{"id":337,"date":"2013-02-23T13:14:00","date_gmt":"2013-02-23T05:14:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/241"},"modified":"2013-02-23T13:14:00","modified_gmt":"2013-02-23T05:14:00","slug":"digital_product_a_combination_of_high-precision_math","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=337","title":{"rendered":"\u6570\u4f4d\u548c\u4e58\u79ef(\u9ad8\u7cbe\u7ec4\u5408\u6570\u5b66)"},"content":{"rendered":"<p>Problem 3 \u6570\u4f4d\u548c\u4e58\u79ef(digit.cpp\/c\/pas)<\/p>\n<p>\u3010\u9898\u76ee\u63cf\u8ff0\u3011<\/p>\n<p>\u4e00\u4e2a\u6570\u5b57\u7684\u6570\u4f4d\u548c\u4e58\u79ef\u4e3a\u5176\u5404\u4f4d\u6570\u5b57\u7684\u4e58\u79ef\u3002\u6c42\u6240\u6709\u7684N\u4f4d\u6570\u4e2d\u6709\u591a\u5c11\u4e2a\u6570\u7684\u6570\u4f4d\u548c\u4e58\u79ef\u6070\u597d\u4e3aK\u3002\u8bf7\u6ce8\u610f\uff0c\u8fd9\u91cc\u7684N\u4f4d\u6570\u662f\u53ef\u4ee5\u6709\u524d\u5bfc\u96f6\u7684\u3002\u6bd4\u598201\uff0c02\u89c6\u4e3a\u4e8c\u4f4d\u6570\uff0c\u4f46\u662f\u4ed6\u4eec\u7684\u6570\u4f4d\u548c\u4e58\u79ef\u90fd\u662f0\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u3010\u8f93\u5165&#26684;\u5f0f\u3011<\/p>\n<p>\u4e00\u884c\u4e24\u4e2a\u6574\u6570N\uff0cK<\/p>\n<p>&nbsp;<\/p>\n<p>\u3010\u8f93\u51fa&#26684;\u5f0f\u3011<\/p>\n<p>\u4e00\u4e2a\u884c\u4e00\u4e2a\u6574\u6570\u8868\u793a\u7ed3\u679c\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u5165\u3011<\/p>\n<p>2 3<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u51fa\u3011<\/p>\n<p>2<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u51652\u3011<\/p>\n<p>2 0<\/p>\n<p>\u3010\u6837\u4f8b\u8f93\u51fa2\u3011<\/p>\n<p>19<\/p>\n<p align=\"left\">&nbsp;<\/p>\n<p>\u3010\u6570\u636e\u8303\u56f4\u3011<\/p>\n<p>\u5bf9\u4e8e20%\uff1aN &lt;= 6\u3002<\/p>\n<p>\u5bf9\u4e8e50%\uff1aN&lt;=16<\/p>\n<p>\u5b58\u5728\u53e6\u591630%\uff1aK=0\u3002<\/p>\n<p>\u5bf9\u4e8e100%\uff1aN&nbsp;&lt;= 50\uff0c0 &lt;= K &lt;= 10^9\u3002<\/p>\n<p><span style=\"font-size:14px\">\u6cd51\uff1a<\/span><\/p>\n<p><span style=\"font-size:14px\">k=0\u65f6\uff0cans=10^n-9^n<\/span><\/p>\n<p><span style=\"font-size:14px\">\u5426\u5219\u5c31\u7528\u8bb0\u5fc6\u5316\u641c\u7d22\u586b1..9\u7684\u4e2a\u6570<\/span><\/p>\n<p><span style=\"font-size:14px\"><\/span><\/p>\n<pre name=\"code\" class=\"cpp\">#include&lt;cstdio&gt;\n#include&lt;cstring&gt;\n#include&lt;algorithm&gt;\n#include&lt;functional&gt;\n#include&lt;iostream&gt;\n#include&lt;cstdlib&gt;\n#include&lt;cmath&gt;\n#include&lt;cctype&gt;\nusing namespace std;\n#define MAXN (50+10)\n#define F (10000)\nint n,k;\nstruct highn\n{\n\tint len,a[900];\n\thighn():len(1){memset(a,0,sizeof(a));}\n\thighn(int x)\n\t{\n\t\tmemset(a,0,sizeof(a));\n\t\tint i=0;\n\t\twhile (x)\n\t\t{\n\t\t\ta[++i]=x%F;\n\t\t\tx\/=F;\n\t\t}\n\t\tlen=i;\n\t}\n\tvoid print()\n\t{\n\t\tprintf(&quot;%d&quot;,a[len]);\n\t\tfor (int i=len-1;i;i--)\n\t\t{\n\t\/\/\t\tif (a[i]&lt;10000) printf(&quot;0&quot;);\n\t\t\tif (a[i]&lt;1000) printf(&quot;0&quot;);\n\t\t\tif (a[i]&lt;100) printf(&quot;0&quot;);\n\t\t\tif (a[i]&lt;10) printf(&quot;0&quot;);\n\t\t\tprintf(&quot;%d&quot;,a[i]);\n\t\t}\n\n\t}\n\tfriend highn operator+(highn&amp; a,highn&amp; b)\n\t{\n\t\thighn c;\n\t\tint maxlen=max(a.len,b.len);\n\t\tfor (int i=1;i&lt;=maxlen;i++)\n\t\t{\n\t\t\tc.a[i]=c.a[i]+a.a[i]+b.a[i];\n\t\t\tif (c.a[i]&gt;F)\n\t\t\t{\n\t\t\t\tc.a[i+1]+=c.a[i]\/F;\n\t\t\t\tc.a[i]%=F;\n\t\t\t}\n\t\t}\n\t\tc.len=maxlen+1;\n\t\twhile (!c.a[c.len]&amp;&amp;c.len&gt;1) c.len--;\n\t\treturn c;\n\n\t}\n\tfriend highn operator-(highn&amp; a,highn&amp; b)\n\t{\n\t\thighn c;\n\t\tint maxlen=a.len;\n\t\tfor (int i=1;i&lt;=maxlen;i++)\n\t\t{\n\t\t\tc.a[i]+=a.a[i]-b.a[i];\n\t\t\tif (c.a[i]&lt;0)\n\t\t\t{\n\t\t\t\tc.a[i+1]--;\n\t\t\t\tc.a[i]+=F;\n\t\t\t}\n\t\t}\n\t\tc.len=maxlen;\n\t\twhile (!c.a[c.len]&amp;&amp;c.len&gt;1) c.len--;\n\t\treturn c;\n\t}\n\tfriend highn operator*(highn&amp; a,highn&amp; b)\n\t{\n\t\thighn c;\n\t\tfor (int i=1;i&lt;=a.len;i++)\n\t\t{\n\t\t\tfor (int j=1;j&lt;=b.len;j++)\n\t\t\t{\n\t\t\t\tc.a[i+j-1]+=a.a[i]*b.a[j];\n\t\t\t\tif (c.a[i+j-1]&gt;F)\n\t\t\t\t{\n\t\t\t\t\tc.a[i+j]+=c.a[i+j-1]\/F;\n\t\t\t\t\tc.a[i+j-1]%=F;\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\tc.len=a.len+b.len+1;\n\t\twhile (!c.a[c.len]&amp;&amp;c.len&gt;1) c.len--;\n\t\treturn c;\n\t}\n\n};\nhighn pow2(highn a,int b)\n{\n\thighn c;\n\tif (!b) return 1;\n\tif (b%2)\n\t{\n\t\tc=pow2(a,b\/2);\n\t\tc=c*c;\n\t\tc=c*a;\n\t}\n\telse\n\t{\n\t\tc=pow2(a,b\/2);\n\t\tc=c*c;\n\t}\n\treturn c;\n}\nint a[11],tot,b[11];\nhighn ans,C[51][51];\nvoid dfs(int deep,highn rel,int hasget)\n{\n\tif (n&lt;hasget) {return;}\n\tif (deep==0||n==hasget)\n\t{\n\t\tfor (int i=1;i&lt;=9;i++) if (b[i]) return;\n\t\tans=ans+rel;\n\t\treturn;\n\t}\n\telse if (deep==9)\n\t{\n\t\tint m=min(n-hasget,b[3]\/2);\n\t\tfor (int i=0;i&lt;=m;i++)\n\t\t{\n\t\t\tb[3]-=i*2;\n\t\t\tdfs(8,rel*C[n-hasget][i],hasget+i);\n\t\t\tb[3]+=i*2;\n\t\t}\n\t}\n\telse if (deep==8)\n\t{\n\t\tint m=min(n-hasget,b[2]\/3);\n\t\tfor (int i=0;i&lt;=m;i++)\n\t\t{\n\t\t\tb[2]-=i*3;\n\t\t\tdfs(6,rel*C[n-hasget][i],hasget+i);\n\t\t\tb[2]+=i*3;\n\t\t}\n\t}\n\telse if (deep==6)\n\t{\n\t\tint m=min(n-hasget,min(b[2],b[3]));\n\t\tfor (int i=0;i&lt;=m;i++)\n\t\t{\n\t\t\tb[2]-=i;b[3]-=i;\n\t\t\tdfs(4,rel*C[n-hasget][i],hasget+i);\n\t\t\tb[2]+=i,b[3]+=i;\n\t\t}\n\t}\n\telse if (deep==4)\n\t{\n\t\tint m=min(n-hasget,b[2]\/2);\n\t\tfor (int i=0;i&lt;=m;i++)\n\t\t{\n\t\t\tb[2]-=i*2;\n\t\t\tdfs(2,rel*C[n-hasget][i],hasget+i);\n\t\t\tb[2]+=i*2;\n\t\t}\n\t}\n\telse\n\t{\n\t\tif (b[2]+b[3]+b[5]+b[7]+hasget&lt;=n)\n\t\t{\n\t\t\tint f[4]={2,3,5,7};\n\t\t\tfor (int i=0;i&lt;4;i++)\n\t\t\t{\n\t\t\t\trel=rel*C[n-hasget][b[f[i]]];\n\t\t\t\thasget+=b[f[i]];\n\t\t\t}\n\t\t\tans=ans+rel;\n\t\t\treturn ;\n\t\t}\n\t}\n}\nint main()\n{\n\/\/\thighn a=1254321,b=7612345;\n\/\/\thighn c=pow(a,3);\n\/\/\tc.print();\n\tfreopen(&quot;digit.in&quot;,&quot;r&quot;,stdin);\n\tfreopen(&quot;digit.out&quot;,&quot;w&quot;,stdout);\n\tscanf(&quot;%d%d&quot;,&amp;n,&amp;k);\n\tif (!k)\n\t{\n\t\thighn c=pow2(10,n),d=pow2(9,n);\n\t\thighn e=c-d;\n\t\te.print();\n\t}\n\telse\n\t{\n\n\t\tmemset(a,0,sizeof(a));\n\t\ttot=0;\n\t\tC[0][0]=1;\n\t\tfor (int i=1;i&lt;=n;i++)\n\t\t{\n\t\t\tC[i][0]=C[i][1]=1;\n\t\t\tfor (int j=1;j&lt;=i;j++)\n\t\t\t{\n\t\t\t\tC[i][j]=C[i-1][j]+C[i-1][j-1];\n\t\t\t}\n\t\t}\n\/\/\t\tC[16][10].print();\n\n\t\tfor(int i=2;i&lt;=9;i++)\n\t\t{\n\t\t\twhile (k%i==0)\n\t\t\t{\n\t\t\t\ta[i]++;\n\t\t\t\tk\/=i;\n\t\t\t\ttot++;\n\t\t\t}\n\t\t}\n\t\tmemcpy(b,a,sizeof(a));\n\t\tif (k==1) dfs(9,1,0);\n\t\tans.print();\n\t}\n\tcout&lt;&lt;endl;\n\treturn 0;\n}<\/pre>\n<p>\n\u6cd52\uff1a<\/p>\n<p><span style=\"font-size:14px\">f[i][j][k][l][m]\u8868\u793a\u586b\u5230\u7b2ci\u4e2a\u6570,2,3,5,7\u5206\u522b\u7528j,k,l,m\u4e2a\u7684\u65b9\u6848\u6570<\/span><\/p>\n<p><span style=\"font-size:14px\">\u8003\u8651\u540e\u9762\u586b1..9\u7684\u60c5\u51b5(\u663e\u7136\u4e0d\u53ef\u80fd\u586b0)<\/span><\/p>\n<p><span style=\"font-size:14px\">Bug\uff1an=50,C(n,m)\u6700\u5927\u4e3aC(50,25),\u53ef\u7528long long.<\/span><\/p>\n<p><span style=\"font-size:14px\">----<\/span><\/p>\n<p><span style=\"font-size:14px\">----<\/span><\/p>\n<p><span style=\"font-size:14px\">\u6cd53\uff1a<\/span><\/p>\n<p><span style=\"font-size:14px\">\u5bb9\u6613\u53d1\u73b0<\/span><\/p>\n<p><span style=\"font-size:14px\">k=2^a*3^b*5^c*7^d\u65f6\u624d\u6709\u89e3<\/span><\/p>\n<p><span style=\"font-size:14px\">\u800c\u4e145,7\u53d6\u4e86\u5f53\u4e14\u53ea\u5f53\u6570\u4f4d\u4e3a5,7\u7684\u60c5\u51b5.<\/span><\/p>\n<p><span style=\"font-size:14px\">2-2,4,6,8<\/span><\/p>\n<p><span style=\"font-size:14px\">3-3,6,9<\/span><\/p>\n<p><span style=\"font-size:14px\">5-5<\/span><\/p>\n<p><span style=\"font-size:14px\">7-7<\/span><\/p>\n<p><span style=\"font-size:14px\">\u6545\u53ef\u53ea\u8003\u86512,3,\u4e0d<\/span><span style=\"font-size:14px\">\u8003\u86515,7<\/span><\/p>\n<p><span style=\"font-size:14px\">f[i][j]k]\u8868\u793ai\u4f4d\uff0c\u53d6\u4e86j\u4e2a2\u548ck\u4e2a3\u540e\u7684\u65b9\u6848\u6570\uff0c<\/span><\/p>\n<p><span style=\"font-size:14px\">\u56e0\u4e3a\u53ef\u4ee5\u75281\u586b\u5145\uff0c<\/span><\/p>\n<p><span style=\"font-size:14px\">\u6240\u4ee5\u7b54\u6848=\u2211f[p][j][k]*C(p,j&#43;k)*C(n,a[5])*C(n-a[5],a[7]) (p&lt;=n-a[5]-a[7])<\/span><\/p>\n<p><span style=\"font-size:14px\"><br \/>\n<\/span><\/p>\n<p>\n<\/p>\n<p>\n<\/p>\n<p><span style=\"font-size:14px\"><br \/>\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem 3 \u6570\u4f4d\u548c\u4e58\u79ef(digit.cpp\/c\/pas) \u3010\u9898\u76ee\u63cf\u8ff0\u3011 \u4e00\u4e2a\u6570\u5b57\u7684\u6570\u4f4d\u548c\u4e58\u79ef\u4e3a\u5176\u5404\u4f4d\u6570 [&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":[111],"class_list":["post-337","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-combinatorial_mathematics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u6570\u4f4d\u548c\u4e58\u79ef(\u9ad8\u7cbe\u7ec4\u5408\u6570\u5b66) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=337\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u6570\u4f4d\u548c\u4e58\u79ef(\u9ad8\u7cbe\u7ec4\u5408\u6570\u5b66) - nike0good\" \/>\n<meta property=\"og:description\" content=\"Problem 3 \u6570\u4f4d\u548c\u4e58\u79ef(digit.cpp\/c\/pas) \u3010\u9898\u76ee\u63cf\u8ff0\u3011 \u4e00\u4e2a\u6570\u5b57\u7684\u6570\u4f4d\u548c\u4e58\u79ef\u4e3a\u5176\u5404\u4f4d\u6570 [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/nike0good.com\/?p=337\" \/>\n<meta property=\"og:site_name\" content=\"nike0good\" \/>\n<meta property=\"article:published_time\" content=\"2013-02-23T05:14:00+00:00\" \/>\n<meta name=\"author\" content=\"nike0good\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"nike0good\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 \u5206\" \/>\n<script type=\"application\/ld+json\" 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