{"id":880,"date":"2026-04-22T15:57:27","date_gmt":"2026-04-22T07:57:27","guid":{"rendered":"http:\/\/wordpress.fangt.online\/?p=880"},"modified":"2026-04-25T01:01:25","modified_gmt":"2026-04-24T17:01:25","slug":"%e4%ba%8c%e5%88%86%e6%b3%95%ef%bc%88bisection-method%ef%bc%89","status":"publish","type":"post","link":"http:\/\/wordpress.fangt.online\/index.php\/2026\/04\/22\/%e4%ba%8c%e5%88%86%e6%b3%95%ef%bc%88bisection-method%ef%bc%89\/","title":{"rendered":"\u4e8c\u5206\u6cd5\uff08Bisection Method\uff09"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u4e8c\u5206\u6cd5\u662f\u4e00\u79cd\u975e\u5e38\u57fa\u7840\u4e14\u901a\u7528\u7684\u6570\u503c\u8ba1\u7b97\u65b9\u6cd5\uff0c\u4e3b\u8981\u7528\u4e8e\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\uff08\u5373\u627e\u5230\u4f7f\u51fd\u6570\u503c\u4e3a 0 \u7684\u70b9\uff09\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u6838\u5fc3\u539f\u7406\uff1a\u5939\u903c\u5b9a\u7406<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u5206\u6cd5\u7684\u7406\u8bba\u57fa\u7840\u662f\u8fde\u7eed\u51fd\u6570\u7684\u4ecb\u503c\u5b9a\u7406\uff08Intermediate Value Theorem\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b80\u5355\u6765\u8bf4\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u00a0f(x)\u00a0\u5728\u533a\u95f4\u00a0[a,b]\u00a0\u4e0a\u662f\u8fde\u7eed\u7684\uff0c\u5e76\u4e14\u00a0f(a)\u00a0\u548c\u00a0f(b)\u00a0\u7684\u7b26\u53f7\u76f8\u53cd\uff08\u5373\u4e00\u6b63\u4e00\u8d1f\uff0c\u610f\u5473\u7740\u56fe\u50cf\u7a7f\u8fc7\u4e86 x \u8f74\uff09\uff0c\u90a3\u4e48\u5728\u8fd9\u4e2a\u533a\u95f4\u5185\u90e8\u81f3\u5c11\u5b58\u5728\u4e00\u4e2a\u70b9\u00a0c\uff0c\u4f7f\u5f97\u00a0f(c)=0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u65f6\uff0c\u6211\u4eec\u53ea\u9700\u8981\u4e0d\u65ad\u7684\u627e\u4e2d\u5fc3\u70b9\uff0c\u901a\u8fc7\u6bd4\u8f83c\u5728\u4e2d\u5fc3\u70b9\u5de6\u8fd8\u662f\u53f3\u6765\u51cf\u5c0f\u533a\u95f4\uff0c\u6700\u7ec8\u786e\u5b9ac\u7684\u5177\u4f53\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u6570\u5b66\u89d2\u5ea6\u6765\u8bb2\uff0c\u7531\u4e8e\u8fd9\u4e2a\u65b9\u6cd5\u7684\u9c81\u68d2\u6027\u5f3a\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u628a\u5b83\u5f53\u4f5c\u89e3\u51b3\u6c42\u6839\u7684\u6700\u540e\u4e00\u4e2a\u65b9\u6848\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-x-large-font-size\">\u4e8c\u5206\u67e5\u627e<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6838\u5fc3\u601d\u60f3\uff1a\u5728\u6709\u5e8f\u7684\u6570\u7ec4\u91cc\uff0c\u6bcf\u6b21\u780d\u6389\u4e00\u534a\u4e0d\u53ef\u80fd\u7684\u533a\u95f4\uff0c\u5feb\u901f\u627e\u5230\u76ee\u6807\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u524d\u63d0\uff1a\u6570\u7ec4\u5fc5\u987b\u6709\u5e8f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8bbe\u5de6\u8fb9\u754c\u00a0<code>left<\/code>\uff0c\u53f3\u8fb9\u754c\u00a0<code>right<\/code><\/li>\n\n\n\n<li>\u53d6\u4e2d\u70b9\u00a0<code>mid = (left + right) \/ 2<\/code><\/li>\n\n\n\n<li>\u6bd4\u8f83\u00a0<code>a[mid]<\/code>\u00a0\u548c\u76ee\u6807\u503c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u7b49\u4e8e \u2192 \u627e\u5230\u4e86<\/li>\n\n\n\n<li>\u5c0f\u4e8e \u2192 \u7b54\u6848\u5728\u53f3\u8fb9\uff0c<code>left = mid + 1<\/code><\/li>\n\n\n\n<li>\u5927\u4e8e \u2192 \u7b54\u6848\u5728\u5de6\u8fb9\uff0c<code>right = mid - 1<\/code><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u91cd\u590d\u76f4\u5230\u627e\u5230\u6216\u533a\u95f4\u4e3a\u7a7a<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(log n)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">100 \u4e07\u7684\u6570\u636e\u6700\u591a\u67e5 20 \u6b21\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u5e94\u7528\u573a\u666f<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u627e\u67d0\u4e2a\u6570\u662f\u5426\u5b58\u5728<\/li>\n\n\n\n<li>\u627e\u7b2c\u4e00\u4e2a \u2265 x \u7684\u4f4d\u7f6e\uff08lower_bound\uff09<\/li>\n\n\n\n<li>\u627e\u6700\u540e\u4e00\u4e2a \u2264 x \u7684\u4f4d\u7f6e<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-x-large-font-size\">\u4e8c\u5206\u7b54\u6848<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6838\u5fc3\u601d\u60f3\uff1a\u7b54\u6848\u672c\u8eab\u5177\u6709\u5355\u8c03\u6027\uff0c\u5148\u4e8c\u5206\u7b54\u6848\u7684\u503c\uff0c\u518d\u901a\u8fc7\u51fd\u6570\u5224\u65ad\u8be5\u503c\u662f\u5426\u6b63\u786e\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6700\u5927\u7684\u6700\u5c0f xxx<\/li>\n\n\n\n<li>\u6700\u5c0f\u7684\u6700\u5927 xxx<\/li>\n\n\n\n<li>\u6ee1\u8db3\u6761\u4ef6\u7684\u6700\u5c0f\u503c<\/li>\n\n\n\n<li>\u6ee1\u8db3\u6761\u4ef6\u7684\u6700\u5927\u503c<\/li>\n\n\n\n<li>\u5206\u5272\u6570\u7ec4\u3001\u6700\u5c0f\u6700\u5927\u8ddd\u79bb\u3001\u6700\u5c0f\u82b1\u8d39\u7b49<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u5e94\u7528\u573a\u666f<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5148\u786e\u5b9a\u9898\u76ee\u8981\u6c42\u7684\u5185\u5bb9<\/li>\n\n\n\n<li>\u6839\u636e\u6c42\u7684\u5185\u5bb9\u786e\u5b9a\u7b54\u6848\u7684\u533a\u95f4[L,R]<\/li>\n\n\n\n<li>\u6839\u636e\u5f53\u524d\u533a\u95f4\uff0c\u4e8c\u5206\u51fa\u7b54\u6848mid<\/li>\n\n\n\n<li>\u5199\u4e00\u4e2acheck(mid)\u51fd\u6570\uff1a\n<ul class=\"wp-block-list\">\n<li>\u8fd4\u56detrue\uff1a\u5c1d\u8bd5\u66f4\u4f18\u7b54\u6848<\/li>\n\n\n\n<li>\u8fd4\u56defalse\uff1a\u8c03\u6574\u65b9\u5411<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u901a\u8fc7\u4e0d\u65ad\u7f29\u5c0f\u533a\u95f4\u6700\u540e\u786e\u5b9a\u6700\u4f18\u89e3<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u4ee3\u7801\u76f8\u5173<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>\u786e\u5b9a\u7b54\u6848\u8303\u56f4\uff1aL\u548cR\n\u521d\u59cb\u5316ans\uff1a-1\u3001L\u6216R\n\u521d\u59cb\u5316mid\uff1a\u4f5c\u4e3a\u533a\u95f4\u4e2d\u5fc3\u70b9\n\nwhile (L &lt;= R) { \n    mid = L + (R - L) \/ 2;\n    if (check(mid)) {  \/\/ \u6ee1\u8db3\u6761\u4ef6\n        ans = mid;\n        R = mid - 1;  \/\/ \u5c1d\u8bd5\u66f4\u5c0f\n    }\n    else {\n        L = mid + 1;   \/\/ \u4e0d\u591f\uff0c\u8981\u66f4\u5927\n    }\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u7b97\u6cd5\u5e93\u76f8\u5173<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u67e5\u627evalue\u662f\u5426\u5b58\u5728<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>bool\u00a0binary_search(first,\u00a0last,\u00a0value);<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u67e5\u627e\u7b2c\u4e00\u4e2a\u5927\u4e8e\u7b49\u4e8evalue\u7684\u4f4d\u7f6e<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>iterator\u00a0lower_bound(first,\u00a0last,\u00a0value);<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u67e5\u627e\u7b2c\u4e00\u4e2a\u5927\u4e8evalue\u7684\u4f4d\u7f6e<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>iterator\u00a0upper_bound(first,\u00a0last,\u00a0value);<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u540c\u65f6\u8fd4\u56delower\u548cupper<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>pair&lt;iterator,\u00a0iterator>\u00a0equal_range(&#8230;);<\/li>\n\n\n\n<li>\u5e38\u7528\u4e8e\u6c42value\u51fa\u73b0\u7684\u6b21\u6570<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u4e8c\u5206\u6cd5\u662f\u4e00\u79cd\u975e\u5e38\u57fa\u7840\u4e14\u901a\u7528\u7684\u6570\u503c\u8ba1\u7b97\u65b9\u6cd5\uff0c\u4e3b\u8981\u7528\u4e8e\u6c42\u89e3\u65b9\u7a0b\u7684\u6839\uff08\u5373\u627e\u5230\u4f7f\u51fd\u6570\u503c\u4e3a 0 \u7684\u70b9\uff09\u3002 \u6838\u5fc3\u539f\u7406\uff1a\u5939\u903c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[61],"tags":[],"class_list":["post-880","post","type-post","status-publish","format-standard","hentry","category-zl"],"_links":{"self":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/880","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/comments?post=880"}],"version-history":[{"count":4,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/880\/revisions"}],"predecessor-version":[{"id":884,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/posts\/880\/revisions\/884"}],"wp:attachment":[{"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/media?parent=880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/categories?post=880"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/wordpress.fangt.online\/index.php\/wp-json\/wp\/v2\/tags?post=880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}