From b246d56acd6c4048d123d7935943cee901a821d4 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Sat, 13 Jul 2019 23:58:38 -0400
Subject: [PATCH] Moved 1 to 5 to Python and learned a ton.

---
 .gitignore                    |  4 +-
 python/e001.py                | 11 +++++
 python/e002.py                | 24 +++++++++++
 python/e003.py                |  9 ++++
 python/e004.py                | 66 +++++++++++++++++++++++++++++
 python/e005.py                | 29 +++++++++++++
 python/e006.py                |  5 +++
 python/lib_fibonacci.py       | 44 ++++++++++++++++++++
 python/lib_fibonacci_tests.py | 35 ++++++++++++++++
 python/lib_misc.py            | 78 +++++++++++++++++++++++++++++++++++
 python/lib_misc_tests.py      | 47 +++++++++++++++++++++
 python/lib_prime.py           | 27 ++++++++++++
 python/lib_prime_tests.py     | 25 +++++++++++
 13 files changed, 402 insertions(+), 2 deletions(-)
 create mode 100644 python/e001.py
 create mode 100644 python/e002.py
 create mode 100644 python/e003.py
 create mode 100644 python/e004.py
 create mode 100644 python/e005.py
 create mode 100644 python/e006.py
 create mode 100644 python/lib_fibonacci.py
 create mode 100644 python/lib_fibonacci_tests.py
 create mode 100644 python/lib_misc.py
 create mode 100644 python/lib_misc_tests.py
 create mode 100644 python/lib_prime.py
 create mode 100644 python/lib_prime_tests.py

diff --git a/.gitignore b/.gitignore
index 2bea37b..5cf56ad 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,6 @@
 todo.txt
-euler.sublime-workspace
-euler.sublime-project
+euler-python.sublime-project
+euler-python.sublime-workspace
 *.swp
 __pycache__
 .ipynb_checkpoints
diff --git a/python/e001.py b/python/e001.py
new file mode 100644
index 0000000..42267db
--- /dev/null
+++ b/python/e001.py
@@ -0,0 +1,11 @@
+def get_sum_of_natural_dividable_by_3_and_5_below(m):
+    return sum([x for x in range(m) if x % 3 == 0 or x % 5 == 0])
+
+
+def euler_001():
+    return get_sum_of_natural_dividable_by_3_and_5_below(1000)
+
+
+assert(get_sum_of_natural_dividable_by_3_and_5_below(10) == 23)
+assert(euler_001() == 233168)
+print("e001.py: {}".format(euler_001()))
diff --git a/python/e002.py b/python/e002.py
new file mode 100644
index 0000000..fa23414
--- /dev/null
+++ b/python/e002.py
@@ -0,0 +1,24 @@
+from lib_fibonacci import fibonacci_generator_smaller
+
+
+def euler_002():
+    fs = [f for f in fibonacci_generator_smaller(4000000) if f % 2 == 0]
+    return sum(fs)
+
+
+assert(euler_002() == 4613732)
+print("e002.py: {}".format(euler_002()))
+
+
+def euler_002_simple():
+    """ Sometimes it is nice to keep it simple. Instead of using three
+    library functions just implement one straightforward function. """
+    r, a, b = 0, 0, 1
+    while b < 4000000:
+        if b % 2 == 0:
+            r += b
+        a, b = b, a + b
+    return r
+
+
+assert(euler_002() == euler_002_simple())
diff --git a/python/e003.py b/python/e003.py
new file mode 100644
index 0000000..94bc087
--- /dev/null
+++ b/python/e003.py
@@ -0,0 +1,9 @@
+from lib_prime import prime_factors
+
+
+def euler_003():
+    return prime_factors(600851475143)[-1]
+
+
+assert(euler_003() == 6857)
+print("e003.py: {}".format(euler_003()))
diff --git a/python/e004.py b/python/e004.py
new file mode 100644
index 0000000..62c3d6f
--- /dev/null
+++ b/python/e004.py
@@ -0,0 +1,66 @@
+from lib_misc import is_palindrome
+
+
+def euler_004():
+    r = 0
+    for a in range(999, 99, -1):
+        for b in range(a, r // a, -1):
+            if is_palindrome(a * b) and a * b > r:
+                r = a * b
+    return r
+
+
+def euler_004_original():
+    """ The solution that I came up with originally. """
+    r = 0
+    for a in range(999, 99, -1):
+        if a * a < r:
+            break
+        for b in range(a, 99, -1):
+            c = a * b
+            if c > r and is_palindrome(c):
+                r = c
+    return r
+
+
+def euler_004_forum():
+    """
+    A solution from etatsui in the project Euler forum.
+    It is impressive to see how much fast it is relying on
+    mathematical tricks:
+        11(9091a + 910b + 100c) = mn;
+    Let:
+        11 * 10 < m < 11 * 90
+    """
+    for a in range(9, 0, -1):
+        for b in range(9, -1, -1):
+            for c in range(9, -1, -1):
+                num = 9091 * a + 910 * b + 100 * c
+                for m in range(90, 9, -1):
+                    if num % m == 0:
+                        if num / m > 999:
+                            break
+                        else:
+                            result = num * 11
+                            return result
+
+
+assert(euler_004() == 906609)
+print("e004.py: {}".format(euler_004()))
+
+
+def time_tests():
+    from timeit import timeit
+    assert(euler_004() == 906609)
+    assert(euler_004_original() == 906609)
+    assert(euler_004_forum() == 906609)
+
+    print(timeit(lambda: euler_004(), number=100))
+    print(timeit(lambda: euler_004_original(), number=100))
+    print(timeit(lambda: euler_004_forum(), number=100))
+
+
+# time_tests()
+# 0.5044660240000667
+# 0.7896412069985672
+# 0.04794573199978913
diff --git a/python/e005.py b/python/e005.py
new file mode 100644
index 0000000..ad0ec27
--- /dev/null
+++ b/python/e005.py
@@ -0,0 +1,29 @@
+from lib_prime import prime_factors_count
+from lib_misc import product
+
+
+def get_number_divisible(n):
+    """ Returns the lowest number that is divisible
+    by all numbers from 1 to n.  We calculate the factors
+    for all numbers and make sure that the minimum number
+    for each factor is included in the solution. """
+    f = {}
+    for i in range(2, n + 1):
+        for prime, count in prime_factors_count(i).items():
+            try:
+                f[prime] = max(f[prime], count)
+            except KeyError:
+                f[prime] = count
+    n = product([prime**count for prime, count in f.items()])
+    return n
+
+
+assert(get_number_divisible(10) == 2520)
+
+
+def euler_005():
+    return get_number_divisible(20)
+
+
+assert(euler_005() == 232792560)
+print("e005.py: {}".format(euler_005()))
diff --git a/python/e006.py b/python/e006.py
new file mode 100644
index 0000000..373b303
--- /dev/null
+++ b/python/e006.py
@@ -0,0 +1,5 @@
+def euler_006():
+    return 0
+
+assert(euler_006() == 233168)
+print("e006.py: {}".format(euler_006()))
diff --git a/python/lib_fibonacci.py b/python/lib_fibonacci.py
new file mode 100644
index 0000000..4d2623a
--- /dev/null
+++ b/python/lib_fibonacci.py
@@ -0,0 +1,44 @@
+def fibonacci_generator():
+    """
+    Fibonacci generator function that starts with 1, 1, 2, 3, ...
+
+    :returns: generator that yields fibonacci numbers
+    """
+    a = 0
+    b = 1
+    yield b
+    while True:
+        a, b = b, (a + b)
+        yield b
+
+
+def fibonacci_generator_smaller(n):
+    """
+
+    :param n: generator yields all fibonacci numbers smaller n
+    :returns: generator that yields fibonacci numbers
+
+    """
+    g = fibonacci_generator()
+    x = next(g)
+    while x < n:
+        yield x
+        x = next(g)
+
+
+def fibonacci_nth(n):
+    """
+
+    :param n: index of fibonacci that should be returned
+    :returns: nth fibonacci number
+
+    """
+    if n < 1:
+        return 0
+    g = fibonacci_generator()
+    i = 1
+    x = next(g)
+    while i < n:
+        i += 1
+        x = next(g)
+    return x
diff --git a/python/lib_fibonacci_tests.py b/python/lib_fibonacci_tests.py
new file mode 100644
index 0000000..d6b3a94
--- /dev/null
+++ b/python/lib_fibonacci_tests.py
@@ -0,0 +1,35 @@
+import unittest
+try:
+    from .lib_fibonacci import fibonacci_generator
+    from .lib_fibonacci import fibonacci_generator_smaller
+    from .lib_fibonacci import fibonacci_nth
+except ModuleNotFoundError:
+    from lib_fibonacci import fibonacci_generator
+    from lib_fibonacci import fibonacci_generator_smaller
+    from lib_fibonacci import fibonacci_nth
+
+
+class TestFibonacciMethods(unittest.TestCase):
+
+    def test_fibonacci_generator(self):
+        g = fibonacci_generator()
+        fs = [next(g) for _ in range(10)]
+        self.assertEqual(fs, [1, 1, 2, 3, 5, 8, 13, 21, 34, 55])
+        self.assertNotEqual(fs, [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55])
+
+    def test_fibonacci_generator_smaller(self):
+        g = fibonacci_generator_smaller(20)
+        self.assertEqual(list(g), [1, 1, 2, 3, 5, 8, 13])
+
+    def test_fibonacci_nth(self):
+        self.assertEqual(fibonacci_nth(0), 0)
+        self.assertEqual(fibonacci_nth(1), 1)
+        self.assertEqual(fibonacci_nth(2), 1)
+        self.assertEqual(fibonacci_nth(3), 2)
+        self.assertEqual(fibonacci_nth(4), 3)
+        self.assertEqual(fibonacci_nth(5), 5)
+        self.assertEqual(fibonacci_nth(6), 8)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/lib_misc.py b/python/lib_misc.py
new file mode 100644
index 0000000..ccba0f8
--- /dev/null
+++ b/python/lib_misc.py
@@ -0,0 +1,78 @@
+def get_digits_reversed(n):
+    """
+    Returns a list of digits for n.
+    """
+    digits, rest = [], n
+    while rest != 0:
+        digits.append(rest % 10)
+        rest //= 10
+    return digits
+
+
+def is_palindrome_string(n):
+    """
+    Checks whether n is a palindrome number
+    with a string based algorithm.
+
+    :param n: number to check
+    :returns: boolean
+
+    """
+    s = str(n)
+    return s == s[::-1]
+
+
+def is_palindrome_integer(n):
+    """
+    Checks whether n is a palindrome number
+    with an integer based algorithm.
+
+    :param n: number to check
+    :returns: boolean
+    """
+    digits = get_digits_reversed(n)
+    digits_count = len(digits)
+    for i in range(digits_count // 2):
+        if digits[i] != digits[digits_count - i - 1]:
+            return False
+    return True
+
+
+def time_is_palindrom():
+    """ I just want to check which option is faster. """
+    from timeit import timeit
+    print(timeit(lambda: is_palindrome_integer(82445254428), number=100000))
+    print(timeit(lambda: is_palindrome_string(82445254428), number=100000))
+    # > 0.42330633100027626
+    # > 0.07605635199979588
+
+
+is_palindrome = is_palindrome_string
+
+
+def get_item_counts(l):
+    """
+    Counts how often each element is part of the list.
+
+    :param l: a list
+    :returns: a dictionary
+    """
+    d = {}
+    for e in l:
+        try:
+            d[e] += 1
+        except KeyError:
+            d[e] = 1
+    return d
+
+
+def product(l):
+    """
+    Calculates the product of all items in the list.
+
+    :param l: a list
+    :returns: a number that is the product of all elements in the list
+    """
+    from functools import reduce
+    import operator
+    return reduce(operator.mul, l, 1)
diff --git a/python/lib_misc_tests.py b/python/lib_misc_tests.py
new file mode 100644
index 0000000..dd0375c
--- /dev/null
+++ b/python/lib_misc_tests.py
@@ -0,0 +1,47 @@
+import unittest
+try:
+    from .lib_misc import is_palindrome_integer
+    from .lib_misc import is_palindrome_string
+    from .lib_misc import get_digits_reversed
+    from .lib_misc import get_item_counts
+    from .lib_misc import product
+except ModuleNotFoundError:
+    from lib_misc import is_palindrome_integer
+    from lib_misc import is_palindrome_string
+    from lib_misc import get_digits_reversed
+    from lib_misc import get_item_counts
+    from lib_misc import product
+
+
+class TestPrimeMethods(unittest.TestCase):
+
+    def test_is_palindrome_integer(self):
+        self.assertEqual(is_palindrome_integer(2), True)
+        self.assertEqual(is_palindrome_integer(888), True)
+        self.assertEqual(is_palindrome_integer(9009), True)
+        self.assertEqual(is_palindrome_integer(23), False)
+        self.assertEqual(is_palindrome_integer(9008), False)
+
+    def test_is_palindrome_string(self):
+        self.assertEqual(is_palindrome_string(2), True)
+        self.assertEqual(is_palindrome_string(888), True)
+        self.assertEqual(is_palindrome_string(9009), True)
+        self.assertEqual(is_palindrome_string(23), False)
+        self.assertEqual(is_palindrome_string(9008), False)
+
+    def test_get_digits_reversed(self):
+        self.assertEqual(get_digits_reversed(3), [3])
+        self.assertEqual(get_digits_reversed(1234), [4, 3, 2, 1])
+        self.assertEqual(get_digits_reversed(1000), [0, 0, 0, 1])
+
+    def test_get_item_counts(self):
+        self.assertEqual(get_item_counts([]), {})
+        self.assertEqual(get_item_counts([1, 1, 3]), {1: 2, 3: 1})
+
+    def test_product(self):
+        self.assertEqual(product([2, 4, 8]), 64)
+        self.assertEqual(product([]), 1)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/lib_prime.py b/python/lib_prime.py
new file mode 100644
index 0000000..2f57935
--- /dev/null
+++ b/python/lib_prime.py
@@ -0,0 +1,27 @@
+try:
+    from lib_misc import get_item_counts
+except ModuleNotFoundError:
+    from .lib_misc import get_item_counts
+
+
+def prime_factors(n):
+    # TODO: Look into using a prime wheel instead.
+    factors = []
+    rest = n
+    divisor = 2
+    while rest % divisor == 0:
+        factors.append(divisor)
+        rest //= divisor
+    divisor = 3
+    while divisor * divisor <= rest:
+        while rest % divisor == 0:
+            factors.append(divisor)
+            rest //= divisor
+        divisor += 2
+    if rest != 1:
+        factors.append(rest)
+    return factors
+
+
+def prime_factors_count(n):
+    return get_item_counts(prime_factors(n))
diff --git a/python/lib_prime_tests.py b/python/lib_prime_tests.py
new file mode 100644
index 0000000..1621ea4
--- /dev/null
+++ b/python/lib_prime_tests.py
@@ -0,0 +1,25 @@
+import unittest
+try:
+    from .lib_prime import prime_factors
+    from .lib_prime import prime_factors_count
+except ModuleNotFoundError:
+    from lib_prime import prime_factors
+    from lib_prime import prime_factors_count
+
+
+class TestPrimeMethods(unittest.TestCase):
+
+    def test_prime_factors(self):
+        self.assertEqual(prime_factors(2), [2])
+        self.assertEqual(prime_factors(5), [5])
+        self.assertEqual(prime_factors(10), [2, 5])
+        self.assertEqual(prime_factors(13), [13])
+        self.assertEqual(prime_factors(147), [3, 7, 7])
+
+    def test_prime_factors_count(self):
+        self.assertEqual(prime_factors_count(2), {2: 1})
+        self.assertEqual(prime_factors_count(147), {3: 1, 7: 2})
+
+
+if __name__ == '__main__':
+    unittest.main()