mirror of
https://github.com/donnemartin/interactive-coding-challenges
synced 2026-01-04 00:18:02 +00:00
Add mult other numbers challenge
This commit is contained in:
Donne Martin
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Given a list of ints, find the products of every other int for each index.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Can we use division?\n",
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" * No\n",
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"* Is the output a list of ints?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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"* None -> TypeError\n",
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"* [] -> []\n",
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"* [0] -> []\n",
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"* [0, 1] -> [1, 0]\n",
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"* [0, 1, 2] -> [2, 0, 0]\n",
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"* [1, 2, 3, 4] -> [24, 12, 8, 6]\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"### Brute force:\n",
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"\n",
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"<pre>\n",
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"sum = 1\n",
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" |\n",
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"[1, 2, 3, 4]\n",
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" ^\n",
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"skip if both pointers are pointing to the same spot\n",
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" |\n",
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"[1, 2, 3, 4]\n",
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" ^\n",
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"sum *= 2\n",
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" |\n",
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"[1, 2, 3, 4]\n",
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" ^\n",
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"sum *= 3\n",
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" |\n",
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"[1, 2, 3, 4]\n",
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" ^\n",
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"sum *= 4\n",
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"results.append(sum)\n",
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"results = [24]\n",
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"\n",
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"repeat for every element in the input list to obtain:\n",
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"\n",
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"[24, 12, 8, 6]\n",
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" \n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n^2)\n",
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"* Space: O(n)\n",
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"\n",
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"### Greedy\n",
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"\n",
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"<pre>\n",
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"input = [1, 2, 3, 4]\n",
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"result = [2*3*4, 1*3*4, 1*2*4, 1*2*3]\n",
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"\n",
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"Note we are duplicating multiplications with the brute force approach.\n",
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"\n",
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"We'll calculate all products before an index, and all products after an index.\n",
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"We'll then multiple these two together to form the result.\n",
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"\n",
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"input = [1, 2, 3, 4]\n",
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"before = [1, 1, 1*2, 1*2*3]\n",
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"after = [2*3*4, 1*3*4, 1*2*4, 1]\n",
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"result = [ 24, 12, 8, 6] \n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(n)\n",
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"* Space: O(n)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Solution(object):\n",
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"\n",
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" def mult_other_numbers_brute(self, array):\n",
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" if array is None:\n",
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" raise TypeError('array cannot be None')\n",
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" if not array:\n",
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" return array\n",
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" if len(array) == 1:\n",
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" return []\n",
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" result = []\n",
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" for i in range(len(array)):\n",
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" curr_sum = 1\n",
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" for j in range(len(array)):\n",
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" if i == j:\n",
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" continue\n",
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" curr_sum *= array[j]\n",
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" result.append(curr_sum)\n",
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" return result\n",
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"\n",
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" def mult_other_numbers(self, array):\n",
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" if array is None:\n",
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" raise TypeError('array cannot be None')\n",
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" if not array:\n",
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" return array\n",
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" if len(array) == 1:\n",
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" return []\n",
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" result = [None] * len(array)\n",
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" curr_product = 1\n",
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" for i in range(len(array)):\n",
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" result[i] = curr_product\n",
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" curr_product *= array[i]\n",
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" curr_product = 1\n",
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" for i in range(len(array))[::-1]:\n",
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" result[i] *= curr_product\n",
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" curr_product *= array[i]\n",
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" return result"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_mult_other_numbers.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_mult_other_numbers.py\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestMultOtherNumbers(object):\n",
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"\n",
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" def test_mult_other_numbers(self):\n",
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" solution = Solution()\n",
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" assert_raises(TypeError, solution.mult_other_numbers, None)\n",
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" assert_equal(solution.mult_other_numbers([0]), [])\n",
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" assert_equal(solution.mult_other_numbers([0, 1]), [1, 0])\n",
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" assert_equal(solution.mult_other_numbers([0, 1, 2]), [2, 0, 0])\n",
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" assert_equal(solution.mult_other_numbers([1, 2, 3, 4]), [24, 12, 8, 6])\n",
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" print('Success: test_mult_other_numbers')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestMultOtherNumbers()\n",
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" test.test_mult_other_numbers()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: test_mult_other_numbers\n"
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]
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}
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],
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"source": [
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"%run -i test_mult_other_numbers.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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