{"id":68747,"date":"2025-06-02T18:25:06","date_gmt":"2025-06-02T10:25:06","guid":{"rendered":"https:\/\/fwq.ai\/blog\/?p=68747"},"modified":"2025-06-02T18:25:06","modified_gmt":"2025-06-02T10:25:06","slug":"%e7%90%86%e8%a7%a3c-%e9%80%92%e5%bd%92%e7%ae%97%e6%b3%95%ef%bc%9a%e4%bb%8e%e5%9f%ba%e7%a1%80%e6%a6%82%e5%bf%b5%e5%88%b0%e5%ae%9e%e6%88%98%e6%a1%88%e4%be%8b%ef%bc%8c%e5%8a%a9%e5%8a%9b%e6%8a%80","status":"publish","type":"post","link":"https:\/\/fwq.ai\/blog\/68747\/","title":{"rendered":"\u7406\u89e3C++ \u9012\u5f52\u7b97\u6cd5\uff1a\u4ece\u57fa\u7840\u6982\u5ff5\u5230\u5b9e\u6218\u6848\u4f8b\uff0c\u52a9\u529b\u6280\u672f\u8fdb\u9636"},"content":{"rendered":"<p>&nbsp;<\/p>\n<h2>\u524d\u8a00<\/h2>\n<p>\u5728\u73b0\u4ee3\u7f16\u7a0b\u8bed\u8a00\u7684\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u9012\u5f52\u7b97\u6cd5\u59cb\u7ec8\u5360\u636e\u7740\u4e0d\u53ef\u66ff\u4ee3\u7684\u91cd\u8981\u5730\u4f4d\u3002\u5b83\u4e0d\u4ec5\u662f\u4e00\u79cd\u89e3\u51b3\u590d\u6742\u95ee\u9898\u7684\u5173\u952e\u65b9\u5f0f\uff0c\u4e5f\u662f\u68c0\u9a8c\u903b\u8f91\u601d\u7ef4\u4e0e\u62bd\u8c61\u80fd\u529b\u7684\u6709\u6548\u624b\u6bb5\u3002\u672c\u6587\u5c06\u5e26\u60a8\u6df1\u5165\u7406\u89e3\u9012\u5f52\u7684\u6838\u5fc3\u673a\u5236\uff0c\u901a\u8fc7\u591a\u4e2a\u5b9e\u4f8b\u9010\u6b65\u62c6\u89e3\u5176\u5b9e\u73b0\u65b9\u5f0f\uff0c\u5e76\u63a2\u8ba8\u5176\u5728\u65e5\u5e38\u5f00\u53d1\u4e2d\u7684\u5e94\u7528\u4ef7\u503c\u3002\u540c\u65f6\uff0c\u5982\u679c\u60a8\u4ece\u4e8b\u7b97\u6cd5\u90e8\u7f72\u6216\u7f16\u7a0b\u8bad\u7ec3\uff0c\u9009\u62e9\u6027\u80fd\u5f3a\u5927\u7684<strong>\u7f8e\u56fd\u670d\u52a1\u5668<\/strong>\u80fd\u663e\u8457\u63d0\u5347\u5f00\u53d1\u6548\u7387\u4e0e\u7cfb\u7edf\u54cd\u5e94\u901f\u5ea6\u3002<\/p>\n<hr \/>\n<h2>\u4e00\u3001\u4ec0\u4e48\u662f\u9012\u5f52\u7b97\u6cd5\uff1f<\/h2>\n<p>\u9012\u5f52\uff08Recursion\uff09\u662f\u4e00\u79cd\u7b97\u6cd5\u601d\u60f3\uff0c\u5176\u672c\u8d28\u662f\u5728\u51fd\u6570\u7684\u5b9e\u73b0\u8fc7\u7a0b\u4e2d\u76f4\u63a5\u6216\u95f4\u63a5\u8c03\u7528\u81ea\u8eab\uff0c\u9010\u6b65\u5c06\u95ee\u9898\u89c4\u6a21\u7f29\u5c0f\uff0c\u6700\u7ec8\u8fbe\u5230\u89e3\u51b3\u76ee\u6807\u3002\u9012\u5f52\u7b97\u6cd5\u9002\u7528\u4e8e\u4ee5\u4e0b\u4e09\u79cd\u60c5\u5f62\uff1a<\/p>\n<ol>\n<li><strong>\u6570\u636e\u6309\u9012\u5f52\u65b9\u5f0f\u5b9a\u4e49<\/strong>\uff0c\u5982\u6590\u6ce2\u90a3\u5951\u6570\u5217\u3002<\/li>\n<li><strong>\u95ee\u9898\u672c\u8eab\u9002\u5408\u9012\u5f52\u6c42\u89e3<\/strong>\uff0c\u5982\u7ecf\u5178\u7684\u6c49\u8bfa\u5854\u95ee\u9898\u3002<\/li>\n<li><strong>\u6570\u636e\u7ed3\u6784\u672c\u8eab\u5177\u6709\u9012\u5f52\u6027\u8d28<\/strong>\uff0c\u5982\u6811\u7ed3\u6784\u3001\u5d4c\u5957\u5217\u8868\u7b49\u3002<\/li>\n<\/ol>\n<p>\u5408\u7406\u5e94\u7528\u9012\u5f52\uff0c\u53ef\u4ee5\u4f7f\u4ee3\u7801\u66f4\u4e3a\u7b80\u6d01\uff0c\u903b\u8f91\u66f4\u4e3a\u6e05\u6670\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u5c42\u7ea7\u6216\u5206\u89e3\u5f0f\u95ee\u9898\u5efa\u6a21\u3002<\/p>\n<hr \/>\n<h2>\u4e8c\u3001\u9012\u5f52\u7684\u4e09\u4e2a\u6838\u5fc3\u8981\u7d20<\/h2>\n<p>\u60f3\u8981\u7f16\u5199\u4e00\u4e2a\u7a33\u5b9a\u4e14\u9ad8\u6548\u7684\u9012\u5f52\u51fd\u6570\uff0c\u5fc5\u987b\u660e\u786e\u4ee5\u4e0b\u4e09\u70b9\uff1a<\/p>\n<h3>1. \u660e\u786e\u51fd\u6570\u76ee\u6807<\/h3>\n<p>\u5728\u7f16\u5199\u9012\u5f52\u51fd\u6570\u65f6\uff0c\u7b2c\u4e00\u6b65\u5fc5\u987b\u660e\u786e\u8be5\u51fd\u6570\u7684\u76ee\u6807\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5e0c\u671b\u8ba1\u7b97\u4e00\u4e2a\u6b63\u6574\u6570 <code>n<\/code> \u7684\u9636\u4e58\uff0c\u51fd\u6570\u76ee\u6807\u5c31\u662f\u8fd4\u56de <code>n * (n-1) * (n-2) * ... * 1<\/code>\u3002<\/p>\n<pre><code class=\"language-c\">int factorial(int n) {\r\n    \/\/ \u51fd\u6570\u76ee\u6807\uff1a\u8ba1\u7b97 n \u7684\u9636\u4e58\r\n}\r\n<\/code><\/pre>\n<h3>2. \u8bbe\u7f6e\u9012\u5f52\u7ec8\u6b62\u6761\u4ef6<\/h3>\n<p>\u9012\u5f52\u82e5\u65e0\u7ec8\u6b62\u6761\u4ef6\uff0c\u5c06\u5bfc\u81f4\u65e0\u9650\u5faa\u73af\uff0c\u751a\u81f3\u5bfc\u81f4\u7cfb\u7edf\u6808\u6ea2\u51fa\u3002\u5bf9\u4e8e\u9636\u4e58\u51fd\u6570\u800c\u8a00\uff0c\u5f53 <code>n = 1<\/code> \u65f6\u7ed3\u679c\u5df2\u77e5\uff0c\u5e94\u7acb\u5373\u8fd4\u56de\uff1a<\/p>\n<pre><code class=\"language-c\">if (n == 1) return 1;\r\n<\/code><\/pre>\n<p>\u53ef\u4ee5\u6839\u636e\u95ee\u9898\u7684\u7279\u70b9\u8bbe\u7f6e\u4e0d\u540c\u7684\u7ec8\u6b62\u6761\u4ef6\u3002\u4f8b\u5982\u5bf9\u4e8e <code>n &lt;= 2<\/code> \u76f4\u63a5\u8fd4\u56de <code>n<\/code> \u4e5f\u672a\u5c1d\u4e0d\u53ef\u3002<\/p>\n<h3>3. \u6784\u9020\u7b49\u4ef7\u9012\u5f52\u5173\u7cfb\u5f0f<\/h3>\n<p>\u5728\u9012\u5f52\u903b\u8f91\u4e2d\uff0c\u6211\u4eec\u9700\u8981\u901a\u8fc7\u6784\u5efa\u7b49\u4ef7\u5173\u7cfb\uff0c\u5c06\u5927\u95ee\u9898\u62c6\u5206\u4e3a\u5c0f\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u9636\u4e58\u51fd\u6570\u53ef\u8f6c\u6362\u4e3a\uff1a<code>factorial(n) = n * factorial(n-1)<\/code>\u3002\u5b8c\u6574\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-c\">int factorial(int n) {\r\n    if (n &lt;= 2) return n;\r\n    return n * factorial(n - 1);\r\n}\r\n<\/code><\/pre>\n<hr \/>\n<h2>\u4e09\u3001\u9012\u5f52\u5b9e\u4f8b\u5206\u6790<\/h2>\n<h3>\u5b9e\u4f8b1\uff1a\u6590\u6ce2\u90a3\u5951\u6570\u5217\u8ba1\u7b97<\/h3>\n<p>\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n<pre><code>f(1) = 1\r\nf(2) = 1\r\nf(n) = f(n-1) + f(n-2)\r\n<\/code><\/pre>\n<p>\u5176\u9012\u5f52\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-c\">int fibonacci(int n) {\r\n    if (n &lt;= 2) return 1;\r\n    return fibonacci(n - 1) + fibonacci(n - 2);\r\n}\r\n<\/code><\/pre>\n<p>\u8fd9\u4e2a\u7b97\u6cd5\u867d\u7136\u6e05\u6670\uff0c\u4f46\u5728\u6570\u503c\u8f83\u5927\u65f6\u6548\u7387\u504f\u4f4e\u3002\u82e5\u8981\u63d0\u5347\u6027\u80fd\uff0c\u53ef\u4ee5\u501f\u52a9<strong>\u7f8e\u56fd\u4e91\u670d\u52a1\u5668<\/strong>\u90e8\u7f72\u591a\u7ebf\u7a0b\u8ba1\u7b97\u73af\u5883\uff0c\u901a\u8fc7\u9ad8\u6027\u80fd\u8ba1\u7b97\u8d44\u6e90\u63d0\u5347\u901f\u5ea6\u3002<\/p>\n<hr \/>\n<h3>\u5b9e\u4f8b2\uff1a\u53f0\u9636\u8df3\u6cd5\u95ee\u9898<\/h3>\n<p>\u8bbe\u4e00\u53ea\u5c0f\u732a\u4e00\u6b21\u53ef\u8df3 1 \u7ea7\u6216 2 \u7ea7\u53f0\u9636\uff0c\u6c42\u8df3\u4e0a n \u7ea7\u53f0\u9636\u6709\u591a\u5c11\u79cd\u65b9\u5f0f\uff1f<\/p>\n<p>\u8be5\u95ee\u9898\u4e0e\u6590\u6ce2\u90a3\u5951\u6570\u5217\u672c\u8d28\u76f8\u540c\uff1a<\/p>\n<ul>\n<li>\u5f53 n = 1\uff0c\u53ea\u6709 1 \u79cd\u8df3\u6cd5\uff1b<\/li>\n<li>\u5f53 n = 2\uff0c\u6709 2 \u79cd\u8df3\u6cd5\uff1a1+1 \u6216 2\uff1b<\/li>\n<li>\u5f53 n &gt; 2\uff0c\u8df3\u6cd5\u6570\u91cf\u7b49\u4e8e f(n-1) + f(n-2)\u3002<\/li>\n<\/ul>\n<p>\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-c\">int jump(int n) {\r\n    if (n &lt;= 2) return n;\r\n    return jump(n - 1) + jump(n - 2);\r\n}\r\n<\/code><\/pre>\n<p>\u901a\u8fc7\u5728<strong>\u7f8e\u56fdVPS<\/strong>\u73af\u5883\u4e2d\u8fd0\u884c\u8fd9\u7c7b\u9012\u5f52\u7a0b\u5e8f\uff0c\u8fd8\u53ef\u4ee5\u7ed3\u5408\u7f13\u5b58\u7b56\u7565\uff08\u5982\u8bb0\u5fc6\u5316\u9012\u5f52\uff09\u8fdb\u4e00\u6b65\u63d0\u5347\u8fd0\u7b97\u6548\u7387\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u5e76\u53d1\u8bf7\u6c42\u91cf\u5927\u7684\u5e73\u53f0\u7cfb\u7edf\u3002<\/p>\n<hr \/>\n<h3>\u5b9e\u4f8b3\uff1a\u6c49\u8bfa\u5854\u95ee\u9898<\/h3>\n<p>\u6c49\u8bfa\u5854\u95ee\u9898\u662f\u9012\u5f52\u4e2d\u7684\u7ecf\u5178\u6848\u4f8b\u3002\u5176\u76ee\u6807\u662f\u5c06 n \u4e2a\u76d8\u5b50\u4ece\u67f1\u5b50 A \u79fb\u52a8\u5230\u67f1\u5b50 C\uff0c\u6bcf\u6b21\u53ea\u80fd\u79fb\u52a8\u4e00\u4e2a\u76d8\u5b50\uff0c\u4e14\u4e0d\u80fd\u628a\u5927\u76d8\u653e\u5728\u5c0f\u76d8\u4e0a\u3002<\/p>\n<p>\u6c49\u8bfa\u5854\u7684\u9012\u5f52\u5206\u89e3\u65b9\u5f0f\uff1a<\/p>\n<ol>\n<li>\u5c06\u524d n-1 \u4e2a\u76d8\u5b50\u4ece A \u79fb\u52a8\u5230 B\uff08\u501f\u52a9 C\uff09\uff1b<\/li>\n<li>\u5c06\u7b2c n \u4e2a\u76d8\u5b50\u4ece A \u79fb\u52a8\u5230 C\uff1b<\/li>\n<li>\u5c06 n-1 \u4e2a\u76d8\u5b50\u4ece B \u79fb\u52a8\u5230 C\uff08\u501f\u52a9 A\uff09\u3002<\/li>\n<\/ol>\n<p>\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre><code class=\"language-c\">void hanoi(int n, char A, char B, char C) {\r\n    if (n == 1) {\r\n        printf(\"Move disk 1 from %c to %c\\n\", A, C);\r\n    } else {\r\n        hanoi(n - 1, A, C, B);\r\n        printf(\"Move disk %d from %c to %c\\n\", n, A, C);\r\n        hanoi(n - 1, B, A, C);\r\n    }\r\n}\r\n<\/code><\/pre>\n<p>\u8be5\u7b97\u6cd5\u5728<strong>\u7f8e\u56fd\u670d\u52a1\u5668<\/strong>\u4e0a\u7684\u5e94\u7528\u5178\u578b\u573a\u666f\u5305\u62ec\u6559\u80b2\u5e73\u53f0\u7b97\u6cd5\u6f14\u793a\u3001\u56fe\u5f62\u52a8\u753b\u751f\u6210\u7b49\u7cfb\u7edf\uff0c\u5c24\u5176\u5bf9\u56fe\u5f62\u5904\u7406\u80fd\u529b\u548c\u7a33\u5b9a\u6027\u6709\u4e00\u5b9a\u8981\u6c42\u3002<\/p>\n<hr \/>\n<h2>\u56db\u3001\u9012\u5f52\u7684\u4f18\u52bf\u4e0e\u670d\u52a1\u5668\u73af\u5883\u7684\u7ed3\u5408<\/h2>\n<p>\u9012\u5f52\u7a0b\u5e8f\u5bf9\u7cfb\u7edf\u6808\u7a7a\u95f4\u3001CPU\u7b97\u529b\u6709\u4e00\u5b9a\u4f9d\u8d56\u3002\u82e5\u90e8\u7f72\u5728\u6027\u80fd\u8f83\u4f4e\u7684\u672c\u5730\u73af\u5883\uff0c\u6781\u6613\u9020\u6210\u54cd\u5e94\u5ef6\u8fdf\u6216\u7a0b\u5e8f\u5d29\u6e83\u3002\u800c\u901a\u8fc7\u90e8\u7f72\u5728\u9ad8\u6027\u80fd<strong>\u7f8e\u56fd\u670d\u52a1\u5668<\/strong>\u4e0a\uff0c\u4e0d\u4ec5\u53ef\u83b7\u5f97\u66f4\u9ad8\u7684\u6267\u884c\u6548\u7387\uff0c\u8fd8\u80fd\u4fdd\u969c\u7a0b\u5e8f\u5728\u9ad8\u5e76\u53d1\u548c\u957f\u65f6\u95f4\u8fd0\u884c\u4e0b\u7684\u7a33\u5b9a\u6027\u3002<\/p>\n<p>\u65e0\u8bba\u60a8\u662f\u8fdb\u884c\u7b97\u6cd5\u6559\u5b66\u3001\u5f00\u53d1\u56fe\u5f62\u4ea4\u4e92\u7a0b\u5e8f\uff0c\u8fd8\u662f\u6784\u5efa\u6570\u636e\u5206\u6790\u6a21\u578b\uff0c\u62e5\u6709\u4e00\u4e2a\u7a33\u5b9a\u3001\u4f4e\u5ef6\u8fdf\u7684<strong>\u7f8e\u56fd\u4e91\u670d\u52a1\u5668<\/strong>\u5e73\u53f0\u5c06\u4e3a\u60a8\u7684\u9879\u76ee\u63d0\u4f9b\u575a\u5b9e\u7684\u8ba1\u7b97\u540e\u76fe\u3002<\/p>\n<hr \/>\n<h2>\u7ed3\u8bed<\/h2>\n<p>\u9012\u5f52\u7b97\u6cd5\u4f5c\u4e3a\u7a0b\u5e8f\u5458\u4e0d\u53ef\u6216\u7f3a\u7684\u6280\u80fd\u4e4b\u4e00\uff0c\u5176\u80cc\u540e\u8574\u542b\u7684\u601d\u7ef4\u6a21\u578b\u8fdc\u4e0d\u6b62\u5199\u51e0\u4e2a\u51fd\u6570\u90a3\u4e48\u7b80\u5355\u3002\u901a\u8fc7\u5408\u7406\u5e94\u7528\u9012\u5f52\u3001\u6784\u5efa\u9ad8\u6548\u51fd\u6570\u7ed3\u6784\uff0c\u5e76\u501f\u52a9\u5f3a\u5927\u7684<a 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\u5408\u7406\u5e94\u7528\u9012\u5f52\uff0c\u53ef\u4ee5\u4f7f\u4ee3\u7801\u66f4\u4e3a\u7b80\u6d01\uff0c\u903b\u8f91\u66f4\u4e3a\u6e05\u6670\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u5c42\u7ea7\u6216\u5206\u89e3\u5f0f\u95ee\u9898\u5efa\u6a21\u3002 \u4e8c\u3001\u9012\u5f52\u7684\u4e09\u4e2a\u6838\u5fc3\u8981\u7d20 \u60f3\u8981\u7f16\u5199\u4e00\u4e2a\u7a33\u5b9a\u4e14\u9ad8\u6548\u7684\u9012\u5f52\u51fd\u6570\uff0c\u5fc5\u987b\u660e\u786e\u4ee5\u4e0b\u4e09\u70b9\uff1a 1. \u660e\u786e\u51fd\u6570\u76ee\u6807 \u5728\u7f16\u5199\u9012\u5f52\u51fd\u6570\u65f6\uff0c\u7b2c\u4e00\u6b65\u5fc5\u987b\u660e\u786e\u8be5\u51fd\u6570\u7684\u76ee\u6807\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u5e0c\u671b\u8ba1\u7b97\u4e00\u4e2a\u6b63\u6574\u6570 n \u7684\u9636\u4e58\uff0c\u51fd\u6570\u76ee\u6807\u5c31\u662f\u8fd4\u56de n * (n-1) * (n-2) * &#8230; * 1\u3002 int factorial(int n) { \/\/ \u51fd\u6570\u76ee\u6807\uff1a\u8ba1\u7b97 n \u7684\u9636\u4e58 } 2. \u8bbe\u7f6e\u9012\u5f52\u7ec8\u6b62\u6761\u4ef6 \u9012\u5f52\u82e5\u65e0\u7ec8\u6b62\u6761\u4ef6\uff0c\u5c06\u5bfc\u81f4\u65e0\u9650\u5faa\u73af\uff0c\u751a\u81f3\u5bfc\u81f4\u7cfb\u7edf\u6808\u6ea2\u51fa\u3002\u5bf9\u4e8e\u9636\u4e58\u51fd\u6570\u800c\u8a00\uff0c\u5f53 n = 1 \u65f6\u7ed3\u679c\u5df2\u77e5\uff0c\u5e94\u7acb\u5373\u8fd4\u56de\uff1a if (n == 1) return 1; \u53ef\u4ee5\u6839\u636e\u95ee\u9898\u7684\u7279\u70b9\u8bbe\u7f6e\u4e0d\u540c\u7684\u7ec8\u6b62\u6761\u4ef6\u3002\u4f8b\u5982\u5bf9\u4e8e n &lt;= 2 \u76f4\u63a5\u8fd4\u56de n \u4e5f\u672a\u5c1d\u4e0d\u53ef\u3002 3. 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