Add files via upload
This commit is contained in:
Peter Norvig
GitHub
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"cell_type": "code",
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"cell_type": "code",
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"id": "734de0e3-aafc-438a-8332-09741eef39aa",
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@@ -91,7 +91,7 @@
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"6857"
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"execution_count": 11,
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"execution_count": 2,
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"output_type": "execute_result"
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@@ -105,29 +105,36 @@
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"id": "8bf8dd51-8e06-4572-85fa-fe42875e0305",
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"metadata": {},
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"source": [
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"## Example Factor Tree\n",
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"We can represent the execution of the program as a series of equations, one per line. Using `F` as an abbreviation for `largest_prime_factor`, here is hjow we find the largest prime factor of 360:\n",
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"\n",
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"[Here](https://www.cuemath.com/numbers/factor-tree/) is the \"factor tree\" of *n* = 36:\n",
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"\n",
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"<img src=\"factor36.png\" width=300>\n",
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"\n",
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"\n",
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"We could also represent this as a series of equations, one per line:\n",
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"\n",
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" 36 = 2 × 18\n",
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" 18 = 2 × 9\n",
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" 9 = 3 × 3\n",
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" 3 = 3\n",
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" 36 = 2 × 2 × 3 × 3\n",
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"\n",
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"\n",
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"Or as equations for how `largest_prime_factor(36)` is broken down, with `lpf` as an abbreviation for `largest_prime_factor`:\n",
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"\n",
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" lpf(36) = max(2, lpf(18))\n",
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" lpf(18) = max(2, lpf(9))\n",
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" lpf(9) = max(3, lpf(3))\n",
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" lpf(3) = 3\n",
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" lpf(36) = max(2, max(2, max(3, 3))) = 3"
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" F(360) = max(2, F(180))\n",
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" F(180) = max(2, F(90))\n",
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" F(90) = max(2, F(45))\n",
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" F(45) = max(3, F(15))\n",
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" F(15) = max(3, F(5))\n",
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" F(5) = 5\n",
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" F(36) = max(2, max(2, max(2, 3, 3, 5))) = 5"
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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": "a4aaf952-bf6a-4dec-a950-5c573e1fbef0",
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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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"360"
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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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"2 * 2 * 2 * 3 * 3 * 5"
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]
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},
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{
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@@ -142,34 +149,38 @@
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},
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 4,
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"id": "9bedb1c9-4138-4250-90e6-77b10ba01586",
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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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"'all tests pass'"
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"[11, 'out of', 11, 'tests pass']"
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]
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},
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"execution_count": 12,
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"execution_count": 4,
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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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"def tests():\n",
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" assert largest_prime_factor(1) == 1 # by convention, 1\n",
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" assert largest_prime_factor(2) == 2 # even prime\n",
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" assert largest_prime_factor(3) == 3 # odd prime\n",
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" assert largest_prime_factor(6) == 3 # composite\n",
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" assert largest_prime_factor(8) == 2 # power of 2\n",
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" assert largest_prime_factor(36) == 3 # example from the diagram\n",
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" assert largest_prime_factor(49) == 7 # square of a prime\n",
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" assert largest_prime_factor(97) == 97 # bigger prime\n",
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" assert largest_prime_factor(97 ** 9) == 97 # even bigger prime\n",
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" assert largest_prime_factor(600851475143) == 6857 # really big number\n",
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" return 'all tests pass'\n",
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" \"\"\"Test largest_prime_factor.\"\"\"\n",
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" cases = {1: 1, # by convention, 1\n",
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" 2: 2, # even prime\n",
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" 3: 3, # odd prime\n",
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" 6: 3, # composite\n",
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" 32: 2, # power of 2\n",
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" 49: 7, # square of a prime\n",
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" 97: 97, # bigger prime\n",
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" 99991: 99991, # even bigger prime\n",
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" 97**9: 97, # even bigger power of a prime\n",
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" 360: 5, # test case for equations above\n",
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" 600851475143: 6857 # Project Euler #3\n",
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" }\n",
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" correct = sum(largest_prime_factor(n) == cases[n] for n in cases)\n",
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" return [correct, 'out of', len(cases), 'tests pass']\n",
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"\n",
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"tests()"
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]
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"text": [
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"CPU times: user 633 μs, sys: 71 μs, total: 704 μs\n",
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"Wall time: 706 μs\n"
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"CPU times: user 181 μs, sys: 0 ns, total: 181 μs\n",
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"Wall time: 183 μs\n"
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"6857"
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"execution_count": 13,
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"text": [
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"CPU times: user 1.77 s, sys: 21.7 ms, total: 1.79 s\n",
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"Wall time: 1.79 s\n"
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"CPU times: user 1.9 s, sys: 18.4 ms, total: 1.92 s\n",
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"Wall time: 1.92 s\n"
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"99999989"
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]
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"execution_count": 14,
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"id": "4026dc87-a0aa-4c75-b92a-96ec24cda1b7",
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'all tests pass'"
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"[11, 'out of', 11, 'tests pass']"
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]
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"execution_count": 16,
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"text": [
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"CPU times: user 209 μs, sys: 0 ns, total: 209 μs\n",
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"Wall time: 210 μs\n"
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"CPU times: user 196 μs, sys: 0 ns, total: 196 μs\n",
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"Wall time: 196 μs\n"
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"99999989"
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"execution_count": 17,
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"name": "stdout",
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"CPU times: user 2.15 s, sys: 22 ms, total: 2.17 s\n",
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"Wall time: 2.17 s\n"
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"CPU times: user 1.96 s, sys: 19.3 ms, total: 1.97 s\n",
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"Wall time: 1.97 s\n"
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"9927935178558959"
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"id": "0308612c-6860-49b0-bcd6-856fa08133b1",
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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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"'all tests pass'"
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"[11, 'out of', 11, 'tests pass']"
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]
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},
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"execution_count": 19,
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"execution_count": 11,
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"id": "b8907a8f-872f-4531-825c-fae9c70211c1",
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{
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"data": {
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"text/plain": [
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"'all tests pass'"
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"[11, 'out of', 11, 'tests pass']"
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"execution_count": 20,
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" \n",
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"tests()"
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]
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"cell_type": "code",
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"execution_count": null,
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"id": "5a3de62a-5e7a-4458-b754-6b2ab50e5fb9",
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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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