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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Below is a solution for [exercise 4.1](http://artint.info/2e/html/ArtInt2e.Ch4.S12.html#Ch4.F14). I have added comments to explain my thought process and approach. \n", | |
| "\n", | |
| "I utilized something akin to the first representation (represent the word positions (1-across, 4-across, etc.) as variables, with the set of words as possible values) - reducing the search space at each step via word filtering and board validation, the latter of which ensures domain consistency (I believe this fulfills part a).\n", | |
| "\n", | |
| "First we create a `Crossword_Solver` class." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 89, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "class Crossword_Solver():\n", | |
| "\n", | |
| " WIDTH = None\n", | |
| " HEIGHT = None\n", | |
| " words = None\n", | |
| " board = None\n", | |
| " is_valid = False\n", | |
| " logging = False\n", | |
| " \n", | |
| " # on init add wordlist, width, height and logging props\n", | |
| " def __init__(self, words, width=3, height=3, logging=False):\n", | |
| " self.words = words\n", | |
| " self.WIDTH = width\n", | |
| " self.HEIGHT = height\n", | |
| " self.logging = logging\n", | |
| "\n", | |
| " if self.logging:\n", | |
| " print('Logging is set to True\\n')\n", | |
| "\n", | |
| " # print the incoming message, but only if logging is active\n", | |
| " def print_log(self, msg, indent=0):\n", | |
| " if self.logging:\n", | |
| " print(f'{\" \" * indent}{msg}')\n", | |
| "\n", | |
| " # print the board and validity\n", | |
| " def print_results(self):\n", | |
| " txt_frag = 'VALID' if self.is_valid else 'INVALID'\n", | |
| " print(f'Board is {txt_frag}\\n')\n", | |
| " for r in self.board:\n", | |
| " print(r)\n", | |
| "\n", | |
| " # creates and returns a board object that is self.WIDTH x self.HEIGHT\n", | |
| " def get_board(self):\n", | |
| " return [[' ' for x in range(self.WIDTH)] for y in range(self.HEIGHT)] \n", | |
| "\n", | |
| " # adds the incoming word to the board at the given position. \n", | |
| " # if axis == x, the word is added horizontally\n", | |
| " # if axis == y, the word is added vertically\n", | |
| " def enter_word_at(self, board, word, pos, axis):\n", | |
| " if axis == 'x':\n", | |
| " for i in range(3):\n", | |
| " board[pos][i] = word[i]\n", | |
| " if axis == 'y':\n", | |
| " for i in range(3):\n", | |
| " board[i][pos] = word[i]\n", | |
| "\n", | |
| " # evaluates the board at the given depth. word fragments are evaluated \n", | |
| " # vertically, as all words are added horizontally (with one initial exception)\n", | |
| " # from the provided wordlist and are therefore already assumed to be valid\n", | |
| " def validate_board(self, board, depth):\n", | |
| " is_valid = True\n", | |
| " frag = ''\n", | |
| " for i in range(3):\n", | |
| " frag = ''\n", | |
| " for y in range(depth):\n", | |
| " frag += board[y][i] \n", | |
| " \n", | |
| " filtered_words = [w for w in self.words if w[0] == frag[0]]\n", | |
| " for idx, f in enumerate(frag):\n", | |
| " filtered_words = [w for w in filtered_words if w[idx] == f[0]]\n", | |
| " \n", | |
| " if len(filtered_words) == 0: \n", | |
| " self.print_log('...VALIDATION FAILED!!', depth + 2)\n", | |
| " return False\n", | |
| "\n", | |
| " return is_valid\n", | |
| "\n", | |
| " # operates recursively, trying words that were filtered in previous operations\n", | |
| " # (search space pruning) and checking the validity of each move.\n", | |
| " # if a given move is invalid, it is not reset, but chars will be overwritten\n", | |
| " # by subsequent operations.\n", | |
| " def explore(self, board, root, words, filtered_words, pos):\n", | |
| " self.print_log(f'possible choices {filtered_words}', (pos + 1) * 2) \n", | |
| " tmp_words = words[:]\n", | |
| " is_valid = False\n", | |
| " filtered_inner = []\n", | |
| " \n", | |
| " for f in filtered_words:\n", | |
| " # bail if the current filtered word is not in the wordlist, that means\n", | |
| " # it's already in use \n", | |
| " if f not in tmp_words: continue \n", | |
| " tmp_words.remove(f)\n", | |
| " self.print_log(f'Trying {f} horizontally at position 0,{pos}', (pos + 1) * 2) \n", | |
| " self.enter_word_at(board, f, pos, 'x')\n", | |
| "\n", | |
| " # check if the board appears valid \n", | |
| " # (words horizontally and vertically are in the words list)\n", | |
| " if not self.validate_board(board, pos + 1): \n", | |
| " continue \n", | |
| " else: \n", | |
| " is_valid = True \n", | |
| " \n", | |
| " # recurse\n", | |
| " if pos < WIDTH - 1:\n", | |
| " filtered_inner = [w for w in tmp_words if w[0] == root[pos + 1]]\n", | |
| " self.explore(board, root, tmp_words, filtered_inner, pos+1) \n", | |
| "\n", | |
| " return (is_valid, board, tmp_words, filtered_inner)\n", | |
| " \n", | |
| " # try_word does the following\n", | |
| " # 1. places the given word horizontally at 0,0\n", | |
| " # 2. looks for words valid words (words with the same start char) to place \n", | |
| " # vertically at 0,0 \n", | |
| " # 3. uses self.explore to recursively fill and test the remaining values\n", | |
| " # 4. returns the validity and board resulting from the above operations\n", | |
| " def try_word(self, word):\n", | |
| " self.print_log(f'Trying {word} horizontally at position 0,0')\n", | |
| "\n", | |
| " board = self.get_board()\n", | |
| " is_valid = False\n", | |
| "\n", | |
| " tmp_words = self.words[:]\n", | |
| " tmp_words.remove(word)\n", | |
| "\n", | |
| " self.enter_word_at(board, word, 0, 'x')\n", | |
| "\n", | |
| " filtered_words = [w for w in tmp_words if w[0] == word[0]]\n", | |
| " if len(filtered_words) == 0: return self.get_board()\n", | |
| "\n", | |
| " # add y at 0\n", | |
| " for fw in filtered_words:\n", | |
| " tmp_words = self.words[:]\n", | |
| " tmp_words.remove(word)\n", | |
| " # bail if the current filtered word is not in the wordlist, that means\n", | |
| " # it's already in use\n", | |
| " if fw not in tmp_words: continue\n", | |
| " tmp_words.remove(fw)\n", | |
| " self.print_log(f'Trying {fw} vertically at position 0,0', 2)\n", | |
| " self.enter_word_at(board, fw, 0, 'y')\n", | |
| " r2_filtered_words = [w for w in tmp_words if w[0] == fw[1]]\n", | |
| " if len(r2_filtered_words) == 0: \n", | |
| " self.print_log('...FAILED!! NO VALID FILTERED WORDS', 2) \n", | |
| " continue\n", | |
| "\n", | |
| " is_valid, board, tmp_words, filtered_words = self.explore(board, fw, tmp_words, r2_filtered_words, 1)\n", | |
| "\n", | |
| " return (is_valid, board)\n", | |
| " \n", | |
| " # iterates through the provided wordlist, placing each word horizontally at\n", | |
| " # 0,0 to determine if the crossword may be solved.\n", | |
| " # returns self for chaining purposes\n", | |
| " def solve(self):\n", | |
| " for word in self.words:\n", | |
| " is_valid, board = self.try_word(word)\n", | |
| " if is_valid:\n", | |
| " self.is_valid = is_valid\n", | |
| " self.board = board\n", | |
| " break\n", | |
| "\n", | |
| " print('\\nCOMPLETE!!!\\n')\n", | |
| "\n", | |
| " return self\n", | |
| " " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now, we're ready to define our dimensions and wordlist. After which, we create an instance of Crossword_Solver that solves the thing and prints the results. \n", | |
| "\n", | |
| "*Note: the final arg to Crossword_Solver can be omitted if one wants to run this sans logging.*" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 90, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Logging is set to True\n", | |
| "\n", | |
| "Trying add horizontally at position 0,0\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying age horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying aid horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying aim horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying air horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying are horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying arm horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying art vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying art horizontally at position 0,0\n", | |
| " Trying add vertically at position 0,0\n", | |
| " possible choices ['dim']\n", | |
| " Trying dim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aid vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying aim vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying air vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying are vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| " Trying arm vertically at position 0,0\n", | |
| " ...FAILED!! NO VALID FILTERED WORDS\n", | |
| "Trying bad horizontally at position 0,0\n", | |
| " Trying bat vertically at position 0,0\n", | |
| " possible choices ['add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art']\n", | |
| " Trying add horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying air horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying are horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying arm horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying art horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying bee vertically at position 0,0\n", | |
| " possible choices ['ear', 'eel', 'eft']\n", | |
| " Trying ear horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying eel horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying eft horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying boa vertically at position 0,0\n", | |
| " possible choices ['oaf']\n", | |
| " Trying oaf horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| "Trying bat horizontally at position 0,0\n", | |
| " Trying bad vertically at position 0,0\n", | |
| " possible choices ['add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art']\n", | |
| " Trying add horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying air horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying are horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying arm horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying art horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying bee vertically at position 0,0\n", | |
| " possible choices ['ear', 'eel', 'eft']\n", | |
| " Trying ear horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying eel horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying eft horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying boa vertically at position 0,0\n", | |
| " possible choices ['oaf']\n", | |
| " Trying oaf horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| "Trying bee horizontally at position 0,0\n", | |
| " Trying bad vertically at position 0,0\n", | |
| " possible choices ['add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art']\n", | |
| " Trying add horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying air horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying are horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying arm horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying art horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying bat vertically at position 0,0\n", | |
| " possible choices ['add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art']\n", | |
| " Trying add horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aim horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying air horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying are horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying arm horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying art horizontally at position 0,1\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying boa vertically at position 0,0\n", | |
| " possible choices ['oaf']\n", | |
| " Trying oaf horizontally at position 0,1\n", | |
| " possible choices ['add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art']\n", | |
| " Trying add horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying age horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aid horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying aim horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying air horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying are horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying arm horizontally at position 0,2\n", | |
| " ...VALIDATION FAILED!!\n", | |
| " Trying art horizontally at position 0,2\n", | |
| "\n", | |
| "COMPLETE!!!\n", | |
| "\n", | |
| "Board is VALID\n", | |
| "\n", | |
| "['b', 'e', 'e']\n", | |
| "['o', 'a', 'f']\n", | |
| "['a', 'r', 't']\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "WIDTH = 3\n", | |
| "HEIGHT = 3\n", | |
| "\n", | |
| "words = [\n", | |
| " 'add', 'age', 'aid', 'aim', 'air', 'are', 'arm', 'art', 'bad', 'bat', 'bee', \n", | |
| " 'boa', 'dim', 'ear', 'eel', 'eft', 'lee', 'oaf'\n", | |
| "]\n", | |
| "\n", | |
| "cws = Crossword_Solver(words, WIDTH, HEIGHT, True)\n", | |
| "cws.solve().print_results()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "While the above is a brute-force approach, it does the job. Ideally, we'd modify this to gracefully handle more complex board types (like a real crossword layout, for example), but this increases the scope significantly and is not the goal of this exercise. " | |
| ] | |
| } | |
| ], | |
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| "display_name": "Python 3.9.12 64-bit", | |
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| "pygments_lexer": "ipython3", | |
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