🎉 Finishing rows of cake

Storage/cakes-rows.py

@@ -0,0 +1,83 @@
+def define_epsilon():
+    eps = 1.0
+    while eps + 1 > 1:
+        eps /= 2
+    eps *= 2
+    return eps
+
+
+def is_between(a, b, c):
+    epsilon = define_epsilon()
+    cross_product = (c[1] - a[1]) * (b[0] - a[0]) - (c[0] - a[0]) * (b[1] - a[1])
+
+    # compare versus epsilon for floating point values, or != 0 if using integers
+    if abs(cross_product) > epsilon:
+        return False
+
+    dot_product = (c[0] - a[0]) * (b[0] - a[0]) + (c[1] - a[1]) * (b[1] - a[1])
+    if dot_product < 0:
+        return False
+
+    squared_length_b_a = (b[0] - a[0]) * (b[0] - a[0]) + (b[1] - a[1]) * (b[1] - a[1])
+    if dot_product > squared_length_b_a:
+        return False
+
+    return True
+
+
+def checkio(cakes):
+    lines = []
+    count_cakes = len(cakes)
+    i = 0
+    while i <= count_cakes - 1:
+        first_cake = cakes[i]
+        j = 0
+        while j <= count_cakes - 1:
+            if j <= i:
+                j += 1
+                continue
+            second_cake = cakes[j]
+            k = 0
+            while k <= count_cakes - 1:
+                if k == i or k == j:
+                    k += 1
+                    continue
+                third_cake = cakes[k]
+                if is_between(first_cake, second_cake, third_cake):
+                    line_to_add = [first_cake, second_cake, third_cake]
+                    for line in lines:
+                        count = 0
+                        to_add = []
+                        if first_cake in line:
+                            count += 1
+                        else:
+                            to_add.append(first_cake)
+                        if second_cake in line:
+                            count += 1
+                        else:
+                            to_add.append(second_cake)
+                        if third_cake in line:
+                            count += 1
+                        else:
+                            to_add.append(third_cake)
+                        if count >= 2:
+                            line_to_add = None
+                            for t in to_add:
+                                line.append(t)
+
+                    if line_to_add is not None:
+                        lines.append(line_to_add)
+                k += 1
+            j += 1
+        i += 1
+
+    print(lines)
+    return len(lines)
+
+
+# These "asserts" using only for self-checking and not necessary for auto-testing
+if __name__ == '__main__':
+    assert checkio([[3, 3], [5, 5], [8, 8], [2, 8], [8, 2]]) == 2
+    assert checkio(
+        [[2, 2], [2, 5], [2, 8], [5, 2], [7, 2], [8, 2],
+         [9, 2], [4, 5], [4, 8], [7, 5], [5, 8], [9, 8]]) == 6