add problem 98
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filifa
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "63e2be2b",
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"metadata": {},
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"source": [
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"# [Anagramic Squares](https://projecteuler.net/problem=98)\n",
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"\n",
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"[Itertools](https://docs.python.org/3/library/itertools.html) to the rescue! But first, we'll read the words we're working with."
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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": "6db8ba5d",
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"metadata": {},
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"outputs": [],
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"source": [
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"with open(\"txt/0098_words.txt\") as f:\n",
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" words = [word.strip('\"') for line in f for word in line.split(',')]"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a2171d35",
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"metadata": {},
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"source": [
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"We can then make groups where each word is an anagram of the other words in the group."
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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": "10a18f2f",
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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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"[('BOARD', 'BROAD'),\n",
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" ('CREATION', 'REACTION'),\n",
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" ('CARE', 'RACE'),\n",
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" ('ACT', 'CAT'),\n",
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" ('DANGER', 'GARDEN'),\n",
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" ('DEAL', 'LEAD'),\n",
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" ('PHASE', 'SHAPE'),\n",
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" ('EARTH', 'HEART'),\n",
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" ('HATE', 'HEAT'),\n",
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" ('ARISE', 'RAISE'),\n",
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" ('MALE', 'MEAL'),\n",
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" ('LEAST', 'STEAL'),\n",
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" ('MEAN', 'NAME'),\n",
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" ('EARN', 'NEAR'),\n",
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" ('RATE', 'TEAR'),\n",
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" ('EAST', 'SEAT'),\n",
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" ('EAT', 'TEA'),\n",
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" ('INTRODUCE', 'REDUCTION'),\n",
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" ('CREDIT', 'DIRECT'),\n",
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" ('CENTRE', 'RECENT'),\n",
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" ('EXCEPT', 'EXPECT'),\n",
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" ('COURSE', 'SOURCE'),\n",
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" ('DOG', 'GOD'),\n",
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" ('SHEET', 'THESE'),\n",
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" ('FILE', 'LIFE'),\n",
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" ('FORMER', 'REFORM'),\n",
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" ('IGNORE', 'REGION'),\n",
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" ('ITEM', 'TIME'),\n",
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" ('QUIET', 'QUITE'),\n",
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" ('NOTE', 'TONE'),\n",
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" ('SURE', 'USER'),\n",
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" ('FORM', 'FROM'),\n",
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" ('NIGHT', 'THING'),\n",
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" ('SIGN', 'SING'),\n",
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" ('THROW', 'WORTH'),\n",
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" ('SHOUT', 'SOUTH'),\n",
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" ('HOW', 'WHO'),\n",
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" ('SHUT', 'THUS'),\n",
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" ('ITS', 'SIT'),\n",
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" ('NO', 'ON'),\n",
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" ('NOW', 'OWN'),\n",
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" ('POST', 'SPOT', 'STOP')]"
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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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"from itertools import groupby\n",
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"\n",
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"anagram_groups = []\n",
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"for _, g in groupby(sorted(words, key=sorted), key=sorted):\n",
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" g = tuple(g)\n",
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" if len(g) > 1:\n",
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" anagram_groups.append(g)\n",
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"\n",
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"anagram_groups"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2ff00e54",
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"metadata": {},
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"source": [
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"When looking for square mappings, we only need to consider square numbers with the same number of digits as a given word. This means if word has $n$ characters, we'll only try to map squares between $10^{n-1}$ and $10^n$. Here's a function to iterate over all square numbers with a given number of digits."
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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": "aaf851bb",
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"metadata": {},
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"outputs": [],
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"source": [
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"def n_digit_square_numbers(n):\n",
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" low = ceil(sqrt(10^(n-1)))\n",
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" high = floor(sqrt(10^n - 1))\n",
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" for k in range(low, high + 1):\n",
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" yield k^2"
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]
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},
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{
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"cell_type": "markdown",
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"id": "53dc4e29",
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"metadata": {},
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"source": [
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"Next, a function to generate those mappings. Per the problem, we'll only consider mappings that map distinct characters to distinct digits (i.e. [injective mappings](https://en.wikipedia.org/wiki/Injective_function))."
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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": 4,
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"id": "5e4db377",
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"metadata": {},
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"outputs": [],
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"source": [
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"def square_mappings(word):\n",
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" n = len(word)\n",
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" for k in n_digit_square_numbers(n):\n",
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" tr = dict(zip(word, str(k)))\n",
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" if len(set(tr.values())) != len(tr):\n",
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" continue\n",
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" \n",
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" yield str.maketrans(tr)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b3410bb2",
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"metadata": {},
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"source": [
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"Then, given two anagrams, we'll determine if they are a square anagram word pair by generating square mappings for one word, and checking if any of those mappings also result in a square number for the other word. If there are multiple such mappings, we'll return the one that makes the largest square number."
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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": 5,
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"id": "744be254",
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"metadata": {},
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"outputs": [],
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"source": [
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"def square_anagram_word_pair_mapping(s, t):\n",
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" best = None\n",
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" maximum = float('-inf')\n",
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" \n",
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" for tr in square_mappings(s):\n",
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" m, n = s.translate(tr), t.translate(tr)\n",
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" if m[0] == '0' or n[0] == '0':\n",
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" continue\n",
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"\n",
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" m, n = int(m), int(n)\n",
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" if is_square(m) and is_square(n) and maximum < max(m, n):\n",
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" maximum = max(m, n)\n",
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" best = tr\n",
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" \n",
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" return best"
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]
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},
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{
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"cell_type": "markdown",
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"id": "408ad5a3",
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"metadata": {},
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"source": [
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"Now we'll look at every anagram pair and find their best square mapping, if it exists."
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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": 6,
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"id": "1ea2a13b",
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"metadata": {},
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"outputs": [],
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"source": [
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"from itertools import combinations\n",
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"\n",
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"pairs = dict()\n",
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"for group in anagram_groups:\n",
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" for s, t in combinations(group, 2):\n",
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" pairs[(s, t)] = square_anagram_word_pair_mapping(s, t)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d16f4f48",
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"metadata": {},
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"source": [
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"With the best mappings, we can find the largest square that can be made from each pair."
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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": 7,
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"id": "f064e9e4",
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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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"{('BOARD', 'BROAD'): 18769,\n",
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" ('CARE', 'RACE'): 9216,\n",
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" ('DEAL', 'LEAD'): 4761,\n",
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" ('HATE', 'HEAT'): 1936,\n",
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" ('MALE', 'MEAL'): 1936,\n",
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" ('MEAN', 'NAME'): 9604,\n",
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" ('RATE', 'TEAR'): 9604,\n",
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" ('EAST', 'SEAT'): 2916,\n",
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" ('EAT', 'TEA'): 961,\n",
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" ('DOG', 'GOD'): 961,\n",
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" ('FILE', 'LIFE'): 9216,\n",
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" ('NOTE', 'TONE'): 9216,\n",
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" ('HOW', 'WHO'): 961,\n",
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" ('SHUT', 'THUS'): 4761,\n",
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" ('ITS', 'SIT'): 961,\n",
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" ('NOW', 'OWN'): 961,\n",
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" ('POST', 'SPOT'): 2916,\n",
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" ('POST', 'STOP'): 9604}"
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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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"max_squares = {(s, t): max(int(s.translate(tr)), int(t.translate(tr))) for ((s, t), tr) in pairs.items() if tr is not None}\n",
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"max_squares"
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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": 8,
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"id": "00be066e",
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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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"18769"
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]
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},
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"execution_count": 8,
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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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"max(max_squares.values())"
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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": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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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": "3.11.2"
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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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