{"id":1599,"date":"2024-03-07T14:33:19","date_gmt":"2024-03-07T06:33:19","guid":{"rendered":"http:\/\/darksun190.cn\/blog\/?p=1599"},"modified":"2024-03-07T14:33:19","modified_gmt":"2024-03-07T06:33:19","slug":"%e9%ba%bb%e5%b0%86%e4%b8%ad%e8%83%a1%e5%a4%a7%e5%9b%9b%e5%96%9c%e7%9a%84%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"http:\/\/darksun190.cn\/blog\/?p=1599","title":{"rendered":"\u9ebb\u5c06\u4e2d\u80e1\u5927\u56db\u559c\u7684\u6982\u7387\u8ba1\u7b97"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u5b9a\u4e49\uff1a\u548c\u724c\u578b\u4e2d\uff0c\u6709\u4e1c\u5357\u897f\u53174\u526f\u523b\uff08\u6760\uff09\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0d\u7b97\u82b1\u724c\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u5171\u6709136\u5f20\u724c\u3002\u8ba1\u7b97\u53d1\u724c\u4e0a\u624b\u76f4\u63a5\u5929\u80e1\u5927\u56db\u559c\u7684\u6982\u7387<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\uff0c\u4e1c\u5357\u897f\u5317\u5168\u662f\u523b\u7684\u7ec4\u5408\u79cd\u7c7b\u662f$$\\begin{equation}C^4_3C^4_3C^4_3C^4_3\\tag{1}\\end{equation}$$\u4ece\u5176\u4ed6\u768430\u79cd\u724c\u578b\u91cc\u6311\u4e00\u79cd\u5f53\u5c06\u7684\u79cd\u7c7b\u662f$$C^{30}_1C^4_2$$\u76f8\u4e58\u5373\u5f97\u5230\u6240\u6709\u80e1\u5927\u56db\u559c\u7684\u7ec4\u5408\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5168\u90e8\u7ec4\u5408\u5219\u662f$$C^{136}_{14}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6982\u7387\u4e3a\u2014\u2014<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\frac{C^4_3C^4_3C^4_3C^4_3C^{30}_1C^4_2}{C^{136}_{14}}\u00a0\\approx 1e^{-12}\\%=0.0000000000001\\%$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u5e94\u4e1c\u5357\u897f\u5317\u5206\u522b\u67091\/2\/3\/4\u4e2a\u6760\u7ec4\u5408\u662f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$C^4_1C^4_3C^4_3C^4_3\u00a0\\tag{2.1}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$C^4_2C^4_3C^4_3\u00a0\\tag{2.2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$C^4_3C^4_3\u00a0\\tag{2.3}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$C^4_4\u00a0\u00a0\\tag{2.4}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6982\u7387\u662f$$\\frac{C^4_1C^4_3C^4_3C^4_3C^{30}_1C^4_2}{C^{136}_{15}}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\frac{C^4_2C^4_3C^4_3C^{30}_1C^4_2}{C^{136}_{16}}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\frac{C^4_3C^4_3C^{30}_1C^4_2}{C^{136}_{17}}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\frac{C^4_4C^{30}_1C^4_2}{C^{136}_{18}}\u00a0$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5\u4e2a\u6982\u7387\u76f8\u52a0\u5373\u662f\u603b\u6982\u7387\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u8ba8\u8bba\u8fde\u7eed\u6293\u724c\u4e0b\uff0c\u80e1\u5927\u56db\u559c\u7684\u6982\u7387\uff0c\u5148\u4e0d\u8003\u8651\u5176\u4ed6\u4eba\u7684\u7b56\u7565\u548c\u78b0\uff0c\u5047\u8bbe\u6240\u6709\u724c\u90fd\u968f\u673a\u51fa\u73b0\u4e14\u53ef\u4ee5\u88ab\u4f7f\u7528\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8eN\u5f20\u724c\u4e0d\u51fa\u73b0\u6760\u7684\u6982\u7387\uff0c\u9700\u898112\u5f20\u51d1\u62104\u4e2a\u523b\u5b50\uff0c\u7ec4\u5408\u6570\u91cf\u516c\u5f0f(1)\u8ba1\u7b97\u76f8\u540c\u4e3a$$C^4_3C^4_3C^4_3C^4_3$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5269\u4f59\u7684N-12\u724c\u91cc\u5fc5\u987b\u51fa\u73b0\u81f3\u5c11\u4e00\u4e2a\u5bf9\u5b50\uff0c\u56e0\u4e3a3\u5f20\u4e5f\u662f\u5141\u8bb8\u7684\uff0c\u4e14\u4f1a\u51fa\u73b02\u4e2a\u5bf9\u5b50\u6216\u8005\u66f4\u590d\u6742\u60c5\u51b5\uff0c\u6240\u4ee5\u7528\u4e92\u65a5\u96c6\u5408\u2014\u2014$$\u603b\u7684\u7ec4\u5408\u6570\u91cf-\u51d1\u4e0d\u6210\u5bf9\u5b50\u7684\u7ec4\u5408\u6570\u91cf$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$C^{136-16}_{N-12}-C^{30}_N(C^4_1)^N\\tag{3}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u4e2d\u5f53N>30\u65f6\uff0c\u6839\u636e\u62bd\u5c49\u539f\u7406\u5fc5\u6709\u4e00\u4e2a\u5bf9\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f97\u5230\u516c\u5f0f\uff0c\u5728\u6253\u4e71\u724c\u5e8f\u4e2d\u524dN\u5f20\u724c\uff0c\u53ef\u4ee5\u5f97\u5230\u65e0\u6760\u5927\u56db\u559c\u7684\u6982\u7387\u4e3a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_0 = \\frac{C^4_3C^4_3C^4_3C^4_3(C^{136-16}_{N-12}-C^{30}_{N-12}(C^4_1)^{N-12})}{C^{136}_N}\\tag{4.1}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u6709\u6760\u5927\u56db\u559c\uff0c\u56db\u98ce\u7684\u7ec4\u5408\u5982\u5f0f(2.1-2.4)\uff0c\u5c06\u7684\u7ec4\u5408\u5982\u5f0f(3)\uff0c\u5bf9\u5e94\u7684\u6982\u7387\u4e3a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_1 = \\frac{C^4_1C^4_3C^4_3C^4_3(C^{136-16}_{N-13}-C^{30}_{N-13}(C^4_1)^{N-13})}{C^{136}_N}\\tag{4.2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_2 = \\frac{C^4_2C^4_3C^4_3(C^{136-16}_{N-14}-C^{30}_{N-14}(C^4_1)^{N-14})}{C^{136}_N}\\tag{4.3}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_3 = \\frac{C^4_3C^4_3(C^{136-16}_{N-15}-C^{30}_{N-15}(C^4_1)^{N-15})}{C^{136}_N}\\tag{4.4}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P_4 = \\frac{C^4_4(C^{136-16}_{N-16}-C^{30}_{N-16}(C^4_1)^{N-16})}{C^{136}_N}\\tag{4.5}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\\(N\\geq 18\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P=\\sum_{i=0}^4P_i$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$P=\\frac{C^4_3C^4_3C^4_3C^4_3(C^{136-16}_{N-12}-C^{30}_{N-12}(C^4_1)^{N-12})+C^4_1C^4_3C^4_3C^4_3(C^{136-16}_{N-13}-C^{30}_{N-13}(C^4_1)^{N-13})+C^4_2C^4_3C^4_3(C^{136-16}_{N-14}-C^{30}_{N-14}(C^4_1)^{N-14})+C^4_3C^4_3(C^{136-16}_{N-15}-C^{30}_{N-15}(C^4_1)^{N-15})+C^4_4(C^{136-16}_{N-16}-C^{30}_{N-16}(C^4_1)^{N-16})}{C^{136}_N}$$<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code class=\"\">    public static void combi(int n)\n    {\n        if(n&lt;=18 || n>=136)\n        {\n            return;\n        }\n        \/\/there're 5 situations for dasixi\n        \/\/ 1. each of 4 wind tile have 3 same tiles but not all 4\n        \/\/denominator is 136 choose n\n        double denominator = Combinatorics.Combinations(136, n);\n        double numerator = 4*4*4*4;\n        numerator *= Combinatorics.Combinations(120,n-12) - Combinatorics.Combinations(30,n-12)*Math.Pow(4,n-12);\n\n\n        \/\/ 2. 1 of 4 wind, have 4 same tiles as a Gong, other 3 have 3 same tiles\n        double numerator1 = Combinatorics.Combinations(4,1) *4*4*4;\n        numerator1 *= Combinatorics.Combinations(120,n-13) - Combinatorics.Combinations(30,n-13)*Math.Pow(4,n-13);\n        numerator += numerator1;\n\n        \/\/ 3. 2 of 4 wind, have 4 same tiles as a Gong, other 2 have 3 same tiles\n        double numerator2 = Combinatorics.Combinations(4,2) *4*4;\n        numerator2 *= Combinatorics.Combinations(120,n-14) - Combinatorics.Combinations(30,n-14)*Math.Pow(4,n-14);\n        numerator += numerator2;\n\n        \/\/ 4. 3 of 4 wind, have 4 same tiles as a Gong, other 1 have 3 same tiles\n        double numerator3 = Combinatorics.Combinations(4,3) *4;\n        numerator3 *= Combinatorics.Combinations(120,n-15) - Combinatorics.Combinations(30,n-15)*Math.Pow(4,n-15);\n        numerator += numerator3;\n\n        \/\/ 5. 4 of 4 wind, have 4 same tiles as a Gong\n        double numerator4 = Combinatorics.Combinations(4,4);\n        numerator4 *= Combinatorics.Combinations(120,n-16) - Combinatorics.Combinations(30,n-16)*Math.Pow(4,n-16);\n        numerator += numerator4;\n        \n        double result = numerator\/denominator;\n\n        \/\/console write result as percentage\n        Console.WriteLine(string.Format(\"{1} -- {0:P}\", result,n));\n    }<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6982\u7387\u66f2\u7ebf\uff08\u7ea2\u8272\uff09\u548c\u968f\u673a\u8fd0\u884c100\u4e07\u6b21\u751f\u6210\u7684\u66f2\u7ebf\uff08\u7eff\u8272\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"http:\/\/darksun190.cn\/blog\/wp-content\/uploads\/2024\/03\/Figure_1.png\" alt=\"\" class=\"wp-image-1661\" srcset=\"http:\/\/darksun190.cn\/blog\/wp-content\/uploads\/2024\/03\/Figure_1.png 640w, http:\/\/darksun190.cn\/blog\/wp-content\/uploads\/2024\/03\/Figure_1-300x225.png 300w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 984px) 61vw, (max-width: 1362px) 45vw, 600px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u5b9a\u4e49\uff1a\u548c\u724c\u578b\u4e2d\uff0c\u6709\u4e1c\u5357\u897f\u53174\u526f\u523b\uff08\u6760\uff09\u5b50\u3002 \u4e0d\u7b97\u82b1\u724c\u7684\u60c5\u51b5\u4e0b\uff0c\u4e00\u5171\u6709136\u5f20\u724c\u3002\u8ba1\u7b97\u53d1\u724c\u4e0a\u624b\u76f4\u63a5\u5929\u80e1\u5927\u56db\u559c\u7684\u6982 &hellip; <a href=\"http:\/\/darksun190.cn\/blog\/?p=1599\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u9ebb\u5c06\u4e2d\u80e1\u5927\u56db\u559c\u7684\u6982\u7387\u8ba1\u7b97\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[4],"tags":[],"class_list":["post-1599","post","type-post","status-publish","format-standard","hentry","category-diary"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1599","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1599"}],"version-history":[{"count":60,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1599\/revisions"}],"predecessor-version":[{"id":1662,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1599\/revisions\/1662"}],"wp:attachment":[{"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1599"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/darksun190.cn\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}