{"id":693,"date":"2018-09-09T20:41:27","date_gmt":"2018-09-09T12:41:27","guid":{"rendered":"https:\/\/mnihyc.tk\/blog\/?p=693"},"modified":"2019-01-06T11:44:07","modified_gmt":"2019-01-06T03:44:07","slug":"yzoj-p1800-%e8%b4%a8%e6%95%b0%e7%94%9f%e6%88%90%e5%99%a8","status":"publish","type":"post","link":"https:\/\/mnihyc.com\/blog\/archives\/693","title":{"rendered":"YZOJ   P1800   \u8d28\u6570\u751f\u6210\u5668"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong>[NOIP2015\u56db\u6821\u8054\u8badDay8]\u8d28\u6570\u751f\u6210\u5668<\/strong><\/h2>\n<p style=\"text-align: center;\">\u65f6\u95f4\u9650\u5236\uff1a1000MS    \u5185\u5b58\u9650\u5236\uff1a131072KB<\/p>\n<ul>\n<li>\n<h3><strong>\u9898\u76ee\u63cf\u8ff0<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u751f\u6210\u7ed9\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u8d28\u6570\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u5165\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u6709\u591a\u7ec4\u6570\u636e\u3002<\/p>\n<p>\u8f93\u5165\u6570\u636e\u7b2c\u4e00\u884c\u662f\u4e00\u4e2a\u6574\u6570\\(T(T\\leq10)\\)\uff0c\u8868\u793a\u6d4b\u8bd5\u6570\u636e\u7684\u7ec4\u6570\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\\(T\\)\u884c\uff0c\u6bcf\u884c\u6709\u4e24\u6574\u6570\\(m, n\\)\uff0c\u8868\u793a\u8981\u6c42\u751f\u6210\u8d28\u6570\u7684\u8303\u56f4\u662f\\([m, n] (1 \\leq m \\leq n \\leq 10^9, n-m \\leq 10^6)\\)<\/p>\n<ul>\n<li>\n<h3><strong>\u8f93\u51fa\u683c\u5f0f<\/strong><\/h3>\n<\/li>\n<\/ul>\n<p>\u5bf9\u4e8e\u6bcf\u4e00\u7ec4\u6d4b\u8bd5\u6570\u636e\uff0c\u8f93\u51fa\u6240\u6709\u5728\\([m, n]\\)\u4e2d\u7684\u8d28\u6570\\(p\\)\uff0c\u4e00\u884c\u4e00\u4e2a\u3002<\/p>\n<p>\u4e0d\u540c\u6d4b\u8bd5\u6570\u636e\u4e4b\u95f4\u7528\u4e00\u4e2a\u7a7a\u884c\u5206\u9694\u3002<\/p>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u5165<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre>2\r\n1 10\r\n3 5<\/pre>\n<ul>\n<li>\n<h3><strong>\u6837\u4f8b\u8f93\u51fa<\/strong><\/h3>\n<\/li>\n<\/ul>\n<pre>2\r\n3\r\n5\r\n7\r\n\r\n3\r\n5<\/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\\(30\\%\\)\u7684\u6570\u636e\uff0c\\(m &lt; n \\leq 10^3\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\\(50\\%\\)\u7684\u6570\u636e\uff0c\\(m &lt; n \\leq 10^6 \u4e14 n-m \\leq 10^3\\)\uff1b<\/p>\n<p>\u5bf9\u4e8e\\(100\\%\\)\u7684\u6570\u636e\uff0c\\(m &lt; n \\leq 10^9 \u4e14 n-m \\leq 10^6\\)\uff1b<br \/>\n<!--more--><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<hr \/>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>\u770b\u5230\\(m &lt; n \\leq 10^9\\)\u76f4\u63a5\u88ab\u5413\u5230\u4e86\uff0c\u4f46\u5176\u5b9e\u6ce8\u610f\u5230\\(n-m \\leq 10^6\\)\u6761\u4ef6\uff0c\u8bf4\u660e\u6211\u4eec\u53ea\u8981\u8f93\u51fa\u6700\u591a\\(10^6\\)\u4e2a\u8d28\u6570\uff0c\u8fd9\u662f\u53ef\u4ee5\u63a5\u53d7\u7684\u3002<\/p>\n<p>\u663e\u7136\u6211\u4eec\u65e0\u6cd5\u5b58\u4e0b\u6240\u6709\u7684\u6570\u76f4\u63a5\u5224\u65ad\uff0c\u56e0\u4e3a\u7a7a\u95f4\\(sizeof(int) \\cdot 10^9 Bytes \\approx 3814 MB\\)\u4e14\u65f6\u95f4\u9884\u5904\u7406\\(O(N\\leq10^9)\\)\u8fd9\u662f\u65e0\u6cd5\u63a5\u53d7\u7684\u3002\u6240\u4ee5\u6211\u4eec\u8003\u8651\u5148\u8bb0\u4e0b\u524d\u9762\u51e0\u4e2a\u8d28\u6570\uff0c\u540e\u9762\u7684\u6570\u5c31\u7528\u524d\u9762\u7684\u8d28\u6570\u6765\u7b5b\u5c31\u884c\u3002<\/p>\n<p>\u5148\u7528\u7ebf\u6027\u7b5b\u7b5b\u51fa\u524d\u51e0\u4e2a\u6570\u7684\u8d28\u6570\uff0c\u6bd4\u5982\u6211\u7b5b\u5230\\(10^6\\)<del>\u6bd4\u8f83\u4fdd\u9669<\/del>\uff0c\u5bf9\u4e8e\u6bcf\u6b21\u8be2\u95ee\u7684\\(m, n\\)\uff0c\u5982\u679c\u533a\u95f4\\([m, n]\\)\u4e0e\\([1, 10^6]\\)\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5f88\u5f00\u5fc3\u7684\u8f93\u51fa\u5728\\([1, 10^6]\\)\u533a\u95f4\u91cc\u7684\u8d28\u6570\u3002<\/p>\n<p>\u5982\u679c\u533a\u95f4\\([m, n]\\)\u8fd8\u6709\u8d85\u51fa\u533a\u95f4\\([1, 10^6]\\)\u7684\u90e8\u5206\uff0c\u56e0\u4e3a\u5176\u957f\u5ea6\u6700\u5927\u4e3a\\(10^6\\)\uff08\\(n-m \\leq 10^6\\)\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u5f00\u4e00\u4e2a\\(10^6\\)\u7684\u6570\u7ec4\u4fdd\u5b58\u5f53\u524d\u8fd9\u4e2a\u6570\u662f\u5426\u88ab\u4e4b\u524d\u7684\u8d28\u6570\u7b5b\u8fc7\u3002\u7136\u540e\u904d\u5386\u4e4b\u524d\u6211\u4eec\u7b5b\u51fa\u6765\u7684\u6bcf\u4e00\u4e2a\u8d28\u6570\uff0c\u627e\u5230\u8fd9\u4e2a\u8d28\u6570\u7684\u6240\u6709\u5728\u5f53\u524d\u533a\u95f4\\([max(m, 10^6+1), n]\\)\u7684\u6240\u6709\u500d\u6570\u6253\u4e0a\u6807\u8bb0\uff0c\u8fd9\u6837\u5faa\u73af\u7ed3\u675f\u4e4b\u540e\u518d\u5bf9\u533a\u95f4\u91cc\u7684\u6570\u904d\u5386\uff0c\u6ca1\u6709\u88ab\u6253\u4e0a\u6807\u8bb0\u7684\u5373\u4e3a\u8d28\u6570\uff0c\u8f93\u51fa\u5373\u53ef\u3002<\/p>\n<p>\u7a0b\u5e8f\u5b9e\u73b0\uff1a<\/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 \r\n#define NUM 1050505\r\n \r\nint num[NUM+1];\r\nint prs[NUM+1];\r\nint tn;\r\nbool tmn[NUM+1];\r\n \r\nint main()\r\n{\r\n\tint T;scanf(\"%d\",&amp;T);\r\n\t\r\n\tfor(register int i=2;i&lt;=NUM;i++)\r\n\t{\r\n\t\tif(!num[i])\r\n\t\t\tprs[tn++]=i;\r\n\t\tfor(register int j=0;j&lt;tn;j++)\r\n\t\t{\r\n\t\t\tif(prs[j]*i&lt;=NUM)\r\n\t\t\t\tnum[prs[j]*i]=1;\r\n\t\t\telse\r\n\t\t\t\tbreak;\r\n\t\t\tif(i%prs[j]==0)\r\n\t\t\t\tbreak;\r\n\t\t}\r\n\t}\r\n\tfor(register int lp=1;lp&lt;=T;lp++)\r\n\t{\r\n\t\tint l,r;scanf(\"%d%d\",&amp;l,&amp;r);\r\n\t\tmemset(tmn,0,sizeof(tmn));\r\n\t\t\r\n\t\tif(l&lt;=NUM)\r\n\t\t{\r\n\t\t\tfor(register int j=0;j&lt;tn;j++)\r\n\t\t\t\tif(prs[j]&lt;=r)\r\n\t\t\t\t{\r\n\t\t\t\t\tif(prs[j]&gt;=l)\r\n\t\t\t\t\t\tprintf(\"%d\\n\",prs[j]);\r\n\t\t\t\t}\r\n\t\t\t\telse\r\n\t\t\t\t\tbreak;\r\n\t\t}\r\n\t\tif(r&gt;NUM)\r\n\t\t{\r\n\t\t\tif(l&lt;=NUM)\r\n\t\t\t\tl=NUM+1;\r\n\t\t\tfor(register int j=l;j&lt;=r;j++)\r\n\t\t\t\ttmn[j-l]=true;\r\n\t\t\tfor(register int j=0;j&lt;tn;j++)\r\n\t\t\t{\r\n\t\t\t\tint npm=prs[j];\r\n\t\t\t\tint st=l\/npm*npm;\r\n\t\t\t\tfor(register int k=st;k&lt;=r;k+=npm)\r\n\t\t\t\t{\r\n\t\t\t\t\tif(k&lt;l)\r\n\t\t\t\t\t\tcontinue;\r\n\t\t\t\t\ttmn[k-l]=false;\r\n\t\t\t\t}\r\n\t\t\t}\r\n\t\t\tfor(register int j=l;j&lt;=r;j++)\r\n\t\t\t\tif(tmn[j-l])\r\n\t\t\t\t\tprintf(\"%d\\n\",j);\r\n\t\t}\r\n\t\tprintf(\"\\n\");\r\n\t}\r\n\t\r\n\treturn 0;\r\n}\r\n<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[NOIP2015\u56db\u6821\u8054\u8badDay8]\u8d28\u6570\u751f\u6210\u5668 \u65f6\u95f4\u9650\u5236\uff1a1000MS \u5185\u5b58\u9650\u5236\uff1a131072KB \u9898\u76ee\u63cf\u8ff0  &hellip; <a href=\"https:\/\/mnihyc.com\/blog\/archives\/693\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">YZOJ   P1800   \u8d28\u6570\u751f\u6210\u5668<\/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":[26],"tags":[],"class_list":["post-693","post","type-post","status-publish","format-standard","hentry","category-number-theory"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>YZOJ  P1800  \u8d28\u6570\u751f\u6210\u5668 - mnihyc&#039;s Blog<\/title>\n<meta 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