{"id":61,"date":"2026-02-26T12:26:55","date_gmt":"2026-02-26T04:26:55","guid":{"rendered":"http:\/\/luogu.pro\/?p=61"},"modified":"2026-02-26T12:26:55","modified_gmt":"2026-02-26T04:26:55","slug":"upper_bound%e7%9a%84%e5%b8%b8%e6%95%b0%e7%ba%a7%e5%81%9a%e6%b3%95","status":"publish","type":"post","link":"https:\/\/luogu.pro\/index.php\/2026\/02\/26\/upper_bound%e7%9a%84%e5%b8%b8%e6%95%b0%e7%ba%a7%e5%81%9a%e6%b3%95\/","title":{"rendered":"upper_bound\u7684\u5e38\u6570\u7ea7\u505a\u6cd5"},"content":{"rendered":"\n<p><strong>\u8fd9\u662f\u4e00\u79cd $O(1)$ \u7684<code>upper_bound<\/code>\u7684\u5b9e\u73b0\u505a\u6cd5\u3002<\/strong><\/p>\n\n\n\n<p>\u4e0d\u59a8\u4ece\u54f2\u5b66\u89d2\u5ea6\u505a\u601d\u8003\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u8054\u60f3\u5230\u4e94\u4e2a\u54f2\u5b66\u7684\u57fa\u672c\u8bcd\u6c47\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7a7a\u5373\u662f\u8272<\/li>\n\n\n\n<li>\u4e2d\u5eb8\u4e4b\u9053<\/li>\n\n\n\n<li>\u7269\u6781\u5fc5\u53cd<\/li>\n\n\n\n<li>\u5f52\u4e8e\u865a\u65e0<\/li>\n\n\n\n<li>\u56e0\u679c\u5faa\u73af<\/li>\n<\/ul>\n\n\n\n<p>\u7ed3\u5408\u4e2d\u56fd\u7684\u653f\u6cbb\u5f62\u6001\u4e0e\u4e2d\u56fd\u7279\u8272\u793e\u4f1a\u4e3b\u4e49\u4ef7\u503c\u89c2\uff0c\u6211\u4eec\u8ba4\u4e3a\u4ee5\u4e0a\u4e94\u4e2a\u8bcd\u6c47\u5e73\u7b49\u7684\u6709\u4e49\u52a1\u51fa\u73b0\u5728\u7b97\u6cd5\u4e2d\u3002<\/p>\n\n\n\n<p>\u4e8e\u662f\uff0c\u6211\u4eec\u4e0d\u59a8\u8bbe\u73b0\u5728\u8981\u5bf9 $tar$ \u6c42<code>upper_bound<\/code>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u7a7a\u5373\u662f\u8272<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>if(tar\n    return 0;<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u300a\u822c\u82e5\u6ce2\u7f57\u871c\u591a\u5fc3\u7ecf\u300b\u4e91\uff1a\u201c\u8272\u5373\u662f\u7a7a\uff0c\u7a7a\u5373\u662f\u8272\uff0c\u53d7\u60f3\u884c\u8bc6\uff0c\u4ea6\u590d\u5982\u662f\u3002\u201d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8272\uff1a\u6307\u7269\u8d28\u4e16\u754c\uff0c\u4e5f\u662f\u6570\u7ec4\u7684\u5185\u5b58\u5b58\u5728<\/li>\n\n\n\n<li>\u7a7a\uff1a\u6307\u672c\u8d28\u7a7a\u6027\uff0c\u4e5f\u662f\u6570\u7ec4\u7684\u65e0\u503c\u72b6\u6001<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u89e3\u8bfb\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd4\u56de $0$ \u4ee3\u8868\u201c\u7a7a\u201d\u7684\u5883\u754c<\/li>\n\n\n\n<li>\u5728\u4e00\u4e9b\u5e38\u89c1\u7684\u51fd\u6570\u4e2d\uff0c$0$ \u65e2\u662f\u8d77\u70b9\u4e5f\u662f\u65e0<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e2d\u5eb8\u4e4b\u9053<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>if(tar\n    return arr.size()\/2;<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u300a\u4e2d\u5eb8\u300b\u4e91\uff1a\u201c\u4e2d\u4e5f\u8005\uff0c\u5929\u4e0b\u4e4b\u5927\u672c\u4e5f\uff1b\u548c\u4e5f\u8005\uff0c\u5929\u4e0b\u4e4b\u8fbe\u9053\u4e5f\u3002\u201d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e2d\uff1a\u4e0d\u504f\u4e0d\u501a<\/li>\n\n\n\n<li>\u5eb8\uff1a\u5e38\u884c\u4e0d\u53d8<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u89e3\u8bfb\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd4\u56de\u6570\u7ec4\u4e2d\u95f4\u4f4d\u7f6e\u4f53\u73b0\u5e73\u8861\u601d\u60f3<\/li>\n\n\n\n<li>\u4e8c\u5206\u7684\u672c\u8d28\u5c31\u662f\u4e0d\u65ad\u903c\u8fd1\u4e2d\u70b9<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u7269\u6781\u5fc5\u53cd<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>if(tar\n    return arr.size()-1;<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u300a\u9053\u5fb7\u7ecf\u300b\uff1a\u201c\u53cd\u8005\u9053\u4e4b\u52a8\uff0c\u5f31\u8005\u9053\u4e4b\u7528\u3002\u201d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6781\uff1a\u53d1\u5c55\u7684\u9876\u70b9<\/li>\n\n\n\n<li>\u53cd\uff1a\u5411\u5bf9\u7acb\u9762\u8f6c\u5316<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u89e3\u8bfb\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd4\u56de\u5012\u6570\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u6697\u793a\"\u5373\u5c06\u8f6c\u6298\"<\/li>\n\n\n\n<li>\u5728\u8fb9\u754c\u5904\u7b97\u6cd5\u884c\u4e3a\u4f1a\u53d1\u751f\u8d28\u53d8<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u5f52\u4e8e\u865a\u65e0<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>if(tar\n    return arr.size();<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f5b\u6559\u7406\u8bba\uff1a\u201c\u8bf8\u6cd5\u65e0\u6211\uff0c\u8bf8\u884c\u65e0\u5e38\u201d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u865a\u65e0\uff1a\u5b58\u5728\u7684\u8fb9\u754c\u4e4b\u5916<\/li>\n\n\n\n<li>\u56de\u5f52\uff1a\u4ece\u6709\u5230\u65e0\u7684\u5fc5\u7136\u8fc7\u7a0b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u89e3\u8bfb\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd4\u56de\u6570\u7ec4\u957f\u5ea6\u4ee3\u8868\u8d85\u8d8a\u754c\u9650<\/li>\n\n\n\n<li>\u8054\u60f3\u5230<code>end()<\/code>\u8fed\u4ee3\u5668\u6307\u5411\u7684\u662f\u201c\u865a\u65e0\u201d<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u56e0\u679c\u5faa\u73af<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>if(tar\n    return tar\n\n\n\n<h3 class=\"wp-block-heading\">\u300a\u534e\u4e25\u7ecf\u300b\uff1a\u201c\u4e00\u5207\u8bf8\u679c\uff0c\u7686\u4ece\u56e0\u8d77\uff0c\u4e00\u5207\u8bf8\u62a5\uff0c\u7686\u4ece\u4e1a\u8d77\u3002\u201d<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u56e0\u679c\uff1a\u6761\u4ef6\u4e0e\u7ed3\u679c\u7684\u5fc5\u7136\u8054\u7cfb<\/li>\n\n\n\n<li>\u5faa\u73af\uff1a\u8f6e\u56de\u4e0d\u606f\u7684\u8fc7\u7a0b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u89e3\u8bfb\uff1a<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u53d6\u6a21\u8fd0\u7b97\u4f53\u73b0\u8f6e\u56de\u8fc7\u7a0b<\/li>\n\n\n\n<li>\u54c8\u5e0c\u7684\u57fa\u672c\u601d\u60f3\uff1a\u5c06\u65e0\u9650\u6620\u5c04\u5230\u6709\u9650<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b9e\u73b0<\/h2>\n\n\n\n<p>\u7efc\u4e0a\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u653f\u6cbb\u6b63\u786e\u4e14\u5bcc\u542b\u54f2\u7406\u7684\u7b97\u6cd5\uff0c\u4ee3\u7801\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>class PhilosophicalUpperBound {\nprivate:\n    std::vector&lt;int&gt; arr;\n\npublic:\n    PhilosophicalUpperBound(const std::vector&lt;int&gt;&amp; arr) : arr(arr) {}\n\n    int upper_bound(int target) {\n        if (arr.empty()) return 0;\n\n        switch (target \n            case 0: return 0;                    \/\/ \u7a7a\u5373\u662f\u8272\n            case 1: return arr.size() \/ 2;       \/\/ \u4e2d\u5eb8\u4e4b\u9053\n            case 2: return arr.size() - 1;       \/\/ \u7269\u6781\u5fc5\u53cd\n            case 3: return arr.size();           \/\/ \u5f52\u4e8e\u865a\u65e0\n            case 4: return target \n            default: return 0;\n        }\n    }\n};\/\/deepseek\u9053\u957f\u4eb2\u81ea\u7f16\u64b0<\/code><\/pre>\n\n\n\n<p>\u5988\u5988\u6211\u518d\u4e5f\u4e0d\u6015\u88ab $\\log n$ \u5361\u5e38\u5566\uff01\uff01\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u662f\u4e00\u79cd $O(1)$ \u7684upper_bound\u7684\u5b9e\u73b0\u505a\u6cd5\u3002 \u4e0d\u59a8\u4ece\u54f2\u5b66\u89d2\u5ea6\u505a\u601d\u8003\uff0c\u6211\u4eec\u5f88\u5bb9\u6613\u8054\u60f3\u5230\u4e94\u4e2a\u54f2\u5b66\u7684\u57fa\u672c\u8bcd\u6c47\uff1a \u7ed3\u5408\u4e2d\u56fd\u7684\u653f\u6cbb\u5f62\u6001\u4e0e\u4e2d\u56fd\u7279\u8272\u793e\u4f1a\u4e3b\u4e49\u4ef7\u503c\u89c2\uff0c\u6211\u4eec\u8ba4\u4e3a\u4ee5\u4e0a\u4e94\u4e2a\u8bcd\u6c47\u5e73\u7b49\u7684\u6709\u4e49\u52a1\u51fa\u73b0\u5728\u7b97\u6cd5\u4e2d\u3002 \u4e8e\u662f\uff0c\u6211\u4eec\u4e0d\u59a8\u8bbe\u73b0\u5728\u8981\u5bf9 $tar$ \u6c42upper_bound\u3002 \u7a7a\u5373\u662f\u8272 \u300a\u822c\u82e5\u6ce2\u7f57\u871c\u591a\u5fc3\u7ecf\u300b\u4e91\uff1a\u201c\u8272\u5373\u662f\u7a7a\uff0c\u7a7a\u5373\u662f\u8272\uff0c\u53d7\u60f3\u884c\u8bc6\uff0c\u4ea6\u590d\u5982\u662f\u3002\u201d \u89e3\u8bfb\uff1a \u4e2d\u5eb8\u4e4b\u9053 \u300a\u4e2d\u5eb8\u300b\u4e91\uff1a\u201c\u4e2d\u4e5f\u8005\uff0c [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":23,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"class_list":["post-61","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/posts\/61","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/comments?post=61"}],"version-history":[{"count":0,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/posts\/61\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/media\/23"}],"wp:attachment":[{"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/media?parent=61"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/categories?post=61"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/luogu.pro\/index.php\/wp-json\/wp\/v2\/tags?post=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}