{"id":225,"date":"2012-11-02T21:44:00","date_gmt":"2012-11-02T13:44:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/130"},"modified":"2012-11-02T21:44:00","modified_gmt":"2012-11-02T13:44:00","slug":"poj_2115_linear_congruence_equation_of","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=225","title":{"rendered":"POJ 2115(\u7ebf\u6027\u540c\u4f59\u65b9\u7a0b\uff09"},"content":{"rendered":"<p>\u600e\u6837\u6c42\u89e3\u7ebf\u6027\u540c\u4f59\u65b9\u7a0b\u53ef\u770b\u4e0b\u65b9<\/p>\n<p>\n<\/p>\n<p>\u672c\u9898\u8981\u6c42(b-a)%(2^k)=(cx)%(2^k) &nbsp; -2^k&lt; b-a&lt;2^k &nbsp; \u7684x\u7684\u6700\u5c0f\u6b63\u6574\u6570\u89e3<\/p>\n<p><span style=\"font-size:14px\"><br \/>\n<\/span><\/p>\n<p><span style=\"font-size:14px\">\u89e3\u65b9\u7a0b ax=b (mod n)<\/span><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/nike0good.jp1.rpvhost.net\/wp-content\/uploads\/csdn\/other_site\/img_my_1358654706_2126.png\" alt=\"\" \/><\/p>\n<p>\n<\/p>\n<p>\n<\/p>\n<\/p>\n<pre name=\"code\" class=\"cpp\">#include&lt;cstdio&gt;\n#include&lt;cstring&gt;\n#include&lt;cstdlib&gt;\n#include&lt;cmath&gt;\n#include&lt;iostream&gt;\n#include&lt;algorithm&gt;\n#include&lt;functional&gt;\nusing namespace std;\nlong long a,b,c,k,x,y; \/\/ (b-a)%(2^k)=(cx)%(2^k) -2^k&lt;b-a&lt;2^k\nlong long shl(long long p,long long k)\n{\n\tk--;\n\twhile (k)\n\t{\n\t\tp*=2;\n\t\tk--;\n\t}\n\treturn p;\n\n}\nlong long exgcd(long long a,long long b)\n{\n\tif (b==0)\n\t{\n\t\tx=1;\n\t\ty=0;\n\t\treturn a;\n\t}\n\n\tlong long ans=exgcd(b,a%b);\n\tlong long x1=y;\n\tlong long y1=x-(a\/b)*y;\n\tx=x1;\n\ty=y1;\n\treturn ans;\n\n}\nlong long modular(long long a,long long b,long long n)\n{\n\n\tlong long d=exgcd(a,n);\n\tif (b%d) return -1;\n\tlong long x0=x*(b\/d) % n;\n\t\/*\n\t\td=ax(mod n)\n\t\td*(b\/d)=ax(b\/d) (mod n)\n\t\t\u8bbex(b\/d)=x0\n\t\t\u5219 b=a*x0 (mod n)\n\t\t\u56e0 b=a*(x0+t*(n\/d) )=a*x0+ a*n\/d =[a*x0+(a\/d)*n] (mod n)=a*x0 (mod n)\n\t\t-&gt; \u6c42 [x0+t*(n\/d)]min&gt;0\n\t\t t==d -&gt; (x0+n) mod n -&gt; \u6b63\u6570\u89e3\n\t\t\t\t (x0+n) mod n -k(n\/d)&gt;0   k-&gt;max\n\t\t\t\t (x0+n) mod n mod (n\/d) =(x0+n) mod (n\/d)\n\t*\/\n\/\/\tcout&lt;&lt;x0&lt;&lt;' '&lt;&lt;n\/d&lt;&lt;endl;\n\treturn (x0+n)%(n\/d);\n}\n\/\/long long\n\nint main()\n{\n\twhile (scanf(&quot;%d%d%d%d&quot;,&amp;a,&amp;b,&amp;c,&amp;k)!=EOF )\n\t{\n\t\t\/\/\/ &lt;&lt; -&gt; long long's case\n\t\t \/*\n\t\tlong long p=1LL&lt;&lt;32;\n\t\tlong long m=((long long)1&lt;&lt;32);\n\t\tcout&lt;&lt;p&lt;&lt;' '&lt;&lt;m&lt;&lt;endl;\n\t\t*\/\n\t\tif (a==0&amp;&amp;b==0&amp;&amp;c==0&amp;&amp;k==0) break;   \/\/(b-a)%(2^k)=(cx)%(2^k) b-a&lt;2^k\n\t\tlong long p2_k=shl(2,k);\n\t\tlong long ans=modular(c,(b-a+p2_k)%(p2_k),p2_k);\n\t\tif (ans==-1) cout&lt;&lt;&quot;FOREVERn&quot;;\n\t\telse cout&lt;&lt;ans&lt;&lt;endl;\n\t}\n\treturn 0;\n}<\/pre><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u600e\u6837\u6c42\u89e3\u7ebf\u6027\u540c\u4f59\u65b9\u7a0b\u53ef\u770b\u4e0b\u65b9 \u672c\u9898\u8981\u6c42(b-a)%(2^k)=(cx)%(2^k) &nbsp; -2^k&#038;l [&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":[108],"class_list":["post-225","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-linear_congruence_equation"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - 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