{"id":1235,"date":"2019-07-02T17:42:14","date_gmt":"2019-07-02T09:42:14","guid":{"rendered":"https:\/\/mnihyc.com\/blog\/?p=1235"},"modified":"2020-02-09T02:17:49","modified_gmt":"2020-02-08T18:17:49","slug":"yzoj-p3069-%e5%ad%97%e7%ac%a6%e4%b8%b2%e5%8c%b9%e9%85%8d","status":"publish","type":"post","link":"https:\/\/mnihyc.com\/blog\/archives\/1235","title":{"rendered":"YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d"},"content":{"rendered":"<h1 style=\"text-align: center;\">YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d<\/h1>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB<\/p>\n<p style=\"text-align: center;\">\u96be\u5ea6\uff1a<span style=\"color: #993300;\">\\(7.0\\)<\/span><\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7ed9\u51fa\u4e24\u4e2a\u4e32 \\(A\\) \u548c \\(B\\)\uff0c\u4e32\u4e2d\u4ec5\u5305\u542b\u5c0f\u5199\u5b57\u6bcd\u548c\u5b57\u7b26 <code>*<\/code>\uff0c\u5176\u4e2d <code>*<\/code> \u80fd\u5339\u914d\u4efb\u610f\u7684\u5c0f\u5199\u5b57\u6bcd\uff08\u4e5f\u53ef\u4ee5\u5339\u914d <code>*<\/code>\uff09\u3002<\/p>\n<p>\u8bf7\u4f60\u6c42\u51fa\u5982\u679c\u4ee5 \\(A\\) \u4e3a\u6a21\u677f\u4e32\uff0c\u90a3\u4e48\u6709\u54ea\u4e9b \\(i\\) \u4f7f\u5f97 \\(B[i,i+\\left|A\\right|)\\) \u53ef\u4ee5\u4e0e\u00a0 \\(A\\) \u5339\u914d\uff1f<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u7b2c\u4e00\u884c \\(A\\)\uff0c\u7b2c\u4e8c\u884c \\(B\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6309\u7167\u4ece\u5c0f\u5230\u5927\u8f93\u51fa\u6240\u6709 \\(i\\) \u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">a*b\r\naebr*ob<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre class=\"lang:default decode:true \">1 5<\/pre>\n<ul>\n<li>\n<h3><strong>\u6570\u636e\u89c4\u6a21\u4e0e\u7ea6\u5b9a<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u6240\u6709\u6570\u636e\uff0c\\(\\left|A\\right|, \\left|B\\right| \\leq 500000\\) \u3002<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><!--more--><\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u60f3\u6cd5\u5b8c\u5168\u504f\u79bb\u6b63\u89e3www<\/p>\n<p>\u8bbe <code>*<\/code> \u4e3a \\(0\\) \uff0c\u5176\u4f59\u5b57\u6bcd\u7684\u503c\u90fd\u4e0e ASCII \u76f8\u5bf9\u5e94\u3002<\/p>\n<p>\u6784\u9020 Hash \\(\\sum\\limits_{i=0}^{n-1}(A_i-B_i)^2A_iB_i\\) \uff0c\u5f53\u4e14\u4ec5\u5f53\u5b83\u7684\u503c\u4e3a \\(0\\) \u65f6 \u4e24\u5b57\u7b26\u4e32\u5b8c\u5168\u5339\u914d\uff0c\u56e0\u4e3a\u53ea\u6709\u6bcf\u4e00\u4f4d\u90fd\u76f8\u7b49\u65f6 \u5b83\u7684\u503c\u624d\u53ef\u80fd\u4e3a \\(0\\) \u3002\uff08\u4e3a\u4e86\u6d88\u53bb\u8d1f\u6570\u7684\u5f71\u54cd\u6240\u4ee5\u6709\u4e00\u4e2a\u5e73\u65b9\uff0c\u8003\u8651\u5230 <code>*<\/code> \u6240\u4ee5\u518d\u4e58\u4e0a\u5176\u672c\u8eab\u3002\uff09<\/p>\n<p>\u6240\u4ee5\u53ef\u4ee5\u679a\u4e3e \\(A\\) \u5728 \\(B\\) \u4e2d\u7684\u672b\u5c3e\u4f4d\u7f6e \\(i\\) \uff0c\u5f53\u8fd9\u4e2a\u5b57\u4e32\u5339\u914d\u65f6\uff0c\u6709 \\(\\sum\\limits_{j=0}^{m-1}(A_j-B_{i-m+1+j})^2A_jB_{i-m+1+j}=0\\) \u3002<\/p>\n<p>\u82e5\u628a \\(A\\) \u4e32\u7ffb\u8f6c\uff0c\u540c\u65f6\u540e\u9762\u8865 \\(0\\) \u81f3\u4e0e \\(B\\) \u4e32\u7b49\u957f\uff0c\u5c31\u4f1a\u6709 \\(\\sum\\limits_{j=0}^i(A_j-B_{i-j})^2A_jB_{i-j}=0\\) \u3002<\/p>\n<p>\u5c55\u5f00\uff0c\u6709 \\(\\sum\\limits_{j=0}^iA_{j}^3B_{i-j}-2\\sum\\limits_{j=0}^iA_j^2B_{i-j}^2+\\sum\\limits_{j=0}^iA_{j}B_{i-j}^3\\) \u3002<\/p>\n<p>\u8dd1\u4e09\u6b21 FFT \u5373\u53ef\u3002<\/p>\n<p>&nbsp;<\/p>\n<pre class=\"lang:default decode:true \">#include &lt;cstdio&gt;\r\n#include &lt;cstdlib&gt;\r\n#include &lt;cstring&gt;\r\n#include &lt;climits&gt;\r\n#include &lt;cmath&gt;\r\n#include &lt;algorithm&gt;\r\n\r\n#define eps 1e-3\r\n#define _abs(_x) ((_x)&lt;0?-(_x):(_x))\r\n\r\ninline void getstr(char s[],int&amp;ls)\r\n{\r\n\tls=0;\r\n\tregister char c=0;\r\n\twhile(!(c&gt;='a' &amp;&amp; c&lt;='z') &amp;&amp; c!='*')\r\n\t\tc=getchar();\r\n\twhile((c&gt;='a' &amp;&amp; c&lt;='z') || c=='*')\r\n\t\ts[++ls]=c,c=getchar();\r\n}\r\n\r\ndouble _ta,_tb;\r\nstruct _cm\r\n{\r\n\t\/\/ a+bi\r\n\tdouble a,b;\r\n\t_cm(double na=0,double nb=0){a=na,b=nb;}\r\n\t#define _cm_plus(_x,_a,_b) ((_x).a=(_a).a+(_b).a,(_x).b=(_a).b+(_b).b)\r\n\t#define _cm_minus(_x,_a,_b) ((_x).a=(_a).a-(_b).a,(_x).b=(_a).b-(_b).b)\r\n\t#define _cm_times(_x,_a,_b) (_ta=(_a).a*(_b).a-(_a).b*(_b).b,_tb=(_a).b*(_b).a+(_a).a*(_b).b,(_x).a=_ta,(_x).b=_tb)\r\n}a[3][1050505],b[3][1050505];\r\n\r\nint flip[1050505];\r\ninline void FFT(register int len,_cm c[],bool inverse=false)\r\n{\r\n\t_cm t;\r\n\tfor(register int i=0;i&lt;len;i++)\r\n\t\tif(i&lt;flip[i])\r\n\t\t\tt=c[i],c[i]=c[flip[i]],c[flip[i]]=t;\r\n\tfor(register int step=2;step&lt;=len;step&lt;&lt;=1)\r\n\t{\r\n\t\t_cm wn(std::cos((double)2*M_PI\/step), \\\r\n\t\tstd::sin((double)2*M_PI\/step)*(inverse?-1:1));\r\n\t\tregister int hstep=step&gt;&gt;1;\r\n\t\tstatic _cm pw[1050505];\r\n\t\tpw[0]=(_cm){1,0};\r\n\t\tfor(register int k=1;k&lt;=hstep;k++)\r\n\t\t\t_cm_times(pw[k],pw[k-1],wn);\r\n\t\tfor(register int k=0;k&lt;len;k+=step)\r\n\t\t\tfor(register int i=k;i&lt;k+hstep;i++)\r\n\t\t\t{\r\n\t\t\t\tregister int j=i+hstep;\r\n\t\t\t\t_cm_times(t,c[j],pw[i-k]);\r\n\t\t\t\t_cm_minus(c[j],c[i],t);\r\n\t\t\t\t_cm_plus(c[i],c[i],t);\r\n\t\t\t}\r\n\t}\r\n\tif(inverse)\r\n\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\tc[i].a\/=len;\r\n}\r\n\r\nchar A[505050],B[505050];\r\n\r\nint main()\r\n{\r\n\tint lA,lB;getstr(A,lA),getstr(B,lB);\r\n\tfor(register int i=1;i&lt;lA-i+1;i++)\r\n\t\tA[i]^=A[lA-i+1]^=A[i]^=A[lA-i+1];\r\n\t\r\n\tregister int len=1,dig=0;\r\n\twhile(len&lt;(lB&lt;&lt;1))\r\n\t\tlen&lt;&lt;=1,dig++;\r\n\tfor(register int i=0;i&lt;len;i++)\r\n\t{\r\n\t\ta[0][i]=(_cm){(double)(i+1&gt;lA || A[i+1]=='*' ? 0 : A[i+1]-'a'+1)};\r\n\t\tb[0][i]=(_cm){(double)(i+1&gt;lB || B[i+1]=='*' ? 0 : B[i+1]-'a'+1)};\r\n\t\t_cm_times(a[1][i],a[0][i],a[0][i]),_cm_times(a[2][i],a[1][i],a[0][i]);\r\n\t\t_cm_times(b[1][i],b[0][i],b[0][i]),_cm_times(b[2][i],b[1][i],b[0][i]);\r\n\t\tflip[i]=(flip[i&gt;&gt;1]&gt;&gt;1)|((i&amp;1)&lt;&lt;(dig-1));\r\n\t}\r\n\t\r\n\tfor(register int k=0;k&lt;3;k++)\r\n\t{\r\n\t\tFFT(len,a[k]),FFT(len,b[2-k]);\r\n\t\tfor(register int i=0;i&lt;len;i++)\r\n\t\t\t_cm_times(a[k][i],a[k][i],b[2-k][i]);\r\n\t\tFFT(len,a[k],true);\r\n\t}\r\n\t\r\n\tfor(register int i=lA-1;i&lt;lB;i++)\r\n\t\tif(_abs(a[2][i].a-2*a[1][i].a+a[0][i].a) &lt; eps)\r\n\t\t\tprintf(\"%d \",i-lA+2);\r\n\tprintf(\"\\n\");\r\n\t\r\n\treturn 0;\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d \u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf &hellip; <a href=\"https:\/\/mnihyc.com\/blog\/archives\/1235\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37,82],"tags":[],"class_list":["post-1235","post","type-post","status-publish","format-standard","hentry","category-crazya","category-fftnttfwt"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d - mnihyc&#039;s Blog<\/title>\n<meta name=\"description\" content=\"YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d \u65f6\u95f4\u9650\u5236\uff1a4000MS \u00a0\u00a0\u00a0\u00a0 \u5185\u5b58\u9650\u5236\uff1a262144KB \u96be\u5ea6\uff1a \u9898\u76ee\u63cf\u8ff0 \u7ed9\u51fa\u4e24\u4e2a\u4e32 (A) \u548c (B)\uff0c\u4e32\u4e2d\u4ec5\u5305\u542b\u5c0f\u5199\u5b57\u6bcd\u548c\u5b57\u7b26 *\uff0c\u5176\u4e2d * \u80fd\u5339\u914d\u4efb\u610f\u7684\u5c0f\u5199\u5b57\u6bcd\uff08\u4e5f\u53ef\u4ee5\u5339\u914d *\uff09\u3002 \u8bf7\u4f60\u6c42\u51fa\u5982\u679c\u4ee5 (A) \u4e3a\u6a21\u677f\u4e32\uff0c\u90a3\u4e48\u6709\u54ea\u4e9b (i) \u4f7f\u5f97\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ipv6.mnihyc.com\/blog\/archives\/1235\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d - mnihyc&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"YZOJ P3069 \u5b57\u7b26\u4e32\u5339\u914d 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name=\"twitter:creator\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:site\" content=\"@mnihyc\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"mnihyc\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/ipv6.mnihyc.com\/blog\/archives\/1235#article\",\"isPartOf\":{\"@id\":\"https:\/\/ipv6.mnihyc.com\/blog\/archives\/1235\"},\"author\":{\"name\":\"mnihyc\",\"@id\":\"https:\/\/mnihyc.com\/blog\/#\/schema\/person\/61e167d6d591fdd20dcfee2cf848a751\"},\"headline\":\"YZOJ P3069 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