From 3832de98f4cc91d8e075bf6ac065ce83fab187da Mon Sep 17 00:00:00 2001 From: Peter Norvig Date: Tue, 9 Jun 2020 23:12:34 -0700 Subject: [PATCH] Add files via upload --- ipynb/How To Count Things.ipynb | 387 +++++++++++++++++--------------- 1 file changed, 200 insertions(+), 187 deletions(-) diff --git a/ipynb/How To Count Things.ipynb b/ipynb/How To Count Things.ipynb index 913585c..afbfd98 100644 --- a/ipynb/How To Count Things.ipynb +++ b/ipynb/How To Count Things.ipynb @@ -386,8 +386,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 15.2 ms, sys: 1.9 ms, total: 17.1 ms\n", - "Wall time: 85 ms\n" + "CPU times: user 11.3 ms, sys: 643 µs, total: 12 ms\n", + "Wall time: 12.6 ms\n" ] }, { @@ -844,25 +844,11 @@ " 8: 117440505,\n", " 9: 387420481,\n", " 10: 89999999991,\n", - " 11: 285311670601,\n", - " 12: 98077104930805,\n", - " 13: 302875106592241,\n", - " 14: 144456088732254195,\n", - " 15: 437893890380859361,\n", - " 16: 276701161105643274225,\n", - " 17: 827240261886336764161,\n", - " 18: 668888937280041138782191,\n", - " 19: 1978419655660313589123961,\n", " 20: 1992294399999999999999999981,\n", - " 21: 5842587018385982521381124401,\n", - " 22: 7169985424648610705329581195243,\n", - " 23: 20880467999847912034355032910545,\n", - " 24: 30675922867556534862328873875406825,\n", - " 25: 88817841970012523233890533447265601,\n", - " 26: 153902989505178932769916857210005094375,\n", - " 27: 443426488243037769948249630619149892777,\n", - " 28: 894929124057841121289463662840844356943845,\n", - " 29: 2567686153161211134561828214731016126483441}" + " 30: 5970842830744820999999999999999999999999999971,\n", + " 40: 471481069649705378135408639999999999999999999999999999999999999961,\n", + " 50: 435207425653061363846063613891601562499999999999999999999999999999999999999999999999951,\n", + " 60: 2883547000860666191870042384152701628073990160383999999999999999999999999999999999999999999999999999999999941}" ] }, "execution_count": 26, @@ -873,7 +859,7 @@ "source": [ "assert same(calculate_coconuts, enumerate_coconuts, range(1, 8))\n", "\n", - "{p: calculate_coconuts(p) for p in range(1, 30)}" + "{p: calculate_coconuts(p) for p in [*range(1, 10), *range(10, 61, 10)]}" ] }, { @@ -896,6 +882,33 @@ "calculate_coconuts(1000)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That's a crazy number. Almost $10^{3003}$, and you surely noticed all the \"9\"s and the \"001\" at the end, but did you notice the lone \"8\" in the third digit? What's that doing there? Actually it's simple: you can think of the formula as first giving us $999 \\times 1000^{1000}$, which is \"999\" followed by 3000 \"0\"s, and then subtracting 999, so that third \"9\" is where we borrow 1, and leads to all the following \"0\"s becoming \"9\"s." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(Counter({'9': 2999, '8': 1, '0': 2, '1': 1}), 1.0)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Counter(str(calculate_coconuts(1000))), log(10, 10)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -907,7 +920,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 29, "metadata": {}, "outputs": [ { @@ -922,7 +935,7 @@ " 7: [823537, 6588338, 12353139, 18117940, 23882741, 29647542, 35412343]}" ] }, - "execution_count": 28, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -944,7 +957,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -956,7 +969,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 31, "metadata": {}, "outputs": [ { @@ -971,7 +984,7 @@ " 7: (823537, {5764801})}" ] }, - "execution_count": 30, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -989,7 +1002,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 32, "metadata": {}, "outputs": [ { @@ -998,7 +1011,7 @@ "{1: 1, 2: 8, 3: 81, 4: 1024, 5: 15625, 6: 279936, 7: 5764801}" ] }, - "execution_count": 31, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -1028,7 +1041,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -1050,7 +1063,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 34, "metadata": {}, "outputs": [ { @@ -1066,7 +1079,7 @@ " 7: 86645}" ] }, - "execution_count": 33, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -1077,7 +1090,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 35, "metadata": {}, "outputs": [], "source": [ @@ -1093,7 +1106,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 36, "metadata": {}, "outputs": [ { @@ -1107,7 +1120,7 @@ " 6: {0: 6, 1: 51899, 2: 45419, 3: 40019, 4: 35519, 5: 31769, 6: 28644}}" ] }, - "execution_count": 35, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } @@ -1133,7 +1146,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 37, "metadata": {}, "outputs": [], "source": [ @@ -1154,7 +1167,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 38, "metadata": {}, "outputs": [ { @@ -1163,7 +1176,7 @@ "True" ] }, - "execution_count": 37, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1174,7 +1187,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 39, "metadata": {}, "outputs": [ { @@ -1183,7 +1196,7 @@ "False" ] }, - "execution_count": 38, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -1194,7 +1207,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 40, "metadata": {}, "outputs": [ { @@ -1203,7 +1216,7 @@ "True" ] }, - "execution_count": 39, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -1214,7 +1227,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 41, "metadata": {}, "outputs": [ { @@ -1223,7 +1236,7 @@ "False" ] }, - "execution_count": 40, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -1241,7 +1254,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 42, "metadata": {}, "outputs": [ { @@ -1250,7 +1263,7 @@ "{0: 1, 1: 1, 2: 2, 3: 5, 4: 15, 5: 52, 6: 203, 7: 877}" ] }, - "execution_count": 41, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -1274,7 +1287,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 43, "metadata": {}, "outputs": [], "source": [ @@ -1297,7 +1310,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 44, "metadata": {}, "outputs": [ { @@ -1306,7 +1319,7 @@ "Counter({0: 0, 1: 1, 2: 3, 3: 1})" ] }, - "execution_count": 43, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -1326,7 +1339,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 45, "metadata": {}, "outputs": [ { @@ -1335,7 +1348,7 @@ "True" ] }, - "execution_count": 44, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -1353,7 +1366,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 46, "metadata": {}, "outputs": [ { @@ -1362,7 +1375,7 @@ "29899013356824084214804223538976464839473928098212305047832737888945413625123259596641165872540391578300639147082986964028021802248993382881013411276574829121155811755170830666039838837273971971676782389800810361809319250755399325279656765435255999301529770267107281619733800281695881540007577899106878679451165492535930459233713316342551545242815802367257284852612201081016386308535990145447341800455472334713864080523978960296365736999295932080550928561633025800627524911700149562106895897725047744775812241800937310491797818107578233924187312824632629095993832334781713007323483688294825326897450386817327410532925074613888321264138083842196202242956001314953449497244271843922741908252107652201346933889741070435350690242062001522697855278356012055718392851567813397125419144780476479197990921602015873703820769182603836788465785093563686025690269802153802436873530877006737154523895273029510238745997356292232631282773748762989386003970214423843947094021177989737557020369751561595003372955621411858485959813344799967960196238368337022346946771703060269288691694028444791203978533454759410587065022546491518871238421560825907135885619221776405898771057270555581449229994215739476758785884545723062263992367750091319644861547658472282284005892044371587560711880627741139497818835632120761570174928529697397267899554407350161283097123211048049269727655279783900702416095132827766428865017653366696304131436690232979453876337599721772897049270230544262611264917393374756384152784943607952408782612639220380791445272655004475989064276373713608901650681165467490310898804916827069427310961109285035545084791339423266482359955663377201515204340817580915468489969181643341007197836481461051798995640789292580146918580703759556634019451731530034209189203377522668309771129566108101617727442045637098112678864654309987785463307376544339506878267267349348171320834971956806668304099159992067385998690820326902473886782781499414773179" ] }, - "execution_count": 45, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -1390,7 +1403,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 47, "metadata": {}, "outputs": [], "source": [ @@ -1413,7 +1426,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 48, "metadata": {}, "outputs": [], "source": [ @@ -1431,7 +1444,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 49, "metadata": {}, "outputs": [ { @@ -1440,7 +1453,7 @@ "True" ] }, - "execution_count": 48, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -1475,7 +1488,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 50, "metadata": {}, "outputs": [ { @@ -1484,7 +1497,7 @@ "945.0" ] }, - "execution_count": 49, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } @@ -1504,7 +1517,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 51, "metadata": {}, "outputs": [ { @@ -1513,7 +1526,7 @@ "945" ] }, - "execution_count": 50, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -1533,7 +1546,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 52, "metadata": {}, "outputs": [ { @@ -1542,7 +1555,7 @@ "945" ] }, - "execution_count": 51, + "execution_count": 52, "metadata": {}, "output_type": "execute_result" } @@ -1587,7 +1600,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 53, "metadata": {}, "outputs": [ { @@ -1596,7 +1609,7 @@ "3003" ] }, - "execution_count": 52, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -1615,7 +1628,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -1624,7 +1637,7 @@ "3003" ] }, - "execution_count": 53, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1645,7 +1658,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 55, "metadata": {}, "outputs": [ { @@ -1654,7 +1667,7 @@ "3003" ] }, - "execution_count": 54, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -1681,7 +1694,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 56, "metadata": {}, "outputs": [ { @@ -1690,7 +1703,7 @@ "90548514656103281165404177077484163874504589675413336841320" ] }, - "execution_count": 55, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -1710,7 +1723,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 57, "metadata": {}, "outputs": [], "source": [ @@ -1738,7 +1751,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 58, "metadata": {}, "outputs": [ { @@ -1747,7 +1760,7 @@ "3003" ] }, - "execution_count": 57, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1772,7 +1785,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 59, "metadata": {}, "outputs": [ { @@ -1781,7 +1794,7 @@ "2" ] }, - "execution_count": 58, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -1806,7 +1819,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 60, "metadata": {}, "outputs": [ { @@ -1815,7 +1828,7 @@ "122" ] }, - "execution_count": 59, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } @@ -1840,7 +1853,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 61, "metadata": {}, "outputs": [ { @@ -1849,7 +1862,7 @@ "627084695807418" ] }, - "execution_count": 60, + "execution_count": 61, "metadata": {}, "output_type": "execute_result" } @@ -1885,7 +1898,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 62, "metadata": {}, "outputs": [ { @@ -1894,7 +1907,7 @@ "11468451846417028993973305727890751485" ] }, - "execution_count": 61, + "execution_count": 62, "metadata": {}, "output_type": "execute_result" } @@ -1992,7 +2005,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 63, "metadata": {}, "outputs": [], "source": [ @@ -2019,7 +2032,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 64, "metadata": {}, "outputs": [ { @@ -2035,7 +2048,7 @@ " Path(end=(0, 1), n=2, squares={(0, 1): 4, (0, 0): 3, (1, 0): 2, (1, 1): 1})]" ] }, - "execution_count": 63, + "execution_count": 64, "metadata": {}, "output_type": "execute_result" } @@ -2053,7 +2066,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 65, "metadata": {}, "outputs": [], "source": [ @@ -2077,7 +2090,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 66, "metadata": { "scrolled": false }, @@ -2157,7 +2170,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 67, "metadata": {}, "outputs": [ { @@ -2177,7 +2190,7 @@ " 12: 268}" ] }, - "execution_count": 66, + "execution_count": 67, "metadata": {}, "output_type": "execute_result" } @@ -2198,7 +2211,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 68, "metadata": {}, "outputs": [], "source": [ @@ -2207,7 +2220,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 69, "metadata": {}, "outputs": [ { @@ -2216,7 +2229,7 @@ "True" ] }, - "execution_count": 68, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } @@ -2245,7 +2258,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 70, "metadata": {}, "outputs": [], "source": [ @@ -2261,7 +2274,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 71, "metadata": {}, "outputs": [ { @@ -2270,7 +2283,7 @@ "960" ] }, - "execution_count": 70, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2290,7 +2303,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 72, "metadata": {}, "outputs": [ { @@ -2299,7 +2312,7 @@ "960.0" ] }, - "execution_count": 71, + "execution_count": 72, "metadata": {}, "output_type": "execute_result" } @@ -2321,7 +2334,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 73, "metadata": {}, "outputs": [], "source": [ @@ -2346,7 +2359,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 74, "metadata": {}, "outputs": [], "source": [ @@ -2368,7 +2381,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 75, "metadata": {}, "outputs": [ { @@ -2377,7 +2390,7 @@ "4" ] }, - "execution_count": 74, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -2388,7 +2401,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 76, "metadata": {}, "outputs": [ { @@ -2397,7 +2410,7 @@ "13" ] }, - "execution_count": 75, + "execution_count": 76, "metadata": {}, "output_type": "execute_result" } @@ -2408,7 +2421,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 77, "metadata": {}, "outputs": [ { @@ -2417,7 +2430,7 @@ "252" ] }, - "execution_count": 76, + "execution_count": 77, "metadata": {}, "output_type": "execute_result" } @@ -2435,7 +2448,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 78, "metadata": {}, "outputs": [ { @@ -2444,7 +2457,7 @@ "13398445413854501" ] }, - "execution_count": 77, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" } @@ -2472,7 +2485,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 79, "metadata": { "scrolled": false }, @@ -2514,7 +2527,7 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 80, "metadata": {}, "outputs": [ { @@ -2543,7 +2556,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 81, "metadata": {}, "outputs": [ { @@ -2587,7 +2600,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 82, "metadata": {}, "outputs": [ { @@ -2626,7 +2639,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 83, "metadata": {}, "outputs": [], "source": [ @@ -2645,7 +2658,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 84, "metadata": {}, "outputs": [], "source": [ @@ -2665,7 +2678,7 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 85, "metadata": {}, "outputs": [ { @@ -2677,7 +2690,7 @@ " Purse({1: 11})]" ] }, - "execution_count": 84, + "execution_count": 85, "metadata": {}, "output_type": "execute_result" } @@ -2688,7 +2701,7 @@ }, { "cell_type": "code", - "execution_count": 85, + "execution_count": 86, "metadata": {}, "outputs": [ { @@ -2702,7 +2715,7 @@ " Purse({1: 15})]" ] }, - "execution_count": 85, + "execution_count": 86, "metadata": {}, "output_type": "execute_result" } @@ -2713,7 +2726,7 @@ }, { "cell_type": "code", - "execution_count": 86, + "execution_count": 87, "metadata": {}, "outputs": [ { @@ -2734,7 +2747,7 @@ " Purse({1: 25})]" ] }, - "execution_count": 86, + "execution_count": 87, "metadata": {}, "output_type": "execute_result" } @@ -2756,7 +2769,7 @@ }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 88, "metadata": {}, "outputs": [], "source": [ @@ -2775,7 +2788,7 @@ }, { "cell_type": "code", - "execution_count": 88, + "execution_count": 89, "metadata": {}, "outputs": [ { @@ -2787,7 +2800,7 @@ " Purse({1: 11})]" ] }, - "execution_count": 88, + "execution_count": 89, "metadata": {}, "output_type": "execute_result" } @@ -2798,7 +2811,7 @@ }, { "cell_type": "code", - "execution_count": 89, + "execution_count": 90, "metadata": {}, "outputs": [ { @@ -2807,7 +2820,7 @@ "[Purse({1: 1, 10: 1})]" ] }, - "execution_count": 89, + "execution_count": 90, "metadata": {}, "output_type": "execute_result" } @@ -2818,7 +2831,7 @@ }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 91, "metadata": {}, "outputs": [ { @@ -2827,7 +2840,7 @@ "[Purse({25: 1})]" ] }, - "execution_count": 90, + "execution_count": 91, "metadata": {}, "output_type": "execute_result" } @@ -2838,7 +2851,7 @@ }, { "cell_type": "code", - "execution_count": 91, + "execution_count": 92, "metadata": {}, "outputs": [ { @@ -2847,7 +2860,7 @@ "[]" ] }, - "execution_count": 91, + "execution_count": 92, "metadata": {}, "output_type": "execute_result" } @@ -2874,7 +2887,7 @@ }, { "cell_type": "code", - "execution_count": 92, + "execution_count": 93, "metadata": {}, "outputs": [ { @@ -2883,7 +2896,7 @@ "152096" ] }, - "execution_count": 92, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" } @@ -2914,15 +2927,15 @@ }, { "cell_type": "code", - "execution_count": 93, + "execution_count": 94, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 29.5 s, sys: 2.24 s, total: 31.7 s\n", - "Wall time: 40.2 s\n" + "CPU times: user 33.2 s, sys: 2.42 s, total: 35.7 s\n", + "Wall time: 49.1 s\n" ] } ], @@ -2939,7 +2952,7 @@ }, { "cell_type": "code", - "execution_count": 94, + "execution_count": 95, "metadata": {}, "outputs": [], "source": [ @@ -2948,7 +2961,7 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 96, "metadata": {}, "outputs": [ { @@ -2967,7 +2980,7 @@ " (25, 10, 5, 1): 4.7}" ] }, - "execution_count": 95, + "execution_count": 96, "metadata": {}, "output_type": "execute_result" } @@ -2989,7 +3002,7 @@ }, { "cell_type": "code", - "execution_count": 96, + "execution_count": 97, "metadata": {}, "outputs": [], "source": [ @@ -3024,7 +3037,7 @@ }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 98, "metadata": {}, "outputs": [ { @@ -3033,7 +3046,7 @@ "6" ] }, - "execution_count": 97, + "execution_count": 98, "metadata": {}, "output_type": "execute_result" } @@ -3044,7 +3057,7 @@ }, { "cell_type": "code", - "execution_count": 98, + "execution_count": 99, "metadata": {}, "outputs": [ { @@ -3053,7 +3066,7 @@ "3" ] }, - "execution_count": 98, + "execution_count": 99, "metadata": {}, "output_type": "execute_result" } @@ -3064,7 +3077,7 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 100, "metadata": {}, "outputs": [ { @@ -3073,7 +3086,7 @@ "Purse({25: 1, 1: 5})" ] }, - "execution_count": 99, + "execution_count": 100, "metadata": {}, "output_type": "execute_result" } @@ -3091,7 +3104,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 101, "metadata": {}, "outputs": [ { @@ -3110,7 +3123,7 @@ " (25, 10, 5, 1): (4.7, 4.7, True)}" ] }, - "execution_count": 100, + "execution_count": 101, "metadata": {}, "output_type": "execute_result" } @@ -3140,7 +3153,7 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 102, "metadata": {}, "outputs": [], "source": [ @@ -3173,7 +3186,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 103, "metadata": {}, "outputs": [ { @@ -3182,7 +3195,7 @@ "(5.6928, 4.441767365800834)" ] }, - "execution_count": 102, + "execution_count": 103, "metadata": {}, "output_type": "execute_result" } @@ -3193,7 +3206,7 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 104, "metadata": {}, "outputs": [ { @@ -3202,7 +3215,7 @@ "(6.47408, 4.9299959784987575)" ] }, - "execution_count": 103, + "execution_count": 104, "metadata": {}, "output_type": "execute_result" } @@ -3222,7 +3235,7 @@ }, { "cell_type": "code", - "execution_count": 104, + "execution_count": 105, "metadata": {}, "outputs": [], "source": [ @@ -3236,7 +3249,7 @@ }, { "cell_type": "code", - "execution_count": 105, + "execution_count": 106, "metadata": {}, "outputs": [ { @@ -3245,7 +3258,7 @@ "(94, [1, 1, 1, 1, 5, 10, 25, 50])" ] }, - "execution_count": 105, + "execution_count": 106, "metadata": {}, "output_type": "execute_result" } @@ -3263,7 +3276,7 @@ }, { "cell_type": "code", - "execution_count": 106, + "execution_count": 107, "metadata": {}, "outputs": [], "source": [ @@ -3278,7 +3291,7 @@ }, { "cell_type": "code", - "execution_count": 107, + "execution_count": 108, "metadata": {}, "outputs": [ { @@ -3328,7 +3341,7 @@ }, { "cell_type": "code", - "execution_count": 108, + "execution_count": 109, "metadata": {}, "outputs": [], "source": [ @@ -3355,7 +3368,7 @@ }, { "cell_type": "code", - "execution_count": 109, + "execution_count": 110, "metadata": {}, "outputs": [ { @@ -3364,7 +3377,7 @@ "Dist({1: 1.0})" ] }, - "execution_count": 109, + "execution_count": 110, "metadata": {}, "output_type": "execute_result" } @@ -3382,7 +3395,7 @@ }, { "cell_type": "code", - "execution_count": 110, + "execution_count": 111, "metadata": {}, "outputs": [ { @@ -3391,7 +3404,7 @@ "Dist({2: 0.5, 1: 0.5})" ] }, - "execution_count": 110, + "execution_count": 111, "metadata": {}, "output_type": "execute_result" } @@ -3409,7 +3422,7 @@ }, { "cell_type": "code", - "execution_count": 111, + "execution_count": 112, "metadata": {}, "outputs": [ { @@ -3467,7 +3480,7 @@ " 1: 0.08039316907795838})" ] }, - "execution_count": 111, + "execution_count": 112, "metadata": {}, "output_type": "execute_result" } @@ -3485,7 +3498,7 @@ }, { "cell_type": "code", - "execution_count": 112, + "execution_count": 113, "metadata": {}, "outputs": [ { @@ -3494,7 +3507,7 @@ "7.958923738717876" ] }, - "execution_count": 112, + "execution_count": 113, "metadata": {}, "output_type": "execute_result" } @@ -3518,7 +3531,7 @@ }, { "cell_type": "code", - "execution_count": 113, + "execution_count": 114, "metadata": {}, "outputs": [ { @@ -3527,7 +3540,7 @@ "25.008494650139617" ] }, - "execution_count": 113, + "execution_count": 114, "metadata": {}, "output_type": "execute_result" } @@ -3545,7 +3558,7 @@ }, { "cell_type": "code", - "execution_count": 114, + "execution_count": 115, "metadata": {}, "outputs": [ { @@ -3554,7 +3567,7 @@ "0.5148807410710244" ] }, - "execution_count": 114, + "execution_count": 115, "metadata": {}, "output_type": "execute_result" } @@ -3573,7 +3586,7 @@ }, { "cell_type": "code", - "execution_count": 115, + "execution_count": 116, "metadata": {}, "outputs": [ { @@ -3630,7 +3643,7 @@ }, { "cell_type": "code", - "execution_count": 116, + "execution_count": 117, "metadata": {}, "outputs": [], "source": [ @@ -3653,7 +3666,7 @@ }, { "cell_type": "code", - "execution_count": 117, + "execution_count": 118, "metadata": {}, "outputs": [ { @@ -3662,7 +3675,7 @@ "Matrix(count=5000, d1=10, d2=5)" ] }, - "execution_count": 117, + "execution_count": 118, "metadata": {}, "output_type": "execute_result" } @@ -3675,7 +3688,7 @@ }, { "cell_type": "code", - "execution_count": 118, + "execution_count": 119, "metadata": {}, "outputs": [ { @@ -3684,7 +3697,7 @@ "Matrix(count=10000, d1=100, d2=20)" ] }, - "execution_count": 118, + "execution_count": 119, "metadata": {}, "output_type": "execute_result" } @@ -3695,7 +3708,7 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 120, "metadata": {}, "outputs": [ { @@ -3704,7 +3717,7 @@ "Matrix(count=6000, d1=10, d2=20)" ] }, - "execution_count": 119, + "execution_count": 120, "metadata": {}, "output_type": "execute_result" } @@ -3715,7 +3728,7 @@ }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 121, "metadata": {}, "outputs": [ { @@ -3724,7 +3737,7 @@ "Matrix(count=30000, d1=10, d2=20)" ] }, - "execution_count": 120, + "execution_count": 121, "metadata": {}, "output_type": "execute_result" } @@ -3755,7 +3768,7 @@ }, { "cell_type": "code", - "execution_count": 121, + "execution_count": 122, "metadata": {}, "outputs": [], "source": [ @@ -3771,7 +3784,7 @@ }, { "cell_type": "code", - "execution_count": 122, + "execution_count": 123, "metadata": {}, "outputs": [ { @@ -3784,7 +3797,7 @@ " ('ABCDE', 'F')]" ] }, - "execution_count": 122, + "execution_count": 123, "metadata": {}, "output_type": "execute_result" } @@ -3795,7 +3808,7 @@ }, { "cell_type": "code", - "execution_count": 123, + "execution_count": 124, "metadata": {}, "outputs": [ { @@ -3804,7 +3817,7 @@ "Matrix(count=6000, d1=10, d2=20)" ] }, - "execution_count": 123, + "execution_count": 124, "metadata": {}, "output_type": "execute_result" } @@ -3815,7 +3828,7 @@ }, { "cell_type": "code", - "execution_count": 124, + "execution_count": 125, "metadata": {}, "outputs": [ { @@ -3824,7 +3837,7 @@ "Matrix(count=75350, d1=10, d2=20)" ] }, - "execution_count": 124, + "execution_count": 125, "metadata": {}, "output_type": "execute_result" } @@ -3844,7 +3857,7 @@ }, { "cell_type": "code", - "execution_count": 125, + "execution_count": 126, "metadata": {}, "outputs": [], "source": [ @@ -3857,7 +3870,7 @@ }, { "cell_type": "code", - "execution_count": 126, + "execution_count": 127, "metadata": {}, "outputs": [ { @@ -3866,7 +3879,7 @@ "Matrix(count=3407000, d1=10, d2=20)" ] }, - "execution_count": 126, + "execution_count": 127, "metadata": {}, "output_type": "execute_result" }