
+            yield elem + ps
+
+
+def gcd(a, b):
+    """ Returns the greatest commond divisor of a and b. """
+    if b == 0:
+        return a
+    return gcd(b, a % b)

python/lib_misc_tests.py

@@ -11,6 +11,8 @@ try:
     from .lib_misc import collatz_sequence_length
     from .lib_misc import factorial
     from .lib_misc import proper_divisors, sum_proper_divisors
+    from .lib_misc import permutations
+    from .lib_misc import gcd
 except ModuleNotFoundError:
     from lib_misc import is_palindrome_integer
     from lib_misc import is_palindrome_string
@@ -23,6 +25,8 @@ except ModuleNotFoundError:
     from lib_misc import collatz_sequence_length
     from lib_misc import factorial
     from lib_misc import proper_divisors, sum_proper_divisors
+    from lib_misc import permutations
+    from lib_misc import gcd
 
 
 class TestPrimeMethods(unittest.TestCase):
@@ -95,6 +99,38 @@ class TestPrimeMethods(unittest.TestCase):
         self.assertEqual(sum_proper_divisors(220), 284)
         self.assertEqual(sum_proper_divisors(284), 220)
 
+    def test_permutations(self):
+        from itertools import permutations as std_permutations
+        test_list = []
+        p1 = list(map(tuple, permutations(test_list)))
+        p2 = list(std_permutations(test_list))
+        self.assertEqual(p1, p2)
+
+        test_list = [1]
+        p1 = list(map(tuple, permutations(test_list)))
+        p2 = list(std_permutations(test_list))
+        self.assertEqual(p1, p2)
+
+        test_list = [1, 2, 3]
+        p1 = list(map(tuple, permutations(test_list)))
+        p2 = list(std_permutations(test_list))
+        self.assertEqual(p1, p2)
+
+        test_list = [1, 2, 3, 4, 5, 6]
+        p1 = list(map(tuple, permutations(test_list)))
+        p2 = list(std_permutations(test_list))
+        self.assertEqual(p1, p2)
+
+        test_list = "abc"
+        p1 = list(map(tuple, permutations(test_list)))
+        p2 = list(std_permutations(test_list))
+        self.assertEqual(p1, p2)
+
+    def test_gcd(self):
+        self.assertEqual(gcd(3, 2), 1)
+        self.assertEqual(gcd(15, 6), 3)
+        self.assertEqual(gcd(6, 15), 3)
+
 
 if __name__ == '__main__':
     unittest.main()

python/lib_prime.py

@@ -1,3 +1,4 @@
+from functools import lru_cache
 try:
     from lib_misc import get_item_counts
     from lib_misc import product
@@ -43,6 +44,7 @@ def prime_factors_count(n):
     return get_item_counts(prime_factors(n))
 
 
+@lru_cache(maxsize=10000)
 def is_prime(n):
     """Returns True if n is prime and False otherwise.