easy as a piece of cake

interview_cake/math/highest_product_3_int.py

@@ -0,0 +1,54 @@
+#!/bin/python
+
+"""
+Given a list of integers, find the highest product you can get from three of the integers.
+
+The input list_of_ints will always have at least three integers.
+"""
+
+def highest_num(list_of_ints):
+
+    if len(list_of_ints) == 3:
+        return list_of_ints[0]*list_of_ints[1]*list_of_ints[2]
+
+    sorted_list = sorted(list_of_ints)
+
+    return sorted_list[-3]*sorted_list[-2]*sorted_list[-1]
+
+
+def highest_product_of_3_On(list_of_ints):
+
+    highest = max(list_of_ints[0], list_of_ints[1])
+    lowest  = min(list_of_ints[0], list_of_ints[1])
+    highest_product_of_2 = list_of_ints[0] * list_of_ints[1]
+    lowest_product_of_2  = list_of_ints[0] * list_of_ints[1]
+
+    highest_product_of_3 = list_of_ints[0] * list_of_ints[1] * list_of_ints[2]
+
+    for i in range(2, len(list_of_ints)):
+        current = list_of_ints[i]
+
+        highest_product_of_3 = max(highest_product_of_3,
+                                   current * highest_product_of_2,
+                                   current * lowest_product_of_2)
+
+        highest_product_of_2 = max(highest_product_of_2,
+                                   current * highest,
+                                   current * lowest)
+
+        lowest_product_of_2 = min(lowest_product_of_2,
+                                  current * highest,
+                                  current * lowest)
+
+        highest = max(highest, current)
+
+        lowest = min(lowest, current)
+
+    return highest_product_of_3
+
+list_of_ints = [4, 2, 5, 6]
+print highest_num(list_of_ints)
+print "Should be 120"
+
+print highest_product_of_3_On(list_of_ints)
+print "Should be 120"

interview_cake/math/product_every_int.py

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+#!/bin/python
+
+"""
+You have a list of integers, and for each index you want to find the product of every integer except the integer at that index.
+
+Write a function get_products_of_all_ints_except_at_index() that takes a list of integers and returns a list of the products.
+
+For example, given:
+
+  [1, 7, 3, 4]
+
+your function would return:
+
+  [84, 12, 28, 21]
+ 
+by calculating:
+
+  [7 * 3 * 4,  1 * 3 * 4,  1 * 7 * 4,  1 * 7 * 3]
+ 
+Here's the catch: You can't use division in your solution!
+"""
+
+def get_products_of_all_ints_except_at_index(array):
+    prod_array = []
+
+    for i, num in enumerate(array):
+        prod = 1
+        for other_num in array[:i] + array[i+1:]:
+            prod *= other_num
+            
+        prod_array.append(prod)
+
+    return prod_array
+
+
+array = [1, 7, 3, 4]
+print get_products_of_all_ints_except_at_index(array)
+print "Should be [84, 12, 28, 21]"