{"id":1387,"date":"2023-02-11T14:43:52","date_gmt":"2023-02-11T06:43:52","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=1387"},"modified":"2023-02-15T10:11:36","modified_gmt":"2023-02-15T02:11:36","slug":"gambling","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/gambling\/","title":{"rendered":"\u6b62\u635f\u6295\u6ce8\u6cd5"},"content":{"rendered":"\n<p>\u6b62\u635f\u6295\u6ce8\u6cd5\u7684\u6838\u5fc3\u5c31\u662f\uff1a\u672c\u6b21\u6295\u6ce8\u7684\u76c8\u5229\\(I\\)\uff08Incoming\uff09\uff0c\u5fc5\u987b\u81f3\u5c11\u80fd\u8986\u76d6\u4e0a\u6b21\u7684\u6210\u672c\\(C\\)\uff08Cost\uff09\u3002\u8fd9\u4e2a\u4e5f\u662f\u5546\u4e1a\u884c\u4e3a\u4e2d\u7684\u5178\u578b\u8fb9\u9645\u5229\u6da6\u95ee\u9898\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u731c\u6b63\u53cd<\/h2>\n\n\n\n<p>\u4ee5\u6700\u7b80\u5355\u7684\u629b\u786c\u5e01\u731c\u6b63\u53cd\u4e3a\u4f8b\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\uff1a\u8d4c\u5f92\u6bcf\u6b21\u53ef\u4ee5\u6295\u6ce8\\(p\\)\uff08\\(p&gt;0\\)\uff09\u5143\u3002\u5982\u679c\u731c\u9519\uff0c\u5e84\u5bb6\u5c06\u6536\u8d70\u8d4c\u5f92\u6295\u6ce8\u7684\u5168\u90e8\u91d1\u989d\u3002\u5982\u679c\u731c\u5bf9\uff0c\u90a3\u4e48\u8d4c\u5f92\u53ef\u4ee5\u83b7\u5f97\\(kp\\)\uff08\\(k&gt;0\\)\uff09\u5143\u5956\u52b1\u3002<\/p>\n\n\n\n<p>\u8d4c\u5f92\u4f7f\u7528\u6b62\u635f\u6295\u6ce8\u6cd5\u3002\u5176\u6295\u6ce8\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u4e0b\u6ce8<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u6295\u5165\\(C\\)<\/td><td>\u731c\u5bf9\\(I\\)<\/td><td>\u731c\u9519<\/td><\/tr><tr><td>\u7b2c\u4e00\u6b21<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(p\\)\u5143<\/td><td>\u83b7\u5f97\\(k \\cdot p\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(p\\)\u5143<\/td><\/tr><tr><td>\u7b2c\u4e8c\u6b21<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(2p\\)\u5143<\/td><td>\u83b7\u5f97\\(k\\cdot 2p\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(2p\\)\u5143<\/td><\/tr><tr><td>\u7b2c\u4e09\u6b21<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(3p\\)\u5143<\/td><td>\u83b7\u5f97\\(k \\cdot 3p\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(3p\\)\u5143<\/td><\/tr><tr><td>\u2026\u2026<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u2026\u2026<\/td><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><\/tr><tr><td>\u7b2c\\((n-1)\\)\u6b21<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\((n-1)p\\)\u5143<\/td><td>\u83b7\u5f97\\(k \\cdot (n-1)p\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\((n-1)p\\)\u5143<\/td><\/tr><tr><td>\u7b2c\\(n\\)\u6b21<\/td><td class=\"has-text-align-left\" data-align=\"left\">\\(np\\)\u5143<\/td><td>\u83b7\u5f97\\(k \\cdot np\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(np\\)\u5143<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u4ece\u4e0a\u8ff0\u6570\u636e\u8868\u4e2d\u53ef\u4ee5\u83b7\u5f97\u4e09\u4e2a\u516c\u5f0f\uff1a<\/p>\n\n\n\n<p>\\[ \\left \\{ \\begin{array}{lr} k &gt; 0 &amp; \u2026\u2026(1) \\\\ k \\cdot p \\ge p &amp; \u2026\u2026(2) \\\\ k \\cdot np \\ge np &amp; \u2026\u2026 (3)\\end{array} \\right. \\]<\/p>\n\n\n\n<p>\u5f0f\u5b50\\((1)\\)\u4fdd\u8bc1\u6536\u76ca\u5fc5\u987b\u4e3a\u6b63\u7684\uff0c\u5426\u5219\u8fd9\u4e2a\u6e38\u620f\u4e0d\u4f1a\u6709\u8d4c\u5f92\u53c2\u4e0e\uff1b\u5f0f\u5b50\\((2)\\)\u4fdd\u8bc1\u7b2c\u4e00\u6b21\u6536\u76ca\u5fc5\u987b\u80fd\u8986\u76d6\u6210\u672c\uff0c\u5426\u5219\u8fd9\u4e2a\u6e38\u620f\u4e0d\u4f1a\u6709\u8d4c\u5f92\u53c2\u4e0e\uff1b\u6700\u540e\u4e00\u4e2a\u5f0f\u5b50\\((3)\\)\u5c31\u662f\u8981\u4fdd\u8bc1\u8fb9\u9645\u5229\u6da6\u3002<\/p>\n\n\n\n<p>\u56e0\u6b64\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\uff1a\u53ea\u8981\\(k \\ge 1\\)\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6e38\u620f\u5c31\u53ef\u4ee5\u73a9\u4e0b\u53bb\u3002<\/p>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u731c\u786c\u5e01\u6b63\u53cd\u7684\u6a21\u5f0f\u4e0b\uff1a\u5982\u679c\u8fde\u7eed\u51fa\u73b0\u4e8616\u6b21\u786c\u5e01\u6b63\u9762\u671d\u4e0a\uff0c\u8bd5\u95ee\u8d4c\u5f92\u662f\u5426\u53ef\u4ee5\u7838\u4e86\u5e84\u5bb6\u7684\u6863\u53e3\uff1f<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u798f\u5f69\u53cc\u8272\u7403<\/h2>\n\n\n\n<p>\u4e0b\u9762\u7528\u798f\u5f69\u53cc\u8272\u7403\u7684\u5b9e\u9645\u6570\u636e\u5e26\u5165\u8fdb\u53bb\uff1a<\/p>\n\n\n\n<p>\u8d4c\u5f92\u6bcf\u6b21\u6295\u6ce8\uff0c\u5e84\u5bb6\u9700\u8981\u6536\u53d62\u5143\u6295\u6ce8\u8d39\u3002\u5982\u679c\u731c\u9519\uff0c\u8d4c\u5f92\u5c06\u4e00\u65e0\u6240\u83b7\u3002\u5982\u679c\u731c\u5bf9\uff0c\u90a3\u4e48\u8d4c\u5f92\u5c06\u83b7\u5f97\\(5\\)\u5143\u5956\u91d1\u3002\u5047\u8bbe\uff0c\u8d4c\u5f92\u6bcf\u6b21\u6295\u6ce8\u90fd\u9009\u540c\u4e00\u4e2a\u53f7\u7801\u7684\u84dd\u8272\u7403\uff08\u731c\u4e2d\u7684\u6982\u7387\u4e3a\\(\\frac {1}{16}\\)\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>\u4e0b\u6ce8<\/td><td>\u6295\u5165\\(C\\)<\/td><td>\u731c\u5bf9\\(I\\)<\/td><td>\u731c\u9519<\/td><\/tr><tr><td>\u7b2c\u4e00\u6b21<\/td><td>2\u5143\u4e00\u6ce8<\/td><td>\u83b7\u5f975\u5143<br>\u603b\u8ba1\u6536\u76ca3\u5143<\/td><td>\u603b\u8ba1\u635f\u59312\u5143<\/td><\/tr><tr><td>\u7b2c\u4e8c\u6b21<\/td><td>2\u5143\u4e00\u6ce8<\/td><td>\u83b7\u5f975\u5143<br>\u603b\u8ba1\u6536\u76ca1\u5143<\/td><td>\u603b\u8ba1\u635f\u59314\u5143<\/td><\/tr><tr><td>\u7b2c\u4e09\u6b21<\/td><td>4\u5143\u4e24\u6ce8<\/td><td>\u83b7\u5f9710\u5143<br>\u603b\u8ba1\u6536\u76ca2\u5143<\/td><td>\u603b\u8ba1\u635f\u59318\u5143<\/td><\/tr><tr><td>\u7b2c\u56db\u6b21<\/td><td>6\u5143\u4e09\u6ce8<\/td><td>\u83b7\u5f9715\u5143<br>\u603b\u8ba1\u6536\u76ca1\u5143<\/td><td>\u603b\u8ba1\u635f\u593114\u5143<\/td><\/tr><tr><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><\/tr><tr><td>\u7b2c\\((n-1)\\)\u6b21<\/td><td>\\(C_{n-1}\\)\u5143\\(\\frac {C_{n-1}}{2}\\)\u6ce8<\/td><td>\u83b7\u5f97\\(\\frac {C_{n-1}}{2} \\times 5\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(\\sum \\limits_{i=1}^{n-1} C_i\\)\u5143<\/td><\/tr><tr><td>\u7b2c\\(n\\)\u6b21<\/td><td>\\(C_n\\)\u5143\\(\\frac {C_n}{2}\\)\u6ce8<\/td><td>\u83b7\u5f97\\(\\frac {C_n}{2} \\times 5\\)\u5143<\/td><td>\u603b\u8ba1\u635f\u5931\\(\\sum \\limits_{i=1}^{n} C_i\\)\u5143<\/td><\/tr><tr><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><td>\u2026\u2026<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u6309\u7167\u6b62\u635f\u6cd5\uff0c\u8d4c\u5f92\u5fc5\u987b\u8981\u4fdd\u8bc1\uff1a<\/p>\n\n\n\n<p>\\[\\left \\{ \\begin{array}{lr} [\\frac {\\sum \\limits_{i=1}^{n-1} C_i}{5}] + 1 \\le \\frac {C_n}{2} &amp; &#8230;&#8230;(1) \\\\ \\frac {C_n}{2} \\times 5 \\ge \\sum \\limits_{i=1}^{n-1} C_i + C_n &amp; &#8230;&#8230;(2) \\end{array} \\right. \\]<\/p>\n\n\n\n<p>\u8d4c\u5f92\u901a\u8fc7\u5f0f\u5b50\\((1)\\)\u63a8\u5bfc\u51fa\u4e0b\u4e00\u6b21\u81f3\u5c11\u9700\u8981\u6295\u6ce8\u591a\u5c11\uff1b\u53e6\u5916\u901a\u8fc7\u5f0f\u5b50\\((2)\\)\u6765\u4fdd\u8bc1\u4e0b\u4e00\u6b21\u7684\u6536\u76ca\u5fc5\u987b\u4e0d\u5c0f\u4e8e\u672c\u6b21\u6295\u5165\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u4ee3\u7801\uff08Matlab\uff09<\/h2>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: matlabkey; title: ; notranslate\" title=\"\">\nclear\nclose all\nclc\n\n% \u8d77\u59cb\u503c\nuint64 i;\nCost = int64(16);\nfor i = 1 : 16\n    Cost(i) = 0;\nend\n\n%\u7b2c\u4e00\u6b21\u6295\u6ce8\nCost(1) = 2;\nfprintf(&#039;\u7b2c1\u6b21\u62951\u6ce8\uff0c\u82b1\u8d392\u5143\\r\\n&#039;);\n\n% \u5faa\u73af\u8ba1\u7b97\nfor i = 2: 15\n    % \u8ba1\u7b97\u524d\u9762\u7684\u6210\u672c\u603b\u548c\n    int64 sum;\n    uint64 j;\n    sum = 0;\n    for j = 1 : i - 1\n        sum = sum + Cost(j);\n    end\n    % \u8ba1\u7b97\u6700\u4f4e\u6295\u6ce8\u6570\n    int64 T;\n    T = ceil(sum \/ 5);\n    % \u4fdd\u8bc1\u6536\u76ca\u6c42\u89e3\u6295\u6ce8\u6570\n    int64 t;\n    t = T;\n    while t * 5 &lt; sum + t * 2\n        t = t + 1\n    end\n    Cost(i) = 2 * t;\n    fprintf(&#039;\u7b2c%d\u6b21\u6295%d\u6ce8\uff0c\u82b1\u8d39%d\u5143\uff0c\u6536\u76ca%d\u5143\\r\\n&#039;,i, t, Cost(i), t * 5);\nend\n<\/pre><\/div>\n\n\n<p>\u8fd0\u884c\u540e\uff0c\u6253\u5370\u6210\u672c\u6570\u7ec4\u6570\u636e\uff1a<\/p>\n\n\n<div class=\"wp-block-syntaxhighlighter-code \"><pre class=\"brush: matlabkey; title: ; notranslate\" title=\"\">\n&gt;&gt; Cost\n\nCost =\n\n  1\u00d716 int64 \u884c\u5411\u91cf\n\n      2      2      4      6     10     16     28     46     76    128    212    354    590    984   1640      0\n<\/pre><\/div>\n\n\n<p>\u901a\u8fc7\u6210\u672c\u6570\u7ec4\uff0c\u5c31\u53ef\u4ee5\u8ba1\u7b97\u51fa\u6bcf\u6b21\u9700\u8981\u4e70\u591a\u5c11\u6ce8\u5f69\u7968\u3002\u5f53\u7136\u8fd9\u91cc\u53ea\u5173\u6ce8\u6700\u540e\u7684\u84dd\u8272\u7403\u3002\u5176\u4ed6\u8272\u7403\u7684\u6536\u76ca\uff0c\u90a3\u5c31\u8981\u770b\u5404\u4f4d\u7684\u8fd0\u6c14\u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u62d3\u5c55\u9605\u8bfb<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>AlgMain : <a href=\"http:\/\/www.algmain.com\/index.php\/2023\/02\/07\/office-fc\/\">\u4f7f\u7528Excel\u5236\u4f5c\u7684\u798f\u5f69\u548c\u5927\u4e50\u900f\u5206\u6790\u5de5\u5177<\/a><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\u6b62\u635f\u6295\u6ce8\u6cd5\u7684\u6838\u5fc3\u5c31\u662f\uff1a\u672c\u6b21\u6295\u6ce8\u7684\u76c8\u5229\uff08Incoming\uff09\uff0c\u5fc5\u987b\u81f3\u5c11\u80fd\u8986\u76d6\u4e0a\u6b21\u7684\u6210\u672c\uff08Cost\uff09\u3002\u8fd9\u4e2a\u4e5f\u662f\u5546\u4e1a\u884c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":363,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1387","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1387"}],"collection":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/comments?post=1387"}],"version-history":[{"count":54,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1387\/revisions"}],"predecessor-version":[{"id":1446,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/1387\/revisions\/1446"}],"up":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/363"}],"wp:attachment":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/media?parent=1387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}