{"id":92,"date":"2010-08-22T03:15:39","date_gmt":"2010-08-21T19:15:39","guid":{"rendered":"http:\/\/comzyh.tk\/blog\/?p=92"},"modified":"2013-08-30T17:08:05","modified_gmt":"2013-08-30T09:08:05","slug":"%e5%ba%b7%e6%8b%93%e5%b1%95%e5%bc%80%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/comzyh.com\/blog\/archives\/92\/","title":{"rendered":"\u5eb7\u6258\u5c55\u5f00\u8be6\u89e3"},"content":{"rendered":"<p>\u81ea\u5b66\u5eb7\u6258\u5c55\u5f00\uff08\u505a8\u6570\u7801\u95ee\u9898\uff09\u53bb\u7f51\u4e0a\u67e5\u8d44\u6599\uff0c\u65e0\u65e0\u4e00\u660e\u767d\uff0c\u53c8\u82e6\u4e8e\u8d44\u6599\u592a\u5c11\uff0c\u8bb2\u7684\u592a\u542b\u84c4<br \/>\n\u7136\u800c\u300a\u5468\u6613\u300b\u4e91\uff1a\u5929\u884c\u5065\uff0c\u541b\u5b50\u4ee5\u81ea\u5f3a\u4e0d\u606f<br \/>\n\u4e8e\u662f\u594b\u62186h\u4f5c\u6b64\u6587<br \/>\n\u4e3a\u50cf\u6211\u4e00\u6837\u7684\u83dc\u626b\u6e05\u524d\u884c\u969c\u788d\uff0c\u6545\u540d\u66f0\uff1a\u201c\u8be6\u89e3\u201d<br \/>\n\u5982\u6709\u4e0d\u5f53\u4e4b\u5904\uff0c\u6073\u8bf7\u6307\u6b63<br \/>\n~_~_~_~_~_~_~_\u534e\u4e3d\u7684\u5206\u5272\u7ebf_~_~_~_~_~<br \/>\n\u5eb7\u6258\u5c55\u5f00(x)\u7684\u5b9e\u9645\u610f\u4e49:\u5bf9\u4e8e\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u6570\u5217\u5305\u542b\u5143\u7d20[0..n-1]<br \/>\nx\u8868\u793a\u6b64\u6570\u5217\u662f{0,1,2&#8230;n-1}\u5168\u6392\u5217\u4e2d\u7b2c\u51e0\u5c0f\u7684\u3002\u6700\u5c0f\u7684\u4e3a0<br \/>\n(\u4f46\u662f\u901a\u5e38\u5e94\u7528\u7684\u5eb7\u6258\u5c55\u5f00\u6709\u65f6\u662f[1..n])<br \/>\n\u4f8b\u5982\u5f53n=3\u65f6(\u9ed8\u8ba4[1..n]):<br \/>\n{1,2,3}x=0;{1,3,2}x=1;<br \/>\n{2,1,3}x=2;{2,3,1}x=3;<br \/>\n{3,1,2}x=4;{3,2,1}x=5;<br \/>\n(\u9488\u5bf90..n-1\u662f\u8fde\u7eed\u81ea\u7136\u6570 )<br \/>\n\u5176\u8ba1\u7b97\u65b9\u6cd5:<br \/>\n\\(<br \/>\nX=a[n]\\times (n-1)!+a[n-1]\\times (n-2)!+&#8230;a[i]\\times (i-1)!a[2]\\times 1!+a[1]\\times 0! \\\\<br \/>\n\\)<br \/>\n<span style=\"color: #ffffff;\"> X=a[n]*(n-1)!+a[n-1]*(n-2)!+&#8230;a[i]*(i-1)!+a[2]*1!+a[1]*0!;<br \/>\n<\/span> \u6216(d\u5bf9\u4e8e\u7b2c\u4e00\u4f4d\u4e3aa[1],\u4e0b\u9762\u4ee3\u7801\u5373\u662f\u5982\u6b64):<br \/>\n\\(<br \/>\nX=a[1]\\times (n-1)!+a[2]\\times [n-2]!+&#8230;+a[n-1]\\times 1!+a[n]\\times 0! \\\\<br \/>\n\\)<br \/>\n<span style=\"color: #ffffff;\"> X=a[1]*(n-1)!+a[2]*[n-2]!+&#8230;+a[n-1]*1!+a[n]*0\uff01<br \/>\n<\/span> \u5176\u4e2da[i]\u8868\u793a\u5143\u7d20arr[i]\u5728\u8fd8\u672a\u51fa\u73b0\u7684\u6570\u5b57\u4e2d\u6392\u7b2c\u51e0,\u7b80\u800c\u8a00\u4e4b\u5c31\u662f\u5176\u540e\u9762\u6709\u591a\u5c11\u5143\u7d20\u6bd4arr[i]\u5c0f<br \/>\n\u6838\u5fc3\u4ee3\u7801\uff1a<\/p>\n<pre lang=\"Pascal\">\r\nreadln(n);\r\nfor i:=1 to n do read(arr[i]);\r\nfor i:=1 to n-1 do begin \/\/\u5faa\u73af\u5f53\u524d\u4f4d\r\nt=0;\/\/\u4ee3\u8868\u7b2c\u51e0\u5927\r\nfor j=i+1 to n if arr[j]     ans:=ans+t*fac[n-i-1];\/\/fac[i]\u8868\u793ai\u9636\u4e58\r\nend;\r\nwriteln(ans) ;\r\n<\/pre>\n<p>\u5b9e\u9645\u4ee3\u7801\uff08C\u5b9e\u73b0\uff09\u4e2a\u4eba\u8ba4\u4e3a\u6bd4\u8f83\u8be6\u7ec6\u4e86\uff0c\u5982\u679c\u6709\u4e0d\u7406\u89e3\uff0c<span style=\"color: #ff0000;\"><strong>\u5207\u8bb0<\/strong><\/span>\u770b\u5b8c\u4e0a\u9762\u8bf4\u660e<br \/>\n<!--more--><\/p>\n<pre lang=\"C\">\r\n#include <stdio.h>\r\nint fac[101],arr[101];\r\nint ten[11]={0,1,2,3,4,5,6,7,8,9,10};\/\/\u5168\u6392\u5217\u5143\u7d20\u5e8f\u5217,\u6b64\u5904\u662f[1..10] \r\nint n,e; \r\n\r\n\/* \r\n\u5eb7\u6258\u5c55\u5f00(x)\u7684\u5b9e\u9645\u610f\u4e49:\u5bf9\u4e8e\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u6570\u5217\u5305\u542b\u5143\u7d20[0..n-1]  \r\nx\u8868\u793a\u6b64\u6570\u5217\u662f{0,1,2...n-1}\u5168\u6392\u5217\u4e2d\u7b2c\u51e0\u5c0f\u7684\u3002\u6700\u5c0f\u7684\u4e3a0\r\n(\u4f46\u662f\u901a\u5e38\u5e94\u7528\u7684\u5eb7\u6258\u5c55\u5f00\u6709\u65f6\u662f[1..n])\r\n\u4f8b\u5982\u5f53n=3\u65f6(\u9ed8\u8ba4[1..n]): \r\n{1,2,3}x=0;{1,3,2}x=1;\r\n{2,1,3}x=2;{2,3,1}x=3;\r\n{3,1,2}x=4;{3,2,1}x=5;\r\n(\u9488\u5bf90..n-1\u662f\u8fde\u7eed\u81ea\u7136\u6570 )\r\n\u5176\u8ba1\u7b97\u65b9\u6cd5: \r\nX=a[n]*(n-1)!+a[n-1]*(n-2)!+...a[i]*(i-1)!a[2]*1!+a[1]*0!;\r\n\u6216(d\u5bf9\u4e8e\u7b2c\u4e00\u4f4d\u4e3aa[1],\u4e0b\u9762\u4ee3\u7801\u5373\u662f\u5982\u6b64):\r\nX=a[1]*(n-1)!+a[2]*[n-2]!+...+a[n-1]*1!+a[n]*0\uff01 \r\n\u5176\u4e2da[i]\u8868\u793a\u5143\u7d20arr[i]\u5728\u8fd8\u672a\u51fa\u73b0\u7684\u6570\u5b57\u4e2d\u6392\u7b2c\u51e0,\u7b80\u800c\u8a00\u4e4b\u5c31\u662f\u5176\u540e\u9762\u6709\u591a\u5c11\u5143\u7d20\u6bd4arr[i]\u5c0f \r\nCode: \r\nreadln(n);\r\nfor i:=1 to n do read(arr[i]);\r\nfor i:=1 to n-1 do begin \/\/\u5faa\u73af\u5f53\u524d\u4f4d \r\n    t=0;\/\/\u4ee3\u8868\u7b2c\u51e0\u5927 \r\n    for j=i+1 to n if arr[j]<arr[i] inc(t);\r\n    ans:=ans+t*fac[n-i-1];\/\/fac[i]\u8868\u793ai\uff01 \r\nend;\r\nwriteln(ans) ;\r\n*\/ \r\n    \r\nint cantor(int k){\/\/\u5eb7\u6258\u5c55\u5f00,\u6b64\u5c55\u5f00\u4e0e\u5e8f\u5217\u5143\u7d20\u5927\u5c0f\u65e0\u5173,\u4ec5\u4e0e\u5927\u5c0f\u6392\u5217\u987a\u5e8f\u6709\u5173,{0,1,2}=0\uff1b{1,2,3}=0\uff1b \r\n    int i,j,t,ans=0;\r\n    for (i=1;i<n;i++){\r\n        \/* \r\n        \u5bf9\u4e8e\u5faa\u73af\u5230n-1\u7684\u89e3\u91ca\uff1a\r\n        \u5faa\u73af\u5230n\u65e0\u610f\u4e49(0*0!\u6052\u7b49\u4e8e0),\u4e14 ans=(ans+t)*(n-i);\u4e0d\u5141\u8bb8i=n,\u5176\u672c\u8d28\u539f\u56e0\u662f0!=1\u800c\u4e0d\u662f0 \r\n        *\/\r\n        t=0;\r\n        for (j=i+1;j<=n;j++) if (arr[j]<arr[i]) t++;\r\n        \/\/\u5176\u4e2dt\u8868\u793a\u5143\u7d20arr[i]\u5728\u8fd8\u672a\u51fa\u73b0\u7684\u6570\u5b57\u4e2d\u6392\u7b2c\u51e0,\u7b80\u800c\u8a00\u4e4b\u5c31\u662f\u5176\u540e\u9762\u6709\u591a\u5c11\u5143\u7d20\u6bd4arr[i]\u5c0f \r\n        ans=(ans+t)*(n-i);\/\/\u7b80\u4fbf\u7b97\u6cd5,\u89e3\u91ca\u89c1\u4e0b \r\n        \/*\r\n        \u6b64\u5904\u4ee3\u7801\u672c\u5e94\u4e3a(\u4e8c\u8005\u7b49\u4ef7,\u53ef\u76f8\u4e92\u66ff\u6362):\r\n        ans+=t*fac[n-i]; \r\n        \u5bf9\u4e8e ans=(ans+t)*(n-i); \u6211\u4eec\u53ef\u4ee5\u8fd9\u6837\u7406\u89e3:\r\n        \u5f53i=1\u65f6,ans\u4e3a0,\u6700\u7ec8\u7ed3\u679c\u5e94\u4f7ft*(n-1)!=t*(n-1)*(n-2)*...*1;\r\n        \u5f53i=n\u65f6  \r\n        *\/\r\n        }\r\n    return(ans) ;\r\n    }\r\nint uncantor(int x,int k){\/\/\u9006\u5eb7\u6258\u5c55\u5f00,x\u8868\u793a\u5eb7\u6258\u5c55\u5f00 \r\n    int i,j,l,t,u[12];\r\n    memset(&#038;u,0,sizeof(u));\r\n    for (i=1;i<=k;i++){\/\/\u679a\u4e3e\u5404\u4f4d \r\n        t=x\/fac[k-i];\/\/t\uff1a\u6bd4\u5f53\u524d\u4f4d\u5c0f\u7684\u53ea\u6709t\u4e2a \r\n        x-=t*fac[k-i];\/\/\u5220\u53bb \r\n        for (j=1,l=0;l<=t;j++)if (u[j]==0)l++;\/\/\u6b64\u5904l<=t\u5e76\u4e0d\u6b63\u786e\u7406\u5e94\u662fl<t,\u6545j\u591a\u53d6\u4e861\uff1b \r\n        \/*\r\n        for(j=1,l=0;l<t;j++) \u4e0d\u80fd\u5904\u7406\u5e38\u89c1\u7684t=0\u7684\u60c5\u51b5,\u82e5t=0\u5219\u4f1a\u9020\u6210\u4e0d\u6267\u884c\u5faa\u73af\r\n        \u6545\u5728\u4e0b\u65b9\u505a\u4e00\u51cf\u6cd5 \r\n        *\/ \r\n        j--;\r\n        u[j]=1;\r\n        arr[i]=j;\/\/\u8fd9\u91cc\u9ed8\u8ba4\u662f\u96c6\u5408\u5143\u7d20\u4e3a[1..n]  \r\n        \/\/\u82e5\u6709\u5fc5\u8981,\u6539\u4e3aarr[i]=ten[j]; \r\n        }\r\n    }   \r\nint main(){ \r\n    int i,j;\r\n    fac[0]=1;\r\n    for (i=1;i<=12;i++)fac[i]=fac[i-1]*i;\/\/\u8ba1\u7b97\u9636\u4e58 \r\n    scanf(\"%d\",&#038;n);\r\n    for (i=1;i<=n;i++){\r\n        scanf(\"%d\",&#038;arr[i]);\r\n        }\r\n    printf(\"%d\\n\",e=cantor(n)) ;\r\n    memset(&#038;arr,0,sizeof(arr));\r\n    uncantor(e,n);\r\n    for (i=1;i<=n;i++)printf(\"%3d\",arr[i]);\r\n    getch();\r\n    }\r\n\r\n<\/pre>\n<p>\u9700\u8981\u6ce8\u610f\u7684\uff08\u5176\u5b9e\u4ee3\u7801\u4e2d\u6ce8\u91ca\u5f88\u6e05\u695a\uff09<\/p>\n<p>0\uff01=1<\/p>\n<p>\u5eb7\u6258\u5c55\u5f00<span style=\"color: #ff0000;\">\u53ea<\/span>\u4e0e\u6570\u5217\u5143\u7d20\u4e2a\u6570\u548c\u5176\u5927\u5c0f\u6392\u5217\u987a\u5e8f\u6709\u5173\uff08\u5373\u7b2c\u51e0\u5927\u7684\u5143\u7d20\u6392\u5728\u7b2c\u51e0\u4f4d\uff09<\/p>\n<p>\u9700\u8981\u5eb7\u6258\u5c55\u5f00\u7684\u6570\u5217<span style=\"color: #ff0000;\">\u4e0d\u5141\u8bb8<\/span>\u6709\u91cd\u590d<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u81ea\u5b66\u5eb7\u6258\u5c55\u5f00\uff08\u505a8\u6570\u7801\u95ee\u9898\uff09\u53bb\u7f51\u4e0a\u67e5\u8d44\u6599\uff0c\u65e0\u65e0\u4e00\u660e\u767d\uff0c\u53c8\u82e6\u4e8e\u8d44\u6599\u592a\u5c11\uff0c\u8bb2\u7684\u592a\u542b\u84c4 \u7136\u800c\u300a\u5468\u6613\u300b\u4e91\uff1a\u5929\u884c\u5065\uff0c\u541b\u5b50 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[9,30],"tags":[40],"class_list":["post-92","post","type-post","status-publish","format-standard","hentry","category-9","category-non-solution","tag-40"],"jetpack_publicize_connections":[],"aioseo_notices":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6XQWE-1u","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/comments?post=92"}],"version-history":[{"count":5,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/posts\/92\/revisions\/790"}],"wp:attachment":[{"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/media?parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/categories?post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/comzyh.com\/blog\/wp-json\/wp\/v2\/tags?post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}