1 files changed, 89 insertions, 0 deletions
diff --git a/scratch/data_structures_and_algorithms/highest-product-of-3.py b/scratch/data_structures_and_algorithms/highest-product-of-3.py
new file mode 100644
index 000000000000..889663e058da
--- /dev/null
+++ b/scratch/data_structures_and_algorithms/highest-product-of-3.py
@@ -0,0 +1,89 @@
+import unittest
+
+
+################################################################################
+# Solution
+################################################################################
+# f :: [Int] -> Int
+def highest_product_of_3(xs):
+    """Here we're greedily storing:
+    - current max
+    - largest product of two
+    - largest positive number
+    - second largest positive number
+    - largest negative number
+    """
+    if len(xs) < 3:
+        raise Exception
+
+    cm = None
+    ld = xs[0] * xs[1]
+    l2 = min(xs[0], xs[1])
+    if xs[0] < 0 or xs[1] < 0:
+        ln = min(xs[0], xs[1])
+    else:
+        ln = 1
+    l = max(xs[0], xs[1])
+
+    for x in xs[2:]:
+        if not cm:
+            cm = max(x * ln * l, ld * x, x * l * l2)  # beware
+            ld = max(ld, x * ln, x * l)
+            ln = min(ln, x)
+            l = max(l, x)
+            if x < l:
+                l2 = max(l2, x)
+        else:
+            cm = max(cm, x * ln * l, x * ld, x * l * l2)
+            ld = max(ld, x * ln, x * l)
+            ln = min(ln, x)
+            l = max(l, x)
+            if x < l:
+                l2 = max(l2, x)
+
+    return cm
+
+
+################################################################################
+# Tests
+################################################################################
+class Test(unittest.TestCase):
+    def test_short_list(self):
+        actual = highest_product_of_3([1, 2, 3, 4])
+        expected = 24
+        self.assertEqual(actual, expected)
+
+    def test_longer_list(self):
+        actual = highest_product_of_3([6, 1, 3, 5, 7, 8, 2])
+        expected = 336
+        self.assertEqual(actual, expected)
+
+    def test_list_has_one_negative(self):
+        actual = highest_product_of_3([-5, 4, 8, 2, 3])
+        expected = 96
+        self.assertEqual(actual, expected)
+
+    def test_list_has_two_negatives(self):
+        actual = highest_product_of_3([-10, 1, 3, 2, -10])
+        expected = 300
+        self.assertEqual(actual, expected)
+
+    def test_list_is_all_negatives(self):
+        actual = highest_product_of_3([-5, -1, -3, -2])
+        expected = -6
+        self.assertEqual(actual, expected)
+
+    def test_error_with_empty_list(self):
+        with self.assertRaises(Exception):
+            highest_product_of_3([])
+
+    def test_error_with_one_number(self):
+        with self.assertRaises(Exception):
+            highest_product_of_3([1])
+
+    def test_error_with_two_numbers(self):
+        with self.assertRaises(Exception):
+            highest_product_of_3([1, 1])
+
+
+unittest.main(verbosity=2)