{"id":71,"date":"2020-07-22T01:45:23","date_gmt":"2020-07-21T17:45:23","guid":{"rendered":"http:\/\/121.89.208.222\/?p=71"},"modified":"2020-12-10T14:24:25","modified_gmt":"2020-12-10T06:24:25","slug":"%e5%ae%9e%e7%8e%b0%e6%95%b0%e7%bb%84%e5%b7%a6%e7%a7%bb","status":"publish","type":"post","link":"http:\/\/moyisuiying.com\/index.php\/datastructureandalgorithm\/71.html","title":{"rendered":"\u5b9e\u73b0\u6570\u7ec4\u5de6\u79fb"},"content":{"rendered":"\n<p>\u4e0b\u9762\u8bf7\u770b\u4e00\u9053\u7b97\u6cd5\u9898\uff1a<br>\u8bbe\u5c06n (n>1) \u4e2a\u6574\u6570\u5b58\u653e\u5230\u4e00\u7ef4\u6570\u7ec4R\u4e2d\u3002\u8bd5\u8bbe\u8ba1\u4e00\u4e2a\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u4e24\u65b9\u9762\u90fd\u5c3d\u53ef\u80fd\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u5c06R\u4e2d\u4fdd\u5b58\u7684\u5e8f\u5217\u5faa\u73af\u5de6\u79fbp (0&lt;p&lt;n) \u4e2a\u4f4d\u7f6e\uff0c\u5373\u5c06R\u4e2d\u7684\u6570\u636e\u5e8f\u5217\u7531(x0\uff0c x1\uff0c\u2026\u2026\uff0cxn-1)\u53d8\u6362\u4e3a(xp\uff0cxp+1\uff0c\u2026\u2026\uff0cxn-1\uff0cx0\uff0cx1\uff0c\u2026\u2026\uff0cxp-1)\u3002<br>\u5728\u6ca1\u5b66\u7b97\u6cd5\u4e4b\u524d\uff0c\u6211\u4eec\u4e60\u60ef\u4e86\u4f7f\u7528\u7b80\u5355\u7684\u6c42\u89e3\u65b9\u6cd5\uff1a\u501f\u52a9\u4e00\u4e2a\u4e34\u65f6\u6570\u7ec4B\u9996\u5148\u5c06\u6570\u7ec4R\u524dp\u4e2a\u5143\u7d20\u4fdd\u5b58\uff0c\u7136\u540e\u5c06R\u4e2d\u7684\u6240\u6709\u5143\u7d20\u5f80\u5de6\u79fb\u52a8p\u4e2a\u4f4d\u7f6e\uff0c\u6700\u540e\u5c06\u6570\u7ec4B\u7684\u5143\u7d20\u8fd8\u539f\u5230\u6570\u7ec4R\u7684\u540e\u9762p\u4e2a\u4f4d\u7f6e\u3002\u5177\u4f53\u7684\u4ee3\u7801\u5b9e\u73b0\u4e3a\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>void leftMoveArray(int arr&#91;], int len, int p) {\n\tif (p &lt;= 0 || p > len)\n\t{\n\t\treturn;\n\t}\n\t\/\/\u5f00\u8f9f\u4e34\u65f6\u6570\u7ec4\u7a7a\u95f4\n\tint* B = new int&#91;p];\n\t\/\/\u5c06arr\u6570\u7ec4\u7684\u524dp\u4e2a\u5143\u7d20\u4fdd\u5b58\u5230\u6570\u7ec4B\u4e2d\n\tfor (int i = 0; i &lt; p;i ++) {\n\t\tB&#91;i] = arr&#91;i];\n\t}\n\t\/\/\u5c06\u6570\u7ec4arr\u7684\u5143\u7d20\u5411\u5de6\u79fb\u52a8p\u4e2a\u4f4d\u7f6e\n\tfor (int i = 0; i &lt; len - p; i++)\n\t{\n\t\tarr&#91;i] = arr&#91;i+p];\n\t}\n\t\/\/\u5c06\u6570\u7ec4B\u7684\u5143\u7d20\u8fd8\u539f\u5230\u6570\u7ec4R\u7684\u540e\u9762p\u4e2a\u4f4d\u7f6e\n\tfor (int i = 0; i &lt; p;i++) {\n\t\tarr&#91;len -p  + i ] = B&#91;i];\n\t}\n\t\/\/\u91ca\u653e\u8d44\u6e90\n\tdelete&#91;] B;\n\tcout &lt;&lt; \"\u6570\u7ec4\u5411\u5de6\u79fb\u52a8\" &lt;&lt; p &lt;&lt; \"\u4f4d\u7684\u7ed3\u679c\u662f\uff1a\";\n\tfor (int i = 0; i &lt; len; i++)\n\t{\n\t\tcout &lt;&lt; arr&#91;i] &lt;&lt; \"  \";\n\t}\n\tcout &lt;&lt; endl;\n}\n<\/code><\/pre>\n\n\n\n<p>\u4e0b\u9762\u5f00\u59cb\u6d4b\u8bd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>int main() {\n\tint arr0&#91;] = { 1,5,3,24,8,7,34,23,4 };\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 9; i++)\n\t{\n\t\tcout &lt;&lt; arr0&#91;i] &lt;&lt; \" \";\n\t}\n\tleftMoveArray(arr0, 9, 5);\n\tint arr1&#91;] = {7,5,39,24,2,4,5};\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 7; i++)\n\t{\n\t\tcout &lt;&lt; arr1&#91;i] &lt;&lt; \" \";\n\t}\n\tleftMoveArray(arr1, 7, 5);\n\tint arr2&#91;] = { 1,5,3,24,8,7,5,64,34,23,4 };\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 11; i++)\n\t{\n\t\tcout &lt;&lt; arr2&#91;i] &lt;&lt; \" \";\n\t}\n\tleftMoveArray(arr2, 11, 5);\n\tsystem(\"pause\");\n\treturn 0;\n}<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img   class=\"lazyload\" data-src=\"https:\/\/img-blog.csdnimg.cn\/20200312144921283.png\" src=\"https:\/\/cdn.jsdelivr.net\/gh\/moezx\/cdn@3.0.2\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"\/><\/figure >\n<noscript><img src=\"https:\/\/img-blog.csdnimg.cn\/20200312144921283.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"\/><\/figure><\/noscript>\n\n\n\n<p>\u8be5\u7b97\u6cd5\u6bd4\u8f83\u7b80\u5355\u6613\u61c2\uff0c\u5176\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\uff1aO\uff08n\uff09,\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a\uff1aO\uff08p\uff09\uff0c\u4f46\u9898\u7ed9\u7684\u6761\u4ef6\u662f\uff1a \u8bd5\u8bbe\u8ba1\u4e00\u4e2a\u5728\u65f6\u95f4\u548c\u7a7a\u95f4\u4e24\u65b9\u9762\u90fd\u5c3d\u53ef\u80fd\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u8fd9\u9053\u9898\u8fd8\u6709\u6ca1\u6709\u66f4\u4f18\u7684\u7b97\u6cd5\u5462\uff1f<br>\u4e0b\u9762\u6211\u4eec\u518d\u6765\u5206\u6790\uff1a\u8be5\u9898\u76ee\u7684\u7b49\u4ef7\u547d\u9898\uff1a\u5c06\u6570\u7ec4\u5de6\u79fbp\u4e2a\u5143\u7d20,\u6211\u4eec\u53ef\u4ee5\u770b\u6210\u662f\u5c06\u6570\u7ec4AB(A\u8868\u793a\u6570\u7ec4\u524dp\u4e2a\u5143\u7d20\uff0cB\u8868\u793a\u6570\u7ec4\u7684\u540en-p\u4e2a\u5143\u7d20)\uff0c\u9006\u7f6e\u6210BA\uff0c<br>\u5728\u300a\u7ebf\u6027\u4ee3\u6570\u300b\u4e2d\uff0c\u6839\u636e\u77e9\u9635\u7684\u8fd0\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\uff1a<\/p>\n\n\n\n<p>\u7531\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u77e9\u9635\u7684\u9006\u7f6e\u8fd0\u7b97\u6765\u5165\u624b\uff1a<br>\u5c06\u6570\u7ec4\u5de6\u79fbp\u4e2a\u5143\u7d20,\u6211\u4eec\u53ef\u4ee5\u770b\u627f\u662f\u5c06\u6570\u7ec4AB(A\u8868\u793a\u6570\u7ec4\u524dp\u4e2a\u5143\u7d20\uff0cB\u8868\u793a\u6570\u7ec4\u7684\u540en-p\u4e2a\u5143\u7d20)\uff0c\u9006\u7f6e\u6210BA\uff0c\u6839\u636e\u77e9\u9635\u7684\u8fd0\u7b97\uff0c\u53ef\u4ee5\u7b49\u4ef7\u4e3a\uff1aBA=(A^-1 * B ^ -1)^-1 ,\u90a3\u4e48\u5c06\u6570\u7ec4\u5de6\u79fbp\u4e2a\u5143\u7d20\u5c31\u53ef\u4ee5\u770b\u6210\u662f\uff1a\u5148\u5c06\u6570\u7ec4A\u548cB\u5206\u522b\u9006\u7f6e\u5f97\u5230\uff1aA^-1 * B ^ -1\uff0c\u7136\u540e\u5c06A^-1 * B ^ -1\u6574\u4f53\u9006\u7f6e\u5f97\u5230BA\u3002<br>\u6b65\u9aa4\u4e3a\uff1a<br>(1)\u9996\u5148\u5c06\u6570\u7ec4\u770b\u6210\u4e24\u90e8\u5206\uff1aAB\uff0cA\u8868\u793a\u6570\u7ec4\u524dp\u4e2a\u5143\u7d20\uff0cB\u8868\u793a\u6570\u7ec4\u7684\u540en-p\u4e2a\u5143\u7d20<br>(2)\u5c06\u6570\u7ec4A\u9006\u7f6e\uff08\u5f97\u5230 A^ -1\uff09<br>(3)\u5c06\u6570\u7ec4B\u9006\u7f6e\uff08\u5f97\u5230 B^ -1\uff09<br>(4)\u5c06\u9006\u7f6e\u540e\u7684\u6570\u7ec4\u6574\u4f53\u9006\u7f6e\uff08\u5f97\u5230 (A^ -1 * B^ -1) ^-1 = BA\uff09<br>\u4e0b\u9762\u5f00\u59cb\u7528\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>void reverse(int arr&#91;],int from,int to) {\n\t\/\/\u6570\u7ec4\u79fb\u52a8\u7684\u7d22\u5f15\n\tint i = from, j = to;\n\t\/\/\u4e34\u65f6\u53d8\u91cf\n\tint temp;\n\t\/\/\u5f00\u59cb\u5c06\u6570\u7ec4\u9006\u7f6e\n\twhile (i &lt; j)\n\t{\n\t\t\/\/\u4ea4\u6362\u4f4d\u7f6e\n\t\ttemp = arr&#91;j];\n\t\tarr&#91;j] = arr&#91;i];\n\t\tarr&#91;i] = temp;\n\t\ti++;\n\t\tj--;\n\t}\n\t\n}\n\nvoid leftMove(int arr&#91;], int len, int p) {\n\tif (arr == NULL || p &lt;= 0 || p > len)\n\t{\n\t\treturn;\n\t}\n\t\/\/\u5c06\u6570\u7ec4A\u9006\u7f6e\n\treverse(arr, 0, p - 1);\n\t\/\/\u5c06\u6570\u7ec4B\u9006\u7f6e\n\treverse(arr, p, len - 1);\n\t\/\/\u5c06\u9006\u7f6e\u540e\u7684\u6570\u7ec4\u6574\u4f53\u9006\u7f6e\n\treverse(arr, 0, len - 1);\n\t\/\/\u6253\u5370\u8f93\u51fa\n\tcout &lt;&lt; \"\u6570\u7ec4\u5411\u5de6\u79fb\u52a8\" &lt;&lt; p &lt;&lt; \"\u4f4d\u7684\u7ed3\u679c\u662f\uff1a\";\n\tfor (int i = 0; i &lt; len; i++)\n\t{\n\t\tcout &lt;&lt; arr&#91;i] &lt;&lt; \"  \";\n\t}\n\tcout &lt;&lt; endl;\n}<\/code><\/pre>\n\n\n\n<p>\u6d4b\u8bd5\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>int main() {\n\tint arr0&#91;] = { 1,5,3,24,8,7,34,23,4 };\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 9; i++)\n\t{\n\t\tcout &lt;&lt; arr0&#91;i] &lt;&lt; \" \";\n\t}\n\tleftMoveArray(arr0, 9, 5);\n\tint arr1&#91;] = { 7,5,39,24,2,4,5 };\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 7; i++)\n\t{\n\t\tcout &lt;&lt; arr1&#91;i] &lt;&lt; \" \";\n\t}\n\tcout &lt;&lt; endl;\n\tleftMove(arr1, 7, 2);\n\tint arr2&#91;] = { 1,5,3,24,8,7,5,64,34,23,4 };\n\tcout &lt;&lt; \"\u6570\u7ec4\u79fb\u52a8\u524d\uff1a\";\n\tfor (int i = 0; i &lt; 11; i++)\n\t{\n\t\tcout &lt;&lt; arr2&#91;i] &lt;&lt; \" \";\n\t}\n\tleftMove(arr2, 11, 8);\n\tsystem(\"pause\");\n\treturn 0;\n}\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img   class=\"lazyload\" data-src=\"https:\/\/img-blog.csdnimg.cn\/20200312151143668.png\" src=\"https:\/\/cdn.jsdelivr.net\/gh\/moezx\/cdn@3.0.2\/img\/svg\/loader\/trans.ajax-spinner-preloader.svg\" onerror=\"imgError(this)\"  alt=\"\"\/><\/figure >\n<noscript><img src=\"https:\/\/img-blog.csdnimg.cn\/20200312151143668.png\" alt=\"\"\/><\/figure><\/noscript>\n\n\n\n<p>\u5bb9\u6613\u77e5\u9053\u8be5\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\uff1aO\uff08n\uff09,\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3a\uff1aO\uff081\uff09\uff0c\u663e\u7136\u6bd4\u7b2c\u4e00\u79cd\u65b9\u6cd5\u66f4\u4f18\uff0c\u66f4\u7b26\u5408\u9898\u76ee\u7684\u8981\u6c42\u3002<br>\u7531\u4e8e\u7b14\u8005\u77e5\u8bc6\u6c34\u5e73\u6709\u9650\uff0c\u51fa\u9519\u518d\u6240\u96be\u514d\uff0c\u6b22\u8fce\u5927\u5bb6\u65a7\u6b63\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u636e\u7ed3\u6784\u4e0e\u7b97\u6cd5\u5b9e\u73b0\u6570\u7ec4\u5de6\u79fb<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[6],"tags":[13],"_links":{"self":[{"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/posts\/71"}],"collection":[{"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/comments?post=71"}],"version-history":[{"count":1,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/posts\/71\/revisions"}],"predecessor-version":[{"id":423,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/posts\/71\/revisions\/423"}],"wp:attachment":[{"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/media?parent=71"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/categories?post=71"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/moyisuiying.com\/index.php\/wp-json\/wp\/v2\/tags?post=71"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}