282 lines
7 KiB
Plaintext
282 lines
7 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "373ed1db",
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"metadata": {},
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"source": [
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"# Exercise: Match the tarot cards!\n",
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"\n",
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"Given 2 decks of tarot cards, `deck1` and `deck2`, find all the matching pairs. The output should be a set of tuples `(idx1, idx2)` for every matching pair in `deck1`, `deck2`.\n",
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"\n",
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"For example:\n",
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"```\n",
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"deck1 = ['C', 'B', 'A']\n",
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"deck2 = ['A', 'C', 'B']\n",
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"```\n",
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"\n",
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"should return (in no particular order):\n",
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"\n",
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"```\n",
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"{(0, 1), (1, 2), (2, 0)}\n",
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"```\n",
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"\n",
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"1. Write an algorithm to match the tarot cards\n",
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"2. Compute the Big-O complexity of your algorithm\n"
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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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"id": "cf05b9c4",
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"metadata": {},
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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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"-- Deck 1: --\n",
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" ['The Tower', 'The Star', 'Strength', 'The Devil', 'Judgement', 'The World', 'The High Priestess', 'The Hanged Man', 'The Sun', 'The Lovers', 'The Chariot', 'The Emperor', 'The Fool', 'The Empress', 'Death', 'Temperance', 'Justice', 'The Magician', 'Wheel of Fortune', 'The Hermit', 'The Hierophant', 'The Moon']\n",
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"-- Deck 2: --\n",
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" ['Temperance', 'The Sun', 'The Lovers', 'Strength', 'The High Priestess', 'The Magician', 'Justice', 'Judgement', 'The Empress', 'The Star', 'The Fool', 'The Hierophant', 'The Hanged Man', 'The Tower', 'The Moon', 'The Chariot', 'Death', 'The World', 'The Hermit', 'The Devil', 'Wheel of Fortune', 'The Emperor']\n"
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]
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}
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],
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"source": [
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"import random\n",
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"\n",
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"# List of tarot card names (Major Arcana)\n",
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"tarot_cards = [\n",
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" \"The Fool\", \"The Magician\", \"The High Priestess\", \"The Empress\", \"The Emperor\",\n",
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" \"The Hierophant\", \"The Lovers\", \"The Chariot\", \"Strength\", \"The Hermit\",\n",
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" \"Wheel of Fortune\", \"Justice\", \"The Hanged Man\", \"Death\", \"Temperance\",\n",
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" \"The Devil\", \"The Tower\", \"The Star\", \"The Moon\", \"The Sun\", \"Judgement\",\n",
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" \"The World\"\n",
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"]\n",
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"\n",
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"# Copy the list to create two separate decks\n",
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"deck1 = tarot_cards.copy()\n",
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"deck2 = tarot_cards.copy()\n",
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"\n",
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"# Shuffle both decks\n",
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"random.shuffle(deck1)\n",
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"random.shuffle(deck2)\n",
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"\n",
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"# Print the shuffled decks\n",
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"print(\"-- Deck 1: --\\n\", deck1)\n",
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"print(\"-- Deck 2: --\\n\", deck2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3db3f337",
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"metadata": {},
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"source": [
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"# Simplest implementation: O(N^2)"
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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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"id": "319ef6a9",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{(0, 13),\n",
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" (1, 9),\n",
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" (2, 3),\n",
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" (3, 19),\n",
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" (4, 7),\n",
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" (5, 17),\n",
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" (6, 4),\n",
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" (7, 12),\n",
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" (8, 1),\n",
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" (9, 2),\n",
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" (10, 15),\n",
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" (11, 21),\n",
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" (12, 10),\n",
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" (13, 8),\n",
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" (14, 16),\n",
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" (15, 0),\n",
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" (16, 6),\n",
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" (17, 5),\n",
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" (18, 20),\n",
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" (19, 18),\n",
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" (20, 11),\n",
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" (21, 14)}"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"matches = set()\n",
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"for idx1, card in enumerate(deck1): # O(N)\n",
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" match = (idx1, deck2.index(card)) # O(N)\n",
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" matches.add(match)\n",
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" \n",
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"matches"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3264eb67",
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"metadata": {},
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"source": [
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"# Faster solution: O(N log N)"
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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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"id": "c768a7c2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{(0, 13),\n",
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" (1, 9),\n",
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" (2, 3),\n",
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" (3, 19),\n",
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" (4, 7),\n",
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" (5, 17),\n",
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" (6, 4),\n",
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" (7, 12),\n",
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" (8, 1),\n",
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" (9, 2),\n",
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" (10, 15),\n",
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" (11, 21),\n",
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" (12, 10),\n",
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" (13, 8),\n",
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" (14, 16),\n",
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" (15, 0),\n",
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" (16, 6),\n",
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" (17, 5),\n",
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" (18, 20),\n",
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" (19, 18),\n",
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" (20, 11),\n",
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" (21, 14)}"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Create a list of (tarot_card, idx), and sort it. This is kind of equivalent to np.argsort\n",
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"n_cards = len(deck1)\n",
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"sorted_deck1 = sorted((deck1[idx], idx) for idx in range(n_cards)) # O(N log N)\n",
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"sorted_deck2 = sorted((deck2[idx], idx) for idx in range(n_cards)) # O(N log N)\n",
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"\n",
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"matches = set()\n",
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"for idx in range(n_cards): # O(N)\n",
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" matches.add((sorted_deck1[idx][1], sorted_deck2[idx][1])) # O(1)\n",
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" \n",
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"matches"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5099970a",
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"metadata": {},
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"source": [
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"# 3. Fastest solution: 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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"id": "83c53b82",
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"metadata": {},
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "509dda71",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{(0, 13),\n",
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" (1, 9),\n",
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" (2, 3),\n",
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" (3, 19),\n",
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" (4, 7),\n",
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" (5, 17),\n",
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" (6, 4),\n",
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" (7, 12),\n",
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" (8, 1),\n",
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" (9, 2),\n",
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" (10, 15),\n",
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" (11, 21),\n",
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" (12, 10),\n",
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" (13, 8),\n",
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" (14, 16),\n",
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" (15, 0),\n",
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" (16, 6),\n",
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" (17, 5),\n",
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" (18, 20),\n",
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" (19, 18),\n",
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" (20, 11),\n",
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" (21, 14)}"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# Create a dictionary, mapping cards to the index in deck2\n",
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"deck2_card_to_idx = {}\n",
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"for idx2, card in enumerate(deck2): # O(N)\n",
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" deck2_card_to_idx[card] = idx2\n",
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"\n",
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"# For each card and index in deck1, look up the index in deck2, and store the match\n",
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"matches = set()\n",
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"for idx1, card in enumerate(deck1): # O(N)\n",
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" idx2 = deck2_card_to_idx[card] # O(1)\n",
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" matches.add((idx1, idx2)) # O(1)\n",
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" \n",
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"matches"
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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": null,
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"id": "f403a4ce",
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"metadata": {},
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"outputs": [],
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"source": []
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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 (ipykernel)",
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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": "3.11.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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