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Peter Norvig
GitHub
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905dca4158
@ -20,7 +20,7 @@
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"\n",
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"Let's start by clarifying some concepts:\n",
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"- **State**: denoted by the standard 2-letter abbreviations like `'CA'` (plus `'UP'` and `'LP'` for the Michigan peninsulas). \n",
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"- **States**: a set of states; implemented as a (hashable) `frozenset`. I'll use `states('OR CA')` for `frozenset({'OR', 'CA'})`.\n",
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"- **States**: a set of states; implemented as a (hashable) `frozenset`. I can use `states('OR CA')`.\n",
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"- **Region**: a set of states that are **contiguous**—they are all connected by a single tree of **neighbor** relations.\n",
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"- **Neighbor**: a relation saying two states share a border. Implemented as [adjacency sets](https://en.wikipedia.org/wiki/Adjacency_list) in the dict `neighbors`.\n",
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"- **Cut**: a set of states that, when removed from the map, cuts the map into disjoint regions. \n",
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@ -52,7 +52,7 @@
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"def statedict(**dic) -> dict: \"{State:States}\"; return {s: states(dic[s]) for s in dic}\n",
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"def area(states) -> int: \"Total area\"; return sum(areas[s] for s in states)\n",
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"\n",
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"neighbors = statedict( # https://theincidentaleconomist.com/wordpress/list-of-neighboring-states-with-stata-code/\n",
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"neighbors = statedict(\n",
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" AK='', AL='FL GA MS TN', AR='LA MO MS OK TN TX', AZ='CA CO NM NV UT', CA='AZ NV OR', \n",
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" CO='AZ KS NE NM OK UT WY', CT='MA NY RI', DC='MD VA', DE='MD NJ PA', FL='AL GA', \n",
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" GA='AL FL NC SC TN', HI='', IA='IL MN MO NE SD WI', ID='MT NV OR UT WA WY', IL='IA IN KY MO WI', \n",
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@ -67,7 +67,7 @@
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" UP='WI', LP='IN OH')\n",
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"\n",
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"\n",
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"areas = dict( # https://www.census.gov/geographies/reference-files/2010/geo/state-area.html\n",
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"areas = dict(\n",
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" AK=665384, AL=52420, AZ=113990, AR=53179, CA=163695, CO=104094, CT=5543, DE=2489, DC=68, \n",
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" FL=65758, GA=59425, HI=10932, ID=83569, IL=57914, IN=36420, IA=56273, KS=82278, KY=40408, \n",
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" LA=52378, ME=35380, MD=12406, MA=10554, MI=96714, MN=86936, MS=48432, MO=69707, MT=147040, \n",
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@ -83,9 +83,9 @@
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"border = north | south | west | east\n",
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"\n",
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"# \"Countries\":\n",
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"usa = States(areas) # States plus {UP, LP, DC}\n",
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"usa = States(areas) # 50 states plus UP, LP, DC\n",
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"usa50 = usa - states('DC UP LP') # 50 actual US states\n",
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"usa48 = usa50 - states('AK HI') # 48 continental states\n",
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"usa48 = usa50 - states('AK HI') # 48 contiguous states\n",
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"usa49 = usa - states('DC AK HI MI') # 49 \"states\": MI split into UP, LP\n",
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"western = states('WA OR CA ID NV UT AZ MT WY CO NM') # The 11 states west of the Rockies"
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]
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@ -147,12 +147,12 @@
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{
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"data": {
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"text/plain": [
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"{frozenset({'ID', 'NM', 'UT'}),\n",
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" frozenset({'AZ', 'ID', 'NV'}),\n",
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" frozenset({'AZ', 'ID', 'UT'}),\n",
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"{frozenset({'CA', 'ID', 'OR'}),\n",
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" frozenset({'CA', 'OR', 'WA'}),\n",
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" frozenset({'AZ', 'ID', 'NV'}),\n",
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" frozenset({'ID', 'NM', 'UT'}),\n",
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" frozenset({'CA', 'ID', 'NV'}),\n",
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" frozenset({'CA', 'ID', 'OR'})}"
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" frozenset({'AZ', 'ID', 'UT'})}"
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]
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},
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"execution_count": 3,
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@ -244,12 +244,12 @@
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{
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"data": {
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"text/plain": [
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"[frozenset({'AZ', 'ID', 'UT'}),\n",
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" frozenset({'ID', 'NM', 'UT'}),\n",
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"[frozenset({'CA', 'ID', 'OR'}),\n",
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" frozenset({'AZ', 'ID', 'NV'}),\n",
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" frozenset({'ID', 'NM', 'UT'}),\n",
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" frozenset({'CA', 'ID', 'NV'}),\n",
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" frozenset({'CA', 'ID', 'OR'}),\n",
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" frozenset({'CA', 'OR', 'WA'})]"
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" frozenset({'CA', 'OR', 'WA'}),\n",
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" frozenset({'AZ', 'ID', 'UT'})]"
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]
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},
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"execution_count": 6,
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@ -269,18 +269,18 @@
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{
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"data": {
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"text/plain": [
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"[(frozenset({'CO', 'MT', 'NM', 'WY'}),\n",
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" frozenset({'CA', 'NV', 'OR', 'WA'}),\n",
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" frozenset({'AZ', 'ID', 'UT'})),\n",
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"[(frozenset({'AZ', 'CO', 'MT', 'NM', 'NV', 'UT', 'WY'}),\n",
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" frozenset({'WA'}),\n",
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" frozenset({'CA', 'ID', 'OR'})),\n",
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" (frozenset({'CO', 'MT', 'NM', 'UT', 'WY'}),\n",
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" frozenset({'CA', 'OR', 'WA'}),\n",
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" frozenset({'AZ', 'ID', 'NV'})),\n",
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" (frozenset({'AZ', 'CO', 'MT', 'NM', 'UT', 'WY'}),\n",
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" frozenset({'OR', 'WA'}),\n",
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" frozenset({'CA', 'ID', 'NV'})),\n",
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" (frozenset({'AZ', 'CO', 'MT', 'NM', 'NV', 'UT', 'WY'}),\n",
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" frozenset({'WA'}),\n",
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" frozenset({'CA', 'ID', 'OR'}))]"
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" (frozenset({'CO', 'MT', 'NM', 'WY'}),\n",
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" frozenset({'CA', 'NV', 'OR', 'WA'}),\n",
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" frozenset({'AZ', 'ID', 'UT'}))]"
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]
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},
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"execution_count": 7,
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@ -326,7 +326,7 @@
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" The ∆ row of the table is not a region; it is the difference in area between A and B.\"\"\"\n",
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" A, B, C = split\n",
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" def print_row(name, region, sqmi): \n",
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" statelist = f'{len(region):2d}|{{{\",\".join(sorted(region))}}}' if region else ''\n",
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" statelist = f'{len(region):2d}|{\" \".join(sorted(region))}' if region else ''\n",
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" print(f'{name}|{sqmi:9,d}|{sqmi/area(country):7.3%}|{statelist}')\n",
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" print(f'\\n{title}:')\n",
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" print_row('A', A, area(A))\n",
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@ -347,15 +347,15 @@
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"49 states ⇒ 41,700 cuts (size ≤ 8, area ≤ 624,072) ⇒ 13,146 splits.\n",
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"\n",
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"1. Split that maximizes area(B):\n",
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"A|1,345,558|43.122%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
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"B|1,344,149|43.077%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
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"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
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"A|1,345,558|43.122%|29|AL AR CT DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
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"B|1,344,149|43.077%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
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"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
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"∆| 1,409| 0.045%|\n",
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"\n",
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"2. Split that minimizes ∆ = area(A) - area(B):\n",
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"A|1,267,033|40.605%|14|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,UP,UT,WA,WI,WY}\n",
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"B|1,266,994|40.604%|27|{AL,AR,CT,DE,FL,GA,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TX,VA,VT,WV}\n",
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"C| 586,333|18.791%| 8|{CO,IL,IN,MO,NE,NM,SD,TN}\n",
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"A|1,267,033|40.605%|14|AZ CA IA ID MN MT ND NV OR UP UT WA WI WY\n",
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"B|1,266,994|40.604%|27|AL AR CT DE FL GA KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TX VA VT WV\n",
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"C| 586,333|18.791%| 8|CO IL IN MO NE NM SD TN\n",
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"∆| 39| 0.001%|\n"
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]
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}
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@ -424,18 +424,18 @@
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"49 states ⇒ 547,779 cuts (size ≤ 49, area ≤ 432,062) ⇒ 42,685 splits.\n",
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"\n",
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"1. Split that maximizes area(B):\n",
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"A|1,345,558|43.122%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
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"B|1,344,149|43.077%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
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"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
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"A|1,345,558|43.122%|29|AL AR CT DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
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"B|1,344,149|43.077%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
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"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
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"∆| 1,409| 0.045%|\n",
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"\n",
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"2. Split that minimizes ∆ = area(A) - area(B):\n",
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"A|1,345,558|43.122%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
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"B|1,344,149|43.077%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
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"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
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"A|1,345,558|43.122%|29|AL AR CT DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
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"B|1,344,149|43.077%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
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"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
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"∆| 1,409| 0.045%|\n",
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"CPU times: user 33.5 s, sys: 199 ms, total: 33.7 s\n",
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"Wall time: 33.8 s\n"
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"CPU times: user 35.5 s, sys: 325 ms, total: 35.8 s\n",
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"Wall time: 36 s\n"
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]
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}
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],
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@ -466,18 +466,18 @@
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"49 states ⇒ 1,209,042 cuts (size ≤ 10, area ≤ 1,040,120) ⇒ 278,472 splits.\n",
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"\n",
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"1. Split that maximizes area(B):\n",
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"A|1,345,558|43.122%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
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"B|1,344,149|43.077%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
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"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
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"A|1,345,558|43.122%|29|AL AR CT DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
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"B|1,344,149|43.077%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
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"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
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"∆| 1,409| 0.045%|\n",
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"\n",
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"2. Split that minimizes ∆ = area(A) - area(B):\n",
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"A|1,161,198|37.214%|29|{AL,CT,DE,FL,GA,IA,IL,IN,LP,MA,MD,ME,MN,NC,ND,NH,NJ,NY,OH,PA,RI,SC,SD,TN,UP,VA,VT,WI,WV}\n",
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"B|1,161,195|37.213%|10|{AZ,CA,CO,KS,LA,NM,OR,TX,UT,WA}\n",
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"C| 797,967|25.573%|10|{AR,ID,KY,MO,MS,MT,NE,NV,OK,WY}\n",
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"A|1,161,198|37.214%|29|AL CT DE FL GA IA IL IN LP MA MD ME MN NC ND NH NJ NY OH PA RI SC SD TN UP VA VT WI WV\n",
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"B|1,161,195|37.213%|10|AZ CA CO KS LA NM OR TX UT WA\n",
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"C| 797,967|25.573%|10|AR ID KY MO MS MT NE NV OK WY\n",
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"∆| 3| 0.000%|\n",
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"CPU times: user 1min 1s, sys: 696 ms, total: 1min 1s\n",
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"Wall time: 1min 1s\n"
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"CPU times: user 1min 3s, sys: 911 ms, total: 1min 4s\n",
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"Wall time: 1min 4s\n"
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]
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}
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],
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"49 states ⇒ 3,049,254 cuts (size ≤ 11, area ≤ 1,040,120) ⇒ 430,761 splits.\n",
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"\n",
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"1. Split that maximizes area(B):\n",
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"A|1,345,558|43.122%|29|{AL,AR,CT,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
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"B|1,344,149|43.077%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
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"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
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"A|1,345,558|43.122%|29|AL AR CT DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
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"B|1,344,149|43.077%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
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"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
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"∆| 1,409| 0.045%|\n",
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"\n",
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"2. Split that minimizes ∆ = area(A) - area(B):\n",
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"A|1,161,198|37.214%|29|{AL,CT,DE,FL,GA,IA,IL,IN,LP,MA,MD,ME,MN,NC,ND,NH,NJ,NY,OH,PA,RI,SC,SD,TN,UP,VA,VT,WI,WV}\n",
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"B|1,161,195|37.213%|10|{AZ,CA,CO,KS,LA,NM,OR,TX,UT,WA}\n",
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"C| 797,967|25.573%|10|{AR,ID,KY,MO,MS,MT,NE,NV,OK,WY}\n",
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"A|1,161,198|37.214%|29|AL CT DE FL GA IA IL IN LP MA MD ME MN NC ND NH NJ NY OH PA RI SC SD TN UP VA VT WI WV\n",
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"B|1,161,195|37.213%|10|AZ CA CO KS LA NM OR TX UT WA\n",
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"C| 797,967|25.573%|10|AR ID KY MO MS MT NE NV OK WY\n",
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"∆| 3| 0.000%|\n",
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"CPU times: user 2min 33s, sys: 1.69 s, total: 2min 35s\n",
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"Wall time: 2min 35s\n"
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"CPU times: user 2min 39s, sys: 2.14 s, total: 2min 41s\n",
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"Wall time: 2min 42s\n"
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]
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}
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],
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"\n",
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"\n",
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"\n",
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"However, I'm pretty sure we can two regions with exactly equal areas. I want to allow a cut that might have 30 or 40 states, so instead of enumerating cuts, I'll focus on enumerating the regions *A* and *B*, and yielding pairs of regions that have exactly equal area. I'll use the function `make_cuts` to make contiguous regions *A* and *B*, even though they aren't cuts. I'll keep the regions small, and anchor *A* in the west and *B* in the east:"
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"However, I'm pretty sure we can find two regions with exactly equal areas. I want to allow a cut that might have 30 or 40 states, so instead of enumerating cuts, I'll focus on enumerating the regions *A* and *B*. Given two iterables of regions, `find_equal` will report all pairs (one from *As* and one from *Bs*) of regions that have the exact same area and that are not overlapping: *A* is disjoint from *B* and all its neighbors (the `neighborhood` of *B*)."
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]
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},
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{
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"metadata": {},
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"outputs": [],
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"source": [
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"def find_equal(country: Region, maxsizeA=5, maxsizeB=8, startA=west, startB=east) -> Iterator[Tuple[Region, Region, int]]:\n",
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" \"\"\"Find contiguous regions A and B that have the same area, and yield (A, B, area).\"\"\"\n",
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" Bs = list(make_cuts(country, maxsizeB, start=startB, end=country))\n",
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" for A in make_cuts(country, maxsizeA, start=startA, end=country):\n",
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" for B in Bs:\n",
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" if area(B) == area(A):\n",
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" yield A, B, area(B)"
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"def find_equal(As: Iterable[Region], Bs: Iterable[Region]) -> Iterator[Tuple[Region, Region, int]]:\n",
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" \"\"\"From As and Bs, find disjoint regions A and B that have the exact same area. Yield (A, B, area(B)).\"\"\"\n",
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" area_table = {area(A): A for A in As}\n",
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" for B in Bs:\n",
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" if area(B) in area_table:\n",
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" A = area_table[area(B)]\n",
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" if A.isdisjoint(neighborhood(B)):\n",
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" yield (A, B, area(B))\n",
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"\n",
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"def neighborhood(A: Region) -> Region:\n",
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" \"\"\"The region consisting of A and all the neighbors of any state in A.\"\"\"\n",
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" return A | {s1 for s in A for s1 in neighbors[s]}"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"I'll keep the regions small, and anchor *A* in the west and *B* in the east. If this experiment doesn't yield anything, I'll try larger regions:"
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]
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},
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{
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@ -550,9 +562,24 @@
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{
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"data": {
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"text/plain": [
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"(frozenset({'AZ', 'CA', 'OR'}),\n",
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" frozenset({'IL', 'IN', 'KS', 'MO', 'OH', 'TN', 'VA'}),\n",
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" 376064)"
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"[(frozenset({'CA', 'NV', 'UT'}),\n",
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" frozenset({'GA', 'IA', 'KY', 'MO', 'MS', 'TN', 'VA'}),\n",
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" 359164),\n",
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" (frozenset({'AZ', 'CA', 'OR'}),\n",
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" frozenset({'IA', 'IL', 'KY', 'NE', 'SD', 'VA', 'WV'}),\n",
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" 376064),\n",
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" (frozenset({'AZ', 'CA', 'OR'}),\n",
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" frozenset({'IL', 'IN', 'KS', 'MO', 'OH', 'TN', 'VA'}),\n",
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" 376064),\n",
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" (frozenset({'ID', 'OR', 'UT', 'WY'}),\n",
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" frozenset({'GA', 'IA', 'IL', 'IN', 'MO', 'TN', 'VA'}),\n",
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" 364658),\n",
|
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" (frozenset({'ID', 'NV', 'WA'}),\n",
|
||||
" frozenset({'KY', 'MS', 'NY', 'PA', 'TN', 'VT', 'WV'}),\n",
|
||||
" 265439),\n",
|
||||
" (frozenset({'ID', 'UT', 'WA', 'WY'}),\n",
|
||||
" frozenset({'AL', 'IL', 'IN', 'KY', 'TN', 'VA', 'WI'}),\n",
|
||||
" 337577)]"
|
||||
]
|
||||
},
|
||||
"execution_count": 15,
|
||||
@ -561,14 +588,17 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"next(find_equal(usa49))"
|
||||
"make_regions = make_cuts # make_cuts actually just makes contiguous regions\n",
|
||||
"\n",
|
||||
"list(find_equal(make_regions(usa49, 4, start=west, end=usa49),\n",
|
||||
" make_regions(usa49, 7, start=east, end=usa49)))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"There may be many other solutions; we didn't bother to check, because you can't get a delta of less than zero. Note that the cut (in yellow) is not contiguous, but that's legal: all that matters is that *A* and *B* are contiguous and disjoint.\n",
|
||||
"There are 6 solutions right away (and probably many more solutions with larger regions). I'll show the map for one of them (the smallest one, with area 265,439 square miles for both regions). Note that the cut (in yellow) is not contiguous, but that's in accord with the rules: all that matters is that *A* and *B* are contiguous and disjoint.\n",
|
||||
"\n",
|
||||
""
|
||||
]
|
||||
@ -595,15 +625,15 @@
|
||||
"50 states ⇒ 43,600 cuts (size ≤ 8, area ≤ 624,072) ⇒ 13,134 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,345,626|43.123%|30|{AL,AR,CT,DC,DE,FL,GA,IN,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"B|1,344,149|43.076%|15|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"C| 430,653|13.801%| 5|{CO,IL,MO,NE,NM}\n",
|
||||
"A|1,345,626|43.123%|30|AL AR CT DC DE FL GA IN KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TN TX VA VT WV\n",
|
||||
"B|1,344,149|43.076%|15|AZ CA IA ID MN MT ND NV OR SD UP UT WA WI WY\n",
|
||||
"C| 430,653|13.801%| 5|CO IL MO NE NM\n",
|
||||
"∆| 1,477| 0.047%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,062|40.605%|28|{AL,AR,CT,DC,DE,FL,GA,KS,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,OK,PA,RI,SC,TX,VA,VT,WV}\n",
|
||||
"B|1,267,033|40.604%|14|{AZ,CA,IA,ID,MN,MT,ND,NV,OR,UP,UT,WA,WI,WY}\n",
|
||||
"C| 586,333|18.790%| 8|{CO,IL,IN,MO,NE,NM,SD,TN}\n",
|
||||
"A|1,267,062|40.605%|28|AL AR CT DC DE FL GA KS KY LA LP MA MD ME MS NC NH NJ NY OH OK PA RI SC TX VA VT WV\n",
|
||||
"B|1,267,033|40.604%|14|AZ CA IA ID MN MT ND NV OR UP UT WA WI WY\n",
|
||||
"C| 586,333|18.790%| 8|CO IL IN MO NE NM SD TN\n",
|
||||
"∆| 29| 0.001%|\n"
|
||||
]
|
||||
}
|
||||
@ -640,15 +670,15 @@
|
||||
"48 states ⇒ 41,735 cuts (size ≤ 8, area ≤ 624,072) ⇒ 18,642 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,348,646|43.221%|30|{AL,CT,DE,FL,GA,IA,IL,IN,KY,MA,MD,ME,MI,MN,MT,NC,ND,NH,NJ,NY,OH,PA,RI,SC,SD,TN,VA,VT,WI,WV}\n",
|
||||
"B|1,341,666|42.997%|12|{AZ,CA,CO,KS,LA,NM,NV,OK,OR,TX,UT,WA}\n",
|
||||
"C| 430,048|13.782%| 6|{AR,ID,MO,MS,NE,WY}\n",
|
||||
"A|1,348,646|43.221%|30|AL CT DE FL GA IA IL IN KY MA MD ME MI MN MT NC ND NH NJ NY OH PA RI SC SD TN VA VT WI WV\n",
|
||||
"B|1,341,666|42.997%|12|AZ CA CO KS LA NM NV OK OR TX UT WA\n",
|
||||
"C| 430,048|13.782%| 6|AR ID MO MS NE WY\n",
|
||||
"∆| 6,980| 0.224%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,267,816|40.630%|13|{AZ,CA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UT,WA}\n",
|
||||
"B|1,267,672|40.626%|28|{AL,AR,CT,DE,FL,GA,IL,IN,KY,LA,MA,MD,ME,MI,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 584,872|18.744%| 7|{CO,IA,MO,NM,OK,WI,WY}\n",
|
||||
"A|1,267,816|40.630%|13|AZ CA ID KS MN MT ND NE NV OR SD UT WA\n",
|
||||
"B|1,267,672|40.626%|28|AL AR CT DE FL GA IL IN KY LA MA MD ME MI MS NC NH NJ NY OH PA RI SC TN TX VA VT WV\n",
|
||||
"C| 584,872|18.744%| 7|CO IA MO NM OK WI WY\n",
|
||||
"∆| 144| 0.005%|\n"
|
||||
]
|
||||
}
|
||||
@ -685,15 +715,15 @@
|
||||
"49 states ⇒ 1,237 cuts (size ≤ 4, area ≤ 624,072) ⇒ 384 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|1,607,869|51.528%|18|{AZ,CA,CO,IA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"B|1,193,381|38.245%|27|{AL,AR,CT,DE,FL,GA,IN,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 319,110|10.227%| 4|{IL,MO,NM,OK}\n",
|
||||
"A|1,607,869|51.528%|18|AZ CA CO IA ID KS MN MT ND NE NV OR SD UP UT WA WI WY\n",
|
||||
"B|1,193,381|38.245%|27|AL AR CT DE FL GA IN KY LA LP MA MD ME MS NC NH NJ NY OH PA RI SC TN TX VA VT WV\n",
|
||||
"C| 319,110|10.227%| 4|IL MO NM OK\n",
|
||||
"∆| 414,488|13.283%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|1,607,869|51.528%|18|{AZ,CA,CO,IA,ID,KS,MN,MT,ND,NE,NV,OR,SD,UP,UT,WA,WI,WY}\n",
|
||||
"B|1,193,381|38.245%|27|{AL,AR,CT,DE,FL,GA,IN,KY,LA,LP,MA,MD,ME,MS,NC,NH,NJ,NY,OH,PA,RI,SC,TN,TX,VA,VT,WV}\n",
|
||||
"C| 319,110|10.227%| 4|{IL,MO,NM,OK}\n",
|
||||
"A|1,607,869|51.528%|18|AZ CA CO IA ID KS MN MT ND NE NV OR SD UP UT WA WI WY\n",
|
||||
"B|1,193,381|38.245%|27|AL AR CT DE FL GA IN KY LA LP MA MD ME MS NC NH NJ NY OH PA RI SC TN TX VA VT WV\n",
|
||||
"C| 319,110|10.227%| 4|IL MO NM OK\n",
|
||||
"∆| 414,488|13.283%|\n"
|
||||
]
|
||||
}
|
||||
@ -721,15 +751,15 @@
|
||||
"49 states ⇒ 367 cuts (size ≤ 3, area ≤ 624,072) ⇒ 89 splits.\n",
|
||||
"\n",
|
||||
"1. Split that maximizes area(B):\n",
|
||||
"A|2,393,960|76.721%|42|{AL,AR,CO,CT,DE,FL,GA,IA,IL,IN,KS,KY,LA,LP,MA,MD,ME,MN,MO,MS,MT,NC,ND,NE,NH,NJ,NM,NY,OH,OK,PA,RI,SC,SD,TN,TX,UP,VA,VT,WI,WV,WY}\n",
|
||||
"B| 443,944|14.227%| 4|{CA,NV,OR,WA}\n",
|
||||
"C| 282,456| 9.052%| 3|{AZ,ID,UT}\n",
|
||||
"A|2,393,960|76.721%|42|AL AR CO CT DE FL GA IA IL IN KS KY LA LP MA MD ME MN MO MS MT NC ND NE NH NJ NM NY OH OK PA RI SC SD TN TX UP VA VT WI WV WY\n",
|
||||
"B| 443,944|14.227%| 4|CA NV OR WA\n",
|
||||
"C| 282,456| 9.052%| 3|AZ ID UT\n",
|
||||
"∆|1,950,016|62.493%|\n",
|
||||
"\n",
|
||||
"2. Split that minimizes ∆ = area(A) - area(B):\n",
|
||||
"A|2,393,960|76.721%|42|{AL,AR,CO,CT,DE,FL,GA,IA,IL,IN,KS,KY,LA,LP,MA,MD,ME,MN,MO,MS,MT,NC,ND,NE,NH,NJ,NM,NY,OH,OK,PA,RI,SC,SD,TN,TX,UP,VA,VT,WI,WV,WY}\n",
|
||||
"B| 443,944|14.227%| 4|{CA,NV,OR,WA}\n",
|
||||
"C| 282,456| 9.052%| 3|{AZ,ID,UT}\n",
|
||||
"A|2,393,960|76.721%|42|AL AR CO CT DE FL GA IA IL IN KS KY LA LP MA MD ME MN MO MS MT NC ND NE NH NJ NM NY OH OK PA RI SC SD TN TX UP VA VT WI WV WY\n",
|
||||
"B| 443,944|14.227%| 4|CA NV OR WA\n",
|
||||
"C| 282,456| 9.052%| 3|AZ ID UT\n",
|
||||
"∆|1,950,016|62.493%|\n"
|
||||
]
|
||||
}
|
||||
@ -775,6 +805,8 @@
|
||||
"\n",
|
||||
" assert all((x in neighbors[y]) == (y in neighbors[x]) \n",
|
||||
" for x in neighbors for y in neighbors)\n",
|
||||
"\n",
|
||||
" assert neighborhood(states('CO UT')) == states('NV UT KS AZ NM ID NE OK WY CO')\n",
|
||||
" \n",
|
||||
" assert set(make_cuts(western, 3)) == {\n",
|
||||
" states('AZ ID NV'),\n",
|
||||
@ -794,6 +826,8 @@
|
||||
" \n",
|
||||
" for country in (usa48, usa49, border, western):\n",
|
||||
" assert contiguous(country) == country\n",
|
||||
"\n",
|
||||
" assert contiguous(usa50) != usa50\n",
|
||||
" \n",
|
||||
" return 'ok'\n",
|
||||
" \n",
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user