{"id":349,"date":"2013-03-09T16:41:00","date_gmt":"2013-03-09T08:41:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/253"},"modified":"2013-03-09T16:41:00","modified_gmt":"2013-03-09T08:41:00","slug":"puppet_master_gauss_elimination_the_xor_edition_-_multiple_solutions","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=349","title":{"rendered":"\u4eba\u5076\u5e08(Gauss\u6d88\u5143xor\u7248-\u591a\u89e3)"},"content":{"rendered":"<p>Problem 2 \u4eba\u5076\u5e08(alice.cpp\/c\/pas)<\/p>\n<p>\u3010\u9898\u76ee\u63cf\u8ff0\u3011<\/p>\n<p>n\u70b9m\u53cc\u5411\u8fb9\u7684\u56fe\uff0c\u6bcf\u4e2a\u70b9\u67092\u4e2a\u72b6\u6001\uff1a\u5f00\u548c\u5173\u3002\u6bcf\u6b21\u64cd\u4f5c\u6539\u53d8\u4e00\u4e2a\u70b9\u7684\u72b6\u6001\uff0c\u4ee5\u53ca\u4e0e\u5176\u6709\u8fb9\u76f4\u63a5\u76f8\u8fde\u7684\u70b9\u7684\u72b6\u6001\u3002\u95ee\u5f00\u542f\u6240\u6709\u70b9\u81f3\u5c11\u9700\u8981\u591a\u5c11\u6b21\u64cd\u4f5c\u3002<\/p>\n<p>\u3010\u8f93\u5165&#26684;\u5f0f\u3011<\/p>\n<p>\u7b2c\u4e00\u884c2\u4e2a\u6574\u6570n,m\u3002<\/p>\n<p>\u7b2c\u4e8c\u884cn\u4e2a\u6574\u6570\uff0c\u7b2ci\u4e2a\u6570\u8868\u793a\u7b2ci\u70b9\u7684\u72b6\u6001\uff0c0\u4e3a\u5173\uff0c1\u4e3a\u5f00\u3002<\/p>\n<p>\u7b2c3..m&#43;2\u884c\uff0c\u6bcf\u884c2\u4e2a\u6574\u6570a,b\uff0c\u8868\u793aa\u548cb\u76f4\u63a5\u76f8\u8fde\uff0c\u540c\u4e00\u6761\u8fb9\u4e0d\u4f1a\u51fa\u73b0\u591a\u6b21\u3002<\/p>\n<p>\u3010\u8f93\u51fa&#26684;\u5f0f\u3011<\/p>\n<p>\u7b2c\u4e00\u884c\u4e00\u4e2a\u6574\u6570k\u8868\u793a\u6700\u5c11\u7684\u64cd\u4f5c\u6b21\u6570\uff0c\u6240\u6709\u6570\u636e\u4fdd\u8bc1\u81f3\u5c11\u6709\u4e00\u7ec4\u53ef\u884c\u89e3\u3002<\/p>\n<p>\u7b2c\u4e8c\u884ck\u4e2a\u6574\u6570\uff0c\u8868\u793a\u64cd\u4f5c\u7684\u70b9\u7684\u7f16\u53f7\u3002<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u5165\u3011<\/p>\n<p>4 3<\/p>\n<p>1 1 0 0<\/p>\n<p>2 3<\/p>\n<p>1 3<\/p>\n<p>2 4<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u51fa\u3011<\/p>\n<p>3<\/p>\n<p>1 2 3<\/p>\n<p>\u3010\u6570\u636e\u8303\u56f4\u3011<\/p>\n<p>\u5bf9\u4e8e30%\u7684\u6570\u636e\uff0c1&lt;=n&lt;=10\uff0c0&lt;=m&lt;=40<\/p>\n<p>\u5bf9\u4e8e60%\u7684\u6570\u636e\uff0c1&lt;=n&lt;=30\uff0c0&lt;=m&lt;=100<\/p>\n<p>\u5bf9\u4e8e100%\u7684\u6570\u636e\uff0c1&lt;=n&lt;=40\uff0c0&lt;=m&lt;=500<\/p>\n<p><span style=\"font-size:14px\">\u8fd9\u9898\u8fd8\u662f\u9ad8\u65af\u6d88\u5143xor.<\/span><\/p>\n<p><span style=\"font-size:14px\">\u4e0d\u540c\u7684\u662f\u8981\u8003\u8651\u591a\u89e3.&nbsp;<\/span><\/p>\n<p><span style=\"font-size:14px\">\u9ad8\u65af\u6d88\u5143\u591a\u89e3\u8003\u8651\u65b9\u6cd5\uff1a<\/span><\/p>\n<p><span style=\"font-size:14px\">Gauss();<\/span><\/p>\n<p><span style=\"font-size:14px\">dfs(n,1)\/\/\u628a&#20540;\u5f80\u56de\u4ee3<\/span><\/p>\n<p><span style=\"font-size:14px\">\u5982\u679c\u9047\u5230a[i][i]==0,\u5219\u5206\u60c5\u51b5dfs.<\/span><\/p>\n<p><span style=\"font-size:14px\">\u8fd9\u6837\u505a\u7684\u597d\u5904\u662fO(2^n) &nbsp;<\/span><\/p>\n<p><span style=\"font-size:14px\">\u5982\u679c\u6c42\u51fa\u6240\u6709\u60c5\u51b5\u518d\u5f80\u56de\u4ee3\u5c31\u662fO(n^2*2^n)&nbsp;<\/span><\/p>\n<p><span style=\"font-size:14px\"><br \/>\n<\/span><\/p>\n<p><pre name=\"code\" class=\"cpp\">#include&lt;cstdio&gt;\n#include&lt;cmath&gt;\n#include&lt;algorithm&gt;\n#include&lt;functional&gt;\n#include&lt;iostream&gt;\n#include&lt;cstdlib&gt;\n#include&lt;cstring&gt;\nusing namespace std;\n#define MAXN (40+2)\n#define MAXM (500+10)\nint a[MAXN][MAXN];\nint ans[MAXN],tot=MAXN,tot2=0,ans2[MAXN];\nint n,m;\n\/*\nvoid print(int a[MAXN][MAXN],int _n)\n{\n\tfor (int i=1;i&lt;=_n;i++)\n\t{\n\t\tfor (int j=1;j&lt;=n+1;j++)\n\t\t\tprintf(&quot;%d &quot;,a[i][j]);\n\t\tprintf(&quot;n&quot;);\n\t}\n\tprintf(&quot;===n&quot;);\n}\n\nvoid res(int a[MAXN][MAXN])\n{\n\tint tot2=0;\n\tfor (int i=1;i&lt;=n;i++) if (a[i][n+1]) ans2[++tot2]=i;\n\tif (tot2&lt;tot)\n\t{\n\t\ttot=tot2;\n\t\tmemcpy(ans,ans2,(tot+1)*sizeof(int));\n\t}\n}\n*\/\nvoid gauss()\n{\n\tfor (int i=1;i&lt;=n;i++)\n\t{\n\t\tif (a[i][i]==0)\n\t\t\tfor (int j=i+1;j&lt;=n;j++) if (a[j][i]) {for (int k=1;k&lt;=n+1;k++) swap(a[j][k],a[i][k]);break;}\n\t\tif (a[i][i]==0)\tcontinue;\n\t\tfor (int j=1;j&lt;=n;j++)\n\t\t\tif (a[j][i]&amp;&amp;j!=i)\n\t\t\t{\n\t\t\t\tfor (int k=1;k&lt;=n+1;k++) a[j][k]^=a[i][k];\n\t\t\t}\n\/\/\t\tprint(a,n);\n\t}\n\/\/\tres(a);\n}\nint uknow[MAXN],uq[MAXN],un=0;\nbool b[MAXN]={0};\nvoid dfs(int i,int tot2)\n{\n\tif (tot2&gt;=tot) return;\n\tif (i==0)\n\t{\n\t\tif (tot2&lt;tot)\n\t\t{\n\t\t\ttot=tot2;\n\t\t\tmemcpy(ans,ans2,sizeof(tot)*(tot+1));\n\t\t}\n\t\treturn;\n\t}\n\tans2[tot2+1]=i;\n\tif (a[i][i])\n\t{\n\t\tbool flag=a[i][n+1];\n\t\tfor (int j=i+1;j&lt;=n;j++) if (a[i][j]&amp;b[j]) flag^=1;\n\t\tb[i]=flag;\n\t\tdfs(i-1,tot2+flag);\n\t}\n\telse\n\t{\n\t\tb[i]=1;\n\t\tdfs(i-1,tot2+1);\n\t\tb[i]=0;\n\t\tdfs(i-1,tot2);\n\t}\n\n}\nint main()\n{\n\tfreopen(&quot;alice.in&quot;,&quot;r&quot;,stdin);\n\tfreopen(&quot;alice.out&quot;,&quot;w&quot;,stdout);\n\tmemset(a,0,sizeof(a));\n\tscanf(&quot;%d%d&quot;,&amp;n,&amp;m);\n\tfor (int i=1;i&lt;=n;i++)\n\t{\n\t\tscanf(&quot;%d&quot;,&amp;a[i][n+1]);\n\t\ta[i][n+1]^=1;\n\t\ta[i][i]=1;\n\n\t}\n\tfor (int i=1;i&lt;=m;i++)\n\t{\n\t\tint u,v;\n\t\tscanf(&quot;%d%d&quot;,&amp;u,&amp;v);\n\t\ta[u][v]=a[v][u]=1;\n\t}\n\/\/\tprint();\n\/\/\tmemcpy(a2,a,sizeof(a));\n\tgauss();\n\/\/\tprint(a,n);\n\tfor (int i=1;i&lt;=n;i++)\n\t\tif (!a[i][i]) uknow[++un]=i;\n\tdfs(n,0);\n\/\/\tsort(ans+1,ans+1+tot);\n\tprintf(&quot;%dn&quot;,tot);\n\tfor (int i=1;i&lt;tot;i++) printf(&quot;%d &quot;,ans[i]);\n\tprintf(&quot;%dn&quot;,ans[tot]);\n\treturn 0;\n}<\/pre><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem 2 \u4eba\u5076\u5e08(alice.cpp\/c\/pas) \u3010\u9898\u76ee\u63cf\u8ff0\u3011 n\u70b9m\u53cc\u5411\u8fb9\u7684\u56fe\uff0c\u6bcf\u4e2a\u70b9\u67092\u4e2a\u72b6\u6001 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[125],"class_list":["post-349","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-gaussian_elimination"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u4eba\u5076\u5e08(Gauss\u6d88\u5143xor\u7248-\u591a\u89e3) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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