549e56186b
This problem challenged me: without using division, write a function that maps a list of integers into a list of the product of every integer in the list except for the integer at that index. This was another greedy algorithm. The take-away is to first solve the problem using brute force; this yields an algorithm with O(n*(n-1)) time complexity. Instead of a quadratic time complexity, a linear time complexity can be achieved my iterating over the list of integers twice: 1. Compute the products of every number to the left of the current number. 2. Compute the products of every number to the right of the current number. Finally, iterate over each of these and compute lhs * rhs. Even though I've solved this problem before, I used InterviewCake's hints because I was stuck without them. I should revisit this problem in a few weeks.
68 lines
2 KiB
Python
68 lines
2 KiB
Python
import unittest
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# get_products_of_all_ints_except_at_index :: [Int] -> [Int]
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def get_products_of_all_ints_except_at_index(xs):
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n = len(xs)
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if n < 2:
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raise Exception("Cannot computer without 2 or elements")
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# lhs
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befores = [None] * n
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befores[0] = 1
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for i in range(1, n):
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befores[i] = befores[i - 1] * xs[i - 1]
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# rhs
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afters = [None] * n
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afters[-1] = 1
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for i in range(n - 2, -1, -1):
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afters[i] = afters[i + 1] * xs[i + 1]
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result = [None] * n
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for i in range(n):
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result[i] = befores[i] * afters[i]
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return result
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# Tests
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class Test(unittest.TestCase):
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def test_small_list(self):
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actual = get_products_of_all_ints_except_at_index([1, 2, 3])
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expected = [6, 3, 2]
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self.assertEqual(actual, expected)
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def test_longer_list(self):
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actual = get_products_of_all_ints_except_at_index([8, 2, 4, 3, 1, 5])
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expected = [120, 480, 240, 320, 960, 192]
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self.assertEqual(actual, expected)
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def test_list_has_one_zero(self):
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actual = get_products_of_all_ints_except_at_index([6, 2, 0, 3])
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expected = [0, 0, 36, 0]
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self.assertEqual(actual, expected)
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def test_list_has_two_zeros(self):
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actual = get_products_of_all_ints_except_at_index([4, 0, 9, 1, 0])
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expected = [0, 0, 0, 0, 0]
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self.assertEqual(actual, expected)
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def test_one_negative_number(self):
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actual = get_products_of_all_ints_except_at_index([-3, 8, 4])
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expected = [32, -12, -24]
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self.assertEqual(actual, expected)
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def test_all_negative_numbers(self):
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actual = get_products_of_all_ints_except_at_index([-7, -1, -4, -2])
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expected = [-8, -56, -14, -28]
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self.assertEqual(actual, expected)
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def test_error_with_empty_list(self):
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with self.assertRaises(Exception):
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get_products_of_all_ints_except_at_index([])
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def test_error_with_one_number(self):
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with self.assertRaises(Exception):
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get_products_of_all_ints_except_at_index([1])
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unittest.main(verbosity=2)
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