305 lines
8.1 KiB
Plaintext
305 lines
8.1 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "63e2be2b",
|
|
"metadata": {},
|
|
"source": [
|
|
"# [Anagramic Squares](https://projecteuler.net/problem=98)\n",
|
|
"\n",
|
|
"[Itertools](https://docs.python.org/3/library/itertools.html) to the rescue! But first, we'll read the words we're working with."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "6db8ba5d",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"with open(\"txt/0098_words.txt\") as f:\n",
|
|
" words = [word.strip('\"') for line in f for word in line.split(',')]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "a2171d35",
|
|
"metadata": {},
|
|
"source": [
|
|
"We can then make groups where each word is an anagram of the other words in the group."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 2,
|
|
"id": "10a18f2f",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[('BOARD', 'BROAD'),\n",
|
|
" ('CREATION', 'REACTION'),\n",
|
|
" ('CARE', 'RACE'),\n",
|
|
" ('ACT', 'CAT'),\n",
|
|
" ('DANGER', 'GARDEN'),\n",
|
|
" ('DEAL', 'LEAD'),\n",
|
|
" ('PHASE', 'SHAPE'),\n",
|
|
" ('EARTH', 'HEART'),\n",
|
|
" ('HATE', 'HEAT'),\n",
|
|
" ('ARISE', 'RAISE'),\n",
|
|
" ('MALE', 'MEAL'),\n",
|
|
" ('LEAST', 'STEAL'),\n",
|
|
" ('MEAN', 'NAME'),\n",
|
|
" ('EARN', 'NEAR'),\n",
|
|
" ('RATE', 'TEAR'),\n",
|
|
" ('EAST', 'SEAT'),\n",
|
|
" ('EAT', 'TEA'),\n",
|
|
" ('INTRODUCE', 'REDUCTION'),\n",
|
|
" ('CREDIT', 'DIRECT'),\n",
|
|
" ('CENTRE', 'RECENT'),\n",
|
|
" ('EXCEPT', 'EXPECT'),\n",
|
|
" ('COURSE', 'SOURCE'),\n",
|
|
" ('DOG', 'GOD'),\n",
|
|
" ('SHEET', 'THESE'),\n",
|
|
" ('FILE', 'LIFE'),\n",
|
|
" ('FORMER', 'REFORM'),\n",
|
|
" ('IGNORE', 'REGION'),\n",
|
|
" ('ITEM', 'TIME'),\n",
|
|
" ('QUIET', 'QUITE'),\n",
|
|
" ('NOTE', 'TONE'),\n",
|
|
" ('SURE', 'USER'),\n",
|
|
" ('FORM', 'FROM'),\n",
|
|
" ('NIGHT', 'THING'),\n",
|
|
" ('SIGN', 'SING'),\n",
|
|
" ('THROW', 'WORTH'),\n",
|
|
" ('SHOUT', 'SOUTH'),\n",
|
|
" ('HOW', 'WHO'),\n",
|
|
" ('SHUT', 'THUS'),\n",
|
|
" ('ITS', 'SIT'),\n",
|
|
" ('NO', 'ON'),\n",
|
|
" ('NOW', 'OWN'),\n",
|
|
" ('POST', 'SPOT', 'STOP')]"
|
|
]
|
|
},
|
|
"execution_count": 2,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"from itertools import groupby\n",
|
|
"\n",
|
|
"anagram_groups = []\n",
|
|
"for _, g in groupby(sorted(words, key=sorted), key=sorted):\n",
|
|
" g = tuple(g)\n",
|
|
" if len(g) > 1:\n",
|
|
" anagram_groups.append(g)\n",
|
|
"\n",
|
|
"anagram_groups"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2ff00e54",
|
|
"metadata": {},
|
|
"source": [
|
|
"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."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 3,
|
|
"id": "aaf851bb",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def n_digit_square_numbers(n):\n",
|
|
" low = ceil(sqrt(10^(n-1)))\n",
|
|
" high = floor(sqrt(10^n - 1))\n",
|
|
" for k in range(low, high + 1):\n",
|
|
" yield k^2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "53dc4e29",
|
|
"metadata": {},
|
|
"source": [
|
|
"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))."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 4,
|
|
"id": "5e4db377",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def square_mappings(word):\n",
|
|
" n = len(word)\n",
|
|
" for k in n_digit_square_numbers(n):\n",
|
|
" tr = dict(zip(word, str(k)))\n",
|
|
" if len(set(tr.values())) != len(tr):\n",
|
|
" continue\n",
|
|
" \n",
|
|
" yield str.maketrans(tr)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "b3410bb2",
|
|
"metadata": {},
|
|
"source": [
|
|
"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."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "744be254",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def square_anagram_word_pair_mapping(s, t):\n",
|
|
" best = None\n",
|
|
" maximum = float('-inf')\n",
|
|
" \n",
|
|
" for tr in square_mappings(s):\n",
|
|
" m, n = s.translate(tr), t.translate(tr)\n",
|
|
" if m[0] == '0' or n[0] == '0':\n",
|
|
" continue\n",
|
|
"\n",
|
|
" m, n = int(m), int(n)\n",
|
|
" if is_square(m) and is_square(n) and maximum < max(m, n):\n",
|
|
" maximum = max(m, n)\n",
|
|
" best = tr\n",
|
|
" \n",
|
|
" return best"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "408ad5a3",
|
|
"metadata": {},
|
|
"source": [
|
|
"Now we'll look at every anagram pair and find their best square mapping, if it exists."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "1ea2a13b",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"from itertools import combinations\n",
|
|
"\n",
|
|
"pairs = dict()\n",
|
|
"for group in anagram_groups:\n",
|
|
" for s, t in combinations(group, 2):\n",
|
|
" pairs[(s, t)] = square_anagram_word_pair_mapping(s, t)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d16f4f48",
|
|
"metadata": {},
|
|
"source": [
|
|
"With the best mappings, we can find the largest square that can be made from each pair."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"id": "f064e9e4",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"{('BOARD', 'BROAD'): 18769,\n",
|
|
" ('CARE', 'RACE'): 9216,\n",
|
|
" ('DEAL', 'LEAD'): 4761,\n",
|
|
" ('HATE', 'HEAT'): 1936,\n",
|
|
" ('MALE', 'MEAL'): 1936,\n",
|
|
" ('MEAN', 'NAME'): 9604,\n",
|
|
" ('RATE', 'TEAR'): 9604,\n",
|
|
" ('EAST', 'SEAT'): 2916,\n",
|
|
" ('EAT', 'TEA'): 961,\n",
|
|
" ('DOG', 'GOD'): 961,\n",
|
|
" ('FILE', 'LIFE'): 9216,\n",
|
|
" ('NOTE', 'TONE'): 9216,\n",
|
|
" ('HOW', 'WHO'): 961,\n",
|
|
" ('SHUT', 'THUS'): 4761,\n",
|
|
" ('ITS', 'SIT'): 961,\n",
|
|
" ('NOW', 'OWN'): 961,\n",
|
|
" ('POST', 'SPOT'): 2916,\n",
|
|
" ('POST', 'STOP'): 9604}"
|
|
]
|
|
},
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"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",
|
|
"max_squares"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"id": "00be066e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"18769"
|
|
]
|
|
},
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"max(max_squares.values())"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "69a1b066",
|
|
"metadata": {},
|
|
"source": [
|
|
"#### Copyright (C) 2025 filifa\n",
|
|
"\n",
|
|
"This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "SageMath 9.5",
|
|
"language": "sage",
|
|
"name": "sagemath"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|