Finished existing ipython solutions to python. Ready to continue in pure python.

python/e066.py

@@ -1,8 +1,97 @@
+import math
+from e057 import add_fractions
+
+
+def get_floor_sqrt(n):
+    return math.floor(math.sqrt(n))
+
+
+def next_expansion_1(current_a, current_nominator,
+                     current_denominator, original_number):
+    cn = current_nominator
+    cd = current_denominator
+    cn, cd = cd, (original_number - cd * cd) // cn
+    next_a = math.floor((math.sqrt(original_number) + cn) // cd)
+    cn = cn - next_a * cd
+    cn *= -1
+
+    return next_a, cn, cd
+
+
+def get_continued_fraction_sequence(n):
+
+    # If number is a square number we return it.
+    floor_sqrt = get_floor_sqrt(n)
+    if n == floor_sqrt * floor_sqrt:
+        return ((floor_sqrt), [])
+
+    # Otherwise, we calculate the next expansion till we
+    # encounter a step a second time.
+    a = floor_sqrt
+    cn = a
+    cd = 1
+    sequence = []
+    previous_steps = []
+
+    while not (a, cn, cd) in previous_steps:
+        # print("a: {} cn: {} cd: {}".format(a, cn, cd))
+        previous_steps.append((a, cn, cd))
+        a, cn, cd = next_expansion_1(a, cd, cn, n)
+        sequence.append(a)
+    sequence.pop()
+    return ((floor_sqrt), sequence)
+
+
+def next_expansion_2(previous_numerator, previous_denumerator, value):
+    if previous_numerator == 0:
+        return (value, 1)
+    return add_fractions(previous_denumerator, previous_numerator, value, 1)
+
+
+def get_fractions(n, x):
+    # print("get_fractions(n={}, x={})".format(n, x))
+    # Get sequence of a_x
+    first_value, sequence = get_continued_fraction_sequence(n)
+    sequence = [first_value] + math.ceil(x / len(sequence)) * sequence
+    sequence = sequence[:x + 1]
+    sequence = sequence[::-1]
+
+    n, d = 0, 1
+    for s in sequence:
+        n, d = next_expansion_2(n, d, s)
+    return (n, d)
+
+
+def get_minimal_solution(d):
+    for i in range(0, 100):
+        x, y = get_fractions(d, i)
+        if x * x - d * y * y == 1:
+            return((x, y))
+
+
+def is_square(n):
+    return math.sqrt(n).is_integer()
+
 
 def euler_066():
-    return 0
+    # XXX: This seems really long and complicated. We can do better.
+    x_max = 0
+    d_max = 0
+
+    for d in range(2, 1001):
+        if is_square(d):
+            continue
+
+        x, y = get_minimal_solution(d)
+        if x > x_max:
+            x_max = x
+            d_max = d
+
+    print("d: {} x: {}".format(d_max, x_max))
+    s = d_max
+    return s
 
 
 if __name__ == "__main__":
     print("e066.py: " + str(euler_066()))
-    assert(euler_066() == 0)
+    assert(euler_066() == 661)