{"id":218,"date":"2025-03-29T13:02:57","date_gmt":"2025-03-29T13:02:57","guid":{"rendered":"http:\/\/west.wangyuansheng.cn\/?p=218"},"modified":"2025-03-29T13:08:16","modified_gmt":"2025-03-29T13:08:16","slug":"%e5%ba%b7%e6%89%98%e8%a1%a8cantor","status":"publish","type":"post","link":"http:\/\/west.wangyuansheng.cn\/?p=218","title":{"rendered":"\u5eb7\u6258\u8868(cantor)"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u9898\u76ee\u63cf\u8ff0<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u5eb7\u6258\u662f\u4e00\u540d\u6570\u5b66\u5bb6\uff0c\u4ed6\u8bc1\u660e\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u5b9a\u7406\uff0c\u9700\u8981\u4f7f\u7528\u4e00\u5f20\u8868\uff1a<br>1\/1 2\/1 3\/1 4\/1 5\/1 \u22ef<br>1\/2 2\/2 3\/2 4\/2 5\/2 \u22ef<br>1\/3 2\/3 3\/3 4\/3 5\/3 \u22ef<br>1\/4 2\/4 3\/4 4\/4 5\/4 \u22ef<br>1\/5 2\/5 3\/5 4\/5 5\/5 \u22ef<br>\u22ef \u22ef \u22ef \u22ef \u22ef \u22ef<br>\u8fd9\u4e2a\u8868\u7684\u89c4\u5f8b\u662f\uff1a<br>\u4ece\u4e0a\u5230\u4e0b\uff1a\u6bcf\u4e00\u884c\u7684\u5206\u5b50\u4f9d\u6b21\u589e\u5927\uff1b<br>\u4ece\u5de6\u5230\u53f3\uff1a\u6bcf\u4e00\u5217\u7684\u5206\u6bcd\u4f9d\u6b21\u589e\u5927\u3002<br>\u5eb7\u6258\u4ee5\u4e00\u79cd\u4e0d\u91cd\u590d\u3001\u4e0d\u9057\u6f0f\u7684\u65b9\u5f0f\uff0c\u5c06\u8868\u4e0a\u6240\u6709\u6570\u5b57\u5217\u4e3e\u4e86\u51fa\u6765\u3002\u65b9\u6cd5\u5982\u4e0b\uff1a\u4ece\u5de6\u4e0a\u89d2\u7684 1\/1\u51fa\u53d1\uff0c Z \u5b57\u5f62\u626b\u63cf\uff0c\u5176\u4e2d\uff1a<br>\u7b2c\u4e00\u9879\u662f 1\/1\uff1b<br>\u7b2c\u4e8c\u9879\u662f 1\/2\u3001\u7b2c\u4e09\u9879\u662f 2\/1<br>\u7b2c\u56db\u9879\u662f 3\/1\uff0c\u7b2c\u4e94\u9879\u662f 2\/2\uff0c\u7b2c\u516d\u9879\u662f 1\/3<br>\u63a5\u4e0b\u6765\u51e0\u9879\u5206\u522b\u662f\uff1a<br>1\/4, 2\/3, 3\/2, 4\/1, 5\/1, 4\/2, \u22ef<br>\u9898\u76ee\u63cf\u8ff0\uff1a<br>\u7ed9\u5b9a\u4e00\u4e2a\u5206\u6570 a\/b\uff0c\u8bf7\u8ba1\u7b97\u8be5\u5206\u6570\u5728\u5eb7\u6258\u8868\u4e2d\u6392\u540d\u7b2c\u51e0\u3002<br>\u8f93\u5165\u683c\u5f0f\uff1a(cantor.in)<br>\u4e24\u4e2a\u6574\u6570\uff1aa\u4e0e b\uff0c\u8868\u793a\u4e00\u4e2a\u5206\u6570 a\/b\u3002<br>\u8f93\u51fa\u683c\u5f0f\uff1a(cantor.out)<br>\u5355\u4e2a\u6570\u5b57\uff1a\u8868\u793a\u8f93\u5165\u5206\u6570\u5728\u5eb7\u6258\u8868\u4e2d\u7684\u540d\u6b21\u3002<br>\u8f93\u5165\u8f93\u51fa\u6837\u4f8b<br>\u8f93\u5165\u6837\u4f8b#1\uff1a<br>2 4<br>\u868c\u57e0\u4e8c\u4e2d\u4fe1\u606f\u5b66\u7d20\u517b\u8425<br>8<br>\u8f93\u51fa\u6837\u4f8b#1\uff1a<br>14<br>\u8f93\u5165\u6837\u4f8b#2\uff1a<br>1 4<br>\u8f93\u51fa\u6837\u4f8b#2\uff1a<br>7<br>\u6570\u636e\u8303\u56f4\uff1a<br>\u5bf9\u4e8e 50%\u7684\u5206\u6570\uff0c1\u2264a,b\u2264100\uff1b<br>\u5bf9\u4e8e 100%\u7684\u5206\u6570\uff0c1\u2264a,b\u226410000\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5206\u6790\u95ee\u9898<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u7406\u89e3\u5eb7\u6258\u8868\u7684\u6392\u5217\u89c4\u5f8b\u3002\u5eb7\u6258\u8868\u662f\u4e00\u4e2a\u65e0\u9650\u7684\u5206\u6570\u8868\u683c\uff0c\u6309\u7167\u7279\u5b9a\u7684\u201cZ\u201d\u5b57\u5f62\u987a\u5e8f\u6392\u5217\u3002\u5177\u4f53\u6392\u5217\u987a\u5e8f\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u9879\uff1a1\/1<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u9879\uff1a1\/2\uff0c\u7b2c\u4e09\u9879\uff1a2\/1<\/li>\n\n\n\n<li>\u7b2c\u56db\u9879\uff1a3\/1\uff0c\u7b2c\u4e94\u9879\uff1a2\/2\uff0c\u7b2c\u516d\u9879\uff1a1\/3<\/li>\n\n\n\n<li>\u7b2c\u4e03\u9879\uff1a1\/4\uff0c\u7b2c\u516b\u9879\uff1a2\/3\uff0c\u7b2c\u4e5d\u9879\uff1a3\/2\uff0c\u7b2c\u5341\u9879\uff1a4\/1<\/li>\n\n\n\n<li>\u7b2c\u5341\u4e00\u9879\uff1a5\/1\uff0c\u7b2c\u5341\u4e8c\u9879\uff1a4\/2\uff0c\u7b2c\u5341\u4e09\u9879\uff1a3\/3\uff0c\u7b2c\u5341\u56db\u9879\uff1a2\/4\uff0c\u7b2c\u5341\u4e94\u9879\uff1a1\/5<\/li>\n\n\n\n<li>\u2026<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u4e0a\u9762\u7684\u6392\u5217\u53ef\u4ee5\u770b\u51fa\uff0c\u5eb7\u6258\u8868\u7684\u6392\u5217\u662f\u6309\u7167\u201c\u5bf9\u89d2\u7ebf\u201d\u65b9\u5411\u8fdb\u884c\u7684\u3002\u6bcf\u6761\u5bf9\u89d2\u7ebf\u4e0a\u5206\u6570\u7684\u5206\u5b50\u548c\u5206\u6bcd\u4e4b\u548c\u662f\u56fa\u5b9a\u7684\u3002\u4f8b\u5982\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u6761\u5bf9\u89d2\u7ebf\uff08\u548c\u4e3a2\uff09\uff1a1\/1<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u6761\u5bf9\u89d2\u7ebf\uff08\u548c\u4e3a3\uff09\uff1a1\/2, 2\/1<\/li>\n\n\n\n<li>\u7b2c\u4e09\u6761\u5bf9\u89d2\u7ebf\uff08\u548c\u4e3a4\uff09\uff1a3\/1, 2\/2, 1\/3<\/li>\n\n\n\n<li>\u7b2c\u56db\u6761\u5bf9\u89d2\u7ebf\uff08\u548c\u4e3a5\uff09\uff1a1\/4, 2\/3, 3\/2, 4\/1<\/li>\n\n\n\n<li>\u2026<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u6211\u4eec\u8fd8\u53d1\u73b0\uff0c\u5728\u5bf9\u89d2\u7ebf\u4e0a\uff0c\u6bcf\u7ec4\u5206\u6570\u7684\u5206\u5b50\u52a0\u5206\u6bcd\u7684\u548c\u662f\u76f8\u7b49\u7684\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5efa\u7acb\u6a21\u578b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u627e\u5230\u5206\u6570 <code>a\/b<\/code> \u5728\u5eb7\u6258\u8868\u4e2d\u7684\u4f4d\u7f6e\uff0c\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u8fdb\u884c\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u786e\u5b9a\u5bf9\u89d2\u7ebf\u7684\u548c<\/strong>\uff1a\u5206\u6570 <code>a\/b<\/code> \u6240\u5728\u7684\u5bf9\u89d2\u7ebf\u7684\u548c\u662f <code>s = a + b<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u524d\u9762\u6240\u6709\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c<\/strong>\uff1a\u5728 <code>s<\/code> \u5bf9\u89d2\u7ebf\u4e4b\u524d\u7684\u6240\u6709\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c\u662f <code>1 + 2 + 3 + ... + (s - 1)<\/code>\u3002\u8fd9\u662f\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u7684\u548c\uff0c\u53ef\u4ee5\u7528\u516c\u5f0f <code>(s - 1) * s \/ 2<\/code> \u8ba1\u7b97\u3002<\/li>\n<\/ol>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0a\u7684\u7ed3\u679c\u7531\u7b49\u5dee\u6570\u5217\u516c\u5f0f\u63a8\u51fa\uff0c\u516c\u5f0f\u4e3a\uff1aSn = n * (a1+an)\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee3\u5165\u6570\u503c\u5f97\uff1a Sn = ( s-1\uff09* (1+s-1)\/2 = s* (s-1) \/2<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u7136\uff0c\u6211\u4eec\u4f7f\u7528\u4e5f\u53ef\u4ee5\u4f7f\u7528\u7f16\u7a0b\u7684\u65b9\u6cd5\u3002\u672c\u6848\u4f8b\u6211\u4eec\u4f7f\u7528\u5faa\u73af\u7d2f\u52a0\u7684\u7f16\u7a0b\u65b9\u6cd5\u5f97\u51fa\u3002<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li><strong>\u786e\u5b9a\u5f53\u524d\u5bf9\u89d2\u7ebf\u4e0a\u7684\u4f4d\u7f6e<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c <code>s<\/code> \u662f\u5947\u6570\uff0c\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u6392\u5217\u662f\u4ece\u4e0b\u5230\u4e0a\uff0c\u5373\u5206\u6bcd\u4ece1\u5f00\u59cb\u589e\u52a0\u3002<\/li>\n\n\n\n<li>\u5982\u679c <code>s<\/code> \u662f\u5076\u6570\uff0c\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u6392\u5217\u662f\u4ece\u4e0a\u5230\u4e0b\uff0c\u5373\u5206\u5b50\u4ece1\u5f00\u59cb\u589e\u52a0\u3002<\/li>\n\n\n\n<li>\u6839\u636e <code>a<\/code> \u6216 <code>b<\/code> \u7684\u503c\uff0c\u53ef\u4ee5\u8ba1\u7b97\u51fa\u5f53\u524d\u5bf9\u89d2\u7ebf\u4e0a\u7684\u4f4d\u7f6e\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f16\u5199\u4ee3\u7801<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u662f\u57fa\u4e8e\u4e0a\u8ff0\u601d\u8def\u7684C++\u4ee3\u7801\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#include &lt;bits\/stdc++.h>\nusing namespace std;\n\nint main() {\n    int a, b;\/\/a \u662f\u5206\u5b50  b \u662f\u5206\u6bcd \n    cin >> a >> b;\n    int s = a + b; \/\/ \u5bf9\u89d2\u7ebf\u7684\u548c\n    int rank = 0; \/\/ \u524d\u9762\u5404\u9879\u548c \n    \/\/ \u8ba1\u7b97\u524d\u9762\u6240\u6709\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c\n    for (int i = 1; i &lt; s-1; i++) {\n        rank += i;  \/\/1+2+3+\u2026\u2026 \n    }\n    \/\/ \u786e\u5b9a\u5f53\u524d\u5bf9\u89d2\u7ebf\u4e0a\u7684\u4f4d\u7f6e\n    if (s % 2 == 1) { \/\/\u5206\u5b50\u4e0e\u5206\u6bcd\u548c\u4e3a\u5947\u6570\uff0c\u5206\u5b50\u4ece\u4e0b\u5230\u4e0a\u4ece1\u9012\u589e\uff0c\u6240\u4ee5\u7d2f\u52a0\u5206\u5b50 \n        rank += a;\n    } else { \/\/\u5206\u5b50\u4e0e\u5206\u6bcd\u548c\u4e3a\u5076\u6570\uff0c\u5206\u6bcd\u4ece\u4e0a\u5230\u4e0b\u4ece1\u9012\u589e\uff0c\u6240\u4ee5\u7d2f\u52a0\u5206\u6bcd \n        rank += b;\n    }\n    cout &lt;&lt; rank &lt;&lt; endl;\n    return 0;\n}<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u4ee3\u7801\u89e3\u91ca<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f93\u5165<\/strong>\uff1a\u8bfb\u53d6\u5206\u6570 <code>a<\/code> \u548c <code>b<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u5bf9\u89d2\u7ebf\u548c<\/strong>\uff1a<code>s = a + b<\/code>\u3002<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u524d\u9762\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c<\/strong>\uff1a\u4f7f\u7528\u5faa\u73af\u7d2f\u52a0 <code>1<\/code> \u5230 <code>s - 1<\/code> \u7684\u548c\u3002<\/li>\n\n\n\n<li><strong>\u786e\u5b9a\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u4f4d\u7f6e<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c <code>s<\/code> \u662f\u5947\u6570\uff0c\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u6392\u5217\u662f\u4ece\u4e0b\u5230\u4e0a\uff0c\u6240\u4ee5\u4f4d\u7f6e\u662f <code>b<\/code>\u3002<\/li>\n\n\n\n<li>\u5982\u679c <code>s<\/code> \u662f\u5076\u6570\uff0c\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u6392\u5217\u662f\u4ece\u4e0a\u5230\u4e0b\uff0c\u6240\u4ee5\u4f4d\u7f6e\u662f <code>a<\/code>\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f93\u51fa\u7ed3\u679c<\/strong>\uff1a\u5c06\u524d\u9762\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c\u52a0\u4e0a\u5f53\u524d\u5bf9\u89d2\u7ebf\u7684\u4f4d\u7f6e\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u6392\u540d\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u8f93\u5165 <code>3\/2<\/code> \u4e3a\u4f8b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5bf9\u89d2\u7ebf\u548c <code>s = 3 + 2 = 5<\/code>\u3002<\/li>\n\n\n\n<li>\u524d\u9762\u5bf9\u89d2\u7ebf\u7684\u9879\u6570\u603b\u548c\uff1a<code>1 + 2 + 3 = 6<\/code>\u3002<\/li>\n\n\n\n<li><code>s<\/code> \u662f\u5947\u6570\uff0c\u4ece\u4e0b\u5230\u4e0a\u6392\u5217\uff0c\u4f4d\u7f6e\u662f <code>b = 2<\/code>\u3002\uff08\u8fd9\u662f\u56e0\u4e3a\u5206\u5b50\u4ece1\u5f00\u59cb\u6570\uff0c\u6240\u4ee5\u9009\u62e9\u5206\u5b50\uff09<\/li>\n\n\n\n<li>\u6700\u7ec8\u6392\u540d\uff1a<code>6 + 2 = 8<\/code>\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u8f93\u51fa\u7ed3\u679c\u4e3a <code>8<\/code>\uff0c\u4e0e\u5eb7\u6258\u8868\u7684\u6392\u5217\u4e00\u81f4\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u9898\u76ee\u63cf\u8ff0 \u5eb7\u6258\u662f\u4e00\u540d\u6570\u5b66\u5bb6\uff0c\u4ed6\u8bc1\u660e\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u5b9a\u7406\uff0c\u9700\u8981\u4f7f\u7528\u4e00\u5f20\u8868\uff1a1\/1 2\/1&#8230; <a class=\"read-more\" href=\"http:\/\/west.wangyuansheng.cn\/?p=218\">\u9605\u8bfb\u66f4\u591a&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-218","post","type-post","status-publish","format-standard","hentry","category-problem"],"_links":{"self":[{"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/posts\/218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=218"}],"version-history":[{"count":2,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/posts\/218\/revisions"}],"predecessor-version":[{"id":220,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=\/wp\/v2\/posts\/218\/revisions\/220"}],"wp:attachment":[{"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=218"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/west.wangyuansheng.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}