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Peter Norvig
2021-02-23 12:00:02 -08:00
committed by GitHub
parent d649cf5c52
commit c4f9ae331a
1 changed files with 101 additions and 37 deletions
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138
ipynb/SpellingBee.ipynb
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@@ -63,10 +63,13 @@
"source": [
"Word = str # Type for a word\n",
"\n",
"def valid_words(text) -> List[Word]:\n",
" \"\"\"Words with at least 4 letters, no 'S', and no more than 7 distinct letters.\"\"\"\n",
" return [w for w in text.upper().split() \n",
" if len(w) >= 4 and 'S' not in w and len(set(w)) <= 7]\n",
"def valid(word) -> bool:\n",
" \"\"\"Does word have at least 4 letters, no 'S', and no more than 7 distinct letters?\"\"\"\n",
" return len(word) >= 4 and 'S' not in word and len(set(word)) <= 7\n",
"\n",
"def valid_words(text, valid=valid) -> List[Word]: \n",
" \"\"\"All the valid words in text.\"\"\"\n",
" return [w for w in text.upper().split() if valid(w)]\n",
"\n",
"def pangram_bonus(word) -> int: \n",
" \"\"\"Does a word get a bonus for having 7 distinct letters (some maybe more than once)?\"\"\"\n",
@@ -356,20 +359,20 @@
{
"data": {
"text/plain": [
"[Honeycomb(letters='ACEIORT', center='A'),\n",
" Honeycomb(letters='ACEIORT', center='C'),\n",
" Honeycomb(letters='ACEIORT', center='E'),\n",
" Honeycomb(letters='ACEIORT', center='I'),\n",
" Honeycomb(letters='ACEIORT', center='O'),\n",
" Honeycomb(letters='ACEIORT', center='R'),\n",
" Honeycomb(letters='ACEIORT', center='T'),\n",
" Honeycomb(letters='AEGLMPX', center='A'),\n",
"[Honeycomb(letters='AEGLMPX', center='A'),\n",
" Honeycomb(letters='AEGLMPX', center='E'),\n",
" Honeycomb(letters='AEGLMPX', center='G'),\n",
" Honeycomb(letters='AEGLMPX', center='L'),\n",
" Honeycomb(letters='AEGLMPX', center='M'),\n",
" Honeycomb(letters='AEGLMPX', center='P'),\n",
" Honeycomb(letters='AEGLMPX', center='X')]"
" Honeycomb(letters='AEGLMPX', center='X'),\n",
" Honeycomb(letters='ACEIORT', center='A'),\n",
" Honeycomb(letters='ACEIORT', center='C'),\n",
" Honeycomb(letters='ACEIORT', center='E'),\n",
" Honeycomb(letters='ACEIORT', center='I'),\n",
" Honeycomb(letters='ACEIORT', center='O'),\n",
" Honeycomb(letters='ACEIORT', center='R'),\n",
" Honeycomb(letters='ACEIORT', center='T')]"
]
},
"execution_count": 13,
@@ -536,8 +539,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 9.77 ms, sys: 35 µs, total: 9.8 ms\n",
"Wall time: 9.8 ms\n"
"CPU times: user 9.27 ms, sys: 37 µs, total: 9.31 ms\n",
"Wall time: 9.3 ms\n"
]
},
{
@@ -579,7 +582,7 @@
}
],
"source": [
".01 * 55902 / 60"
"55902 * 10/1000 / 60"
]
},
{
@@ -757,8 +760,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1.81 s, sys: 2.31 ms, total: 1.82 s\n",
"Wall time: 1.82 s\n"
"CPU times: user 1.81 s, sys: 3 ms, total: 1.81 s\n",
"Wall time: 1.81 s\n"
]
},
{
@@ -840,7 +843,7 @@
"metadata": {},
"outputs": [],
"source": [
"def best_honeycomb(words) -> Honeycomb: \n",
"def best_honeycomb2(words) -> Honeycomb: \n",
" \"\"\"Return a honeycomb with highest game score on these words.\"\"\"\n",
" points_table = tabulate_points(words)\n",
" best, best_score = None, 0\n",
@@ -864,8 +867,8 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 406 ms, sys: 1.13 ms, total: 407 ms\n",
"Wall time: 406 ms\n"
"CPU times: user 408 ms, sys: 1.74 ms, total: 410 ms\n",
"Wall time: 409 ms\n"
]
},
{
@@ -880,7 +883,7 @@
}
],
"source": [
"%time best_honeycomb(enable1)"
"%time best_honeycomb2(enable1)"
]
},
{
@@ -987,7 +990,7 @@
{
"data": {
"text/plain": [
"[('has S', 103913), ('valid', 44585), ('> 7', 23400), ('< 4', 922)]"
"Counter({'< 4': 922, 'valid': 44585, 'has S': 103913, '> 7': 23400})"
]
},
"execution_count": 33,
@@ -1000,7 +1003,7 @@
" '< 4' if len(w) < 4 else \n",
" '> 7' if len(set(w)) > 7 else \n",
" 'valid'\n",
" for w in open('enable1.txt').read().upper().split()).most_common()"
" for w in valid_words(open('enable1.txt').read(), lambda w: True))"
]
},
{
@@ -1075,7 +1078,68 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"The best honeycomb is also the highest scoring letter subset on its own (although it only gets 832 of the 3,898 total points from using all seven letters)."
"The best honeycomb is also the highest scoring letter subset on its own (although it only gets 832 of the 3,898 total points from using all seven letters).\n",
"\n",
"### How many honeycombs does `best_honeycomb2` consider?\n",
"\n",
"We know that `best_honeycomb` considers 7,986 × 7 = 55,902 honeycombs. How many does `best_honeycomb2` consider? We can answer that by wrapping `Honeycomb` with a decorator that counts calls:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(Honeycomb(letters='AEGINRT', center='R'), 8084)"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def call_counter(fn):\n",
" \"Return a function that calls fn, and increments a counter on each call.\"\n",
" def wrapped(*args, **kwds):\n",
" wrapped.call_counter += 1\n",
" return fn(*args, **kwds)\n",
" wrapped.call_counter = 0\n",
" return wrapped\n",
" \n",
"Honeycomb = call_counter(Honeycomb)\n",
"\n",
"best_honeycomb2(enable1), Honeycomb.call_counter"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14.0"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(8084 - 7986) / 7"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That means that most pangrams are only considered once; for only 14 pangrams do we consider all seven centers."
]
},
{
@@ -1089,7 +1153,7 @@
},
{
"cell_type": "code",
"execution_count": 36,
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
@@ -1131,7 +1195,7 @@
},
{
"cell_type": "code",
"execution_count": 37,
"execution_count": 39,
"metadata": {},
"outputs": [
{
@@ -1156,7 +1220,7 @@
},
{
"cell_type": "code",
"execution_count": 38,
"execution_count": 40,
"metadata": {},
"outputs": [
{
@@ -1338,7 +1402,7 @@
},
{
"cell_type": "code",
"execution_count": 39,
"execution_count": 41,
"metadata": {},
"outputs": [
{
@@ -1347,14 +1411,14 @@
"(98141, 44585)"
]
},
"execution_count": 39,
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"enable1s = [w for w in open('enable1.txt').read().upper().split() \n",
" if len(w) >= 4 and len(set(w)) <= 7]\n",
"enable1s = valid_words(open('enable1.txt').read(), \n",
" lambda w: len(w) >= 4 and len(set(w)) <= 7)\n",
"\n",
"len(enable1s), len(enable1)"
]
@@ -1368,7 +1432,7 @@
},
{
"cell_type": "code",
"execution_count": 40,
"execution_count": 42,
"metadata": {},
"outputs": [
{
@@ -1664,10 +1728,10 @@
"\n",
"Thanks to a series of ideas, we were able to achieve a substantial reduction in the number of honeycombs that need to be examined (a factor of 400), the run time needed for `game_score` (a factor of about 200), and the overall run time (a factor of about 70,000).\n",
"\n",
"- **Enumeration (10 hours (estimate) run time; 3,364,900 honeycombs)**<br>Try every possible honeycomb.\n",
"- **Pangram Lettersets (10 minutes (estimate) run time; 55,902 honeycombs)**<br>Try just the honeycombs that are pangram lettersets (with every center).\n",
"- **Points Table (under 2 seconds run time; 55,902 honeycombs)**<br>Precompute the score for each letterset, and sum the 64 letter subsets of each honeycomb.\n",
"- **Branch and Bound (under 1/2 second run time; 8,084 honeycombs)**<br>Try every center only for lettersets that score better than the best score so far.\n",
"- **Enumeration (3,364,900 honeycombs; 10 hours (estimate) run time)**<br>Try every possible honeycomb.\n",
"- **Pangram Lettersets (55,902 honeycombs; 10 minutes (estimate) run time)**<br>Try just the honeycombs that are pangram lettersets (with every center).\n",
"- **Points Table (55,902 honeycombs; under 2 seconds run time)**<br>Precompute the score for each letterset, and sum the 64 letter subsets of each honeycomb.\n",
"- **Branch and Bound (8,084 honeycombs; under 1/2 second run time)**<br>Try every center only for lettersets that score better than the best score so far.\n",
"\n",
"\n",
"\n",