{"id":538,"date":"2018-04-09T13:48:13","date_gmt":"2018-04-09T05:48:13","guid":{"rendered":"http:\/\/kylelv.com\/?p=538"},"modified":"2018-05-23T13:49:22","modified_gmt":"2018-05-23T05:49:22","slug":"bzoj-5281-usaco2018-opentalent-show-%e5%88%86%e6%95%b0%e8%a7%84%e5%88%92dp","status":"publish","type":"post","link":"https:\/\/blog.kylelv.com\/?p=538","title":{"rendered":"bzoj 5281: [Usaco2018 Open]Talent Show  &#8212; \u5206\u6570\u89c4\u5212,dp"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_73 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-69fdef5f60f68\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-69fdef5f60f68\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#5281_Usaco2018_OpenTalent_Show\" title=\"5281: [Usaco2018 Open]Talent Show\">5281: [Usaco2018 Open]Talent Show<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#Description\" title=\"Description\">Description<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#Input\" title=\"Input\">Input<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#Output\" title=\"Output\">Output<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#Sample_Input\" title=\"Sample Input\">Sample Input<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#Sample_Output\" title=\"Sample Output\">Sample Output<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.kylelv.com\/?p=538\/#HINT\" title=\"HINT\">HINT<\/a><\/li><\/ul><\/nav><\/div>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"5281_Usaco2018_OpenTalent_Show\"><\/span>5281: [Usaco2018 Open]Talent Show<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: center;\"><span class=\"green\">Time Limit:\u00a0<\/span>10 Sec\u00a0\u00a0<span class=\"green\">Memory Limit:\u00a0<\/span>128 MB<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Description\"><\/span>Description<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"content\">\n<div>FarmerJohn\u8981\u5e26\u7740\u4ed6\u7684N\u5934\u5976\u725b\uff0c\u65b9\u4fbf\u8d77\u89c1\u7f16\u53f7\u4e3a1\u2026N\uff0c\u5230\u519c\u4e1a\u5c55\u89c8\u4f1a\u4e0a\u53bb\uff0c\u53c2\u52a0\u6bcf\u5e74\u7684\u8fbe\u725b\u79c0\uff01\u4ed6\u7684\u7b2ci\u5934\u5976\u725b\u91cd<\/div>\n<div>\u91cf\u4e3awi\uff0c\u624d\u827a\u6c34\u5e73\u4e3ati\uff0c\u4e24\u8005\u90fd\u662f\u6574\u6570\u3002\u5728\u5230\u8fbe\u65f6\uff0cFarmerJohn\u5c31\u88ab\u4eca\u5e74\u8fbe\u725b\u79c0\u7684\u65b0\u89c4\u5219\u5413\u5230\u4e86\uff1a<\/div>\n<div><\/div>\n<div>\uff08\u4e00\uff09\u53c2\u52a0\u6bd4\u8d5b\u7684\u4e00\u7ec4\u5976\u725b\u5fc5\u987b\u603b\u91cd\u91cf\u81f3\u5c11\u4e3aW<\/div>\n<div><\/div>\n<div>\uff08\u8fd9\u662f\u4e3a\u4e86\u786e\u4fdd\u662f\u5f3a\u5927\u7684\u961f\u4f0d\u5728\u6bd4\u8d5b\uff0c\u800c\u4e0d\u4ec5\u662f\u5f3a\u5927\u7684\u67d0\u5934\u5976\u725b\uff09\uff0c\u5e76\u4e14<\/div>\n<div><\/div>\n<div>\uff08\u4e8c\uff09\u603b\u624d\u827a\u503c\u4e0e\u603b\u91cd\u91cf\u7684\u6bd4\u503c\u6700\u5927\u7684\u4e00\u7ec4\u83b7\u5f97\u80dc\u5229\u3002<\/div>\n<div><\/div>\n<div>FJ\u6ce8\u610f\u5230\u4ed6\u7684\u6240\u6709\u5976\u725b\u7684\u603b\u91cd\u91cf\u4e0d\u5c0f\u4e8eW\uff0c\u6240\u4ee5\u4ed6\u80fd\u591f\u6d3e\u51fa\u7b26\u5408\u89c4\u5219\uff08\u4e00\uff09\u7684\u961f\u4f0d\u3002\u5e2e\u52a9\u4ed6\u786e\u5b9a\u8fd9\u6837\u7684\u961f\u4f0d\u4e2d\u80fd\u591f<\/div>\n<div>\u8fbe\u5230\u7684\u6700\u4f73\u7684\u624d\u827a\u4e0e\u91cd\u91cf\u7684\u6bd4\u503c\u3002<\/div>\n<div><\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Input\"><\/span>Input<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"content\">\n<div>\u8f93\u5165\u7684\u7b2c\u4e00\u884c\u5305\u542bN\u548cW\u3002\u4e0b\u9762N\u884c\uff0c\u6bcf\u884c\u7528\u4e24\u4e2a\u6574\u6570wi\u548cti\u63cf\u8ff0\u4e86\u4e00\u5934\u5976\u725b\u3002<\/div>\n<div>1\u2264N\u2264250<\/div>\n<div>1\u2264W\u22641000<\/div>\n<div>1\u2264wi\u226410^6<\/div>\n<div>1\u2264ti\u226410^3<\/div>\n<div><\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Output\"><\/span>Output<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"content\">\n<div>\u8bf7\u6c42\u51faFarmer\u7528\u4e00\u7ec4\u603b\u91cd\u91cf\u6700\u5c11\u4e3aW\u7684\u5976\u725b\u6700\u5927\u53ef\u80fd\u8fbe\u5230\u7684\u603b\u624d\u827a\u503c\u4e0e\u603b\u91cd\u91cf\u7684\u6bd4\u503c\u3002<\/div>\n<div>\u5982\u679c\u4f60\u7684\u7b54\u6848\u662fA\uff0c\u8f93\u51fa1000A\u5411\u4e0b\u53d6\u6574\u7684\u503c\uff0c\u4ee5\u4f7f\u5f97\u8f93\u51fa\u662f\u6574\u6570<\/div>\n<div>\uff08\u5f53\u95ee\u9898\u4e2d\u7684\u6570\u4e0d\u662f\u4e00\u4e2a\u6574\u6570\u7684\u65f6\u5019\uff0c\u5411\u4e0b\u53d6\u6574\u64cd\u4f5c\u5728\u5411\u4e0b\u820d\u5165\u5230\u6574\u6570\u7684\u65f6\u5019\u53bb\u9664\u6240\u6709\u5c0f\u6570\u90e8\u5206\uff09\u3002<\/div>\n<div><\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Sample_Input\"><\/span>Sample Input<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"content\"><span class=\"sampledata\">315<br \/>\n2021<br \/>\n1011<br \/>\n3031<\/span><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Sample_Output\"><\/span>Sample Output<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"content\"><span class=\"sampledata\">1066<br \/>\n\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u603b\u4f53\u6765\u770b\u6700\u4f73\u7684\u624d\u827a\u4e0e\u91cd\u91cf\u7684\u6bd4\u503c\u5e94\u8be5\u662f\u4ec5\u7528\u4e00\u5934\u624d\u827a\u503c\u4e3a11\u3001\u91cd\u91cf\u4e3a10\u7684\u5976\u725b\uff0c\u4f46\u662f\u7531\u4e8e\u6211\u4eec\u9700<br \/>\n\u8981\u81f3\u5c1115\u5355\u4f4d\u7684\u91cd\u91cf\uff0c\u6700\u4f18\u89e3\u6700\u7ec8\u4e3a\u4f7f\u7528\u8fd9\u5934\u5976\u725b\u52a0\u4e0a\u624d\u827a\u503c\u4e3a21\u3001\u91cd\u91cf\u4e3a20\u7684\u5976\u725b\u3002\u8fd9\u6837\u7684\u8bdd\u624d\u827a\u4e0e\u91cd\u91cf\u7684\u6bd4\u503c<br \/>\n\u4e3a(11+21)\/(10+20)=32\/30=1.0666666\u2026\uff0c\u4e58\u4ee51000\u5411\u4e0b\u53d6\u6574\u4e4b\u540e\u5f97\u52301066\u3002<\/span><\/div>\n<h2><span class=\"ez-toc-section\" id=\"HINT\"><\/span>HINT<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9996\u5148\u4e00\u773c01\u5206\u6570\u89c4\u5212<\/p>\n<p>\u4f46\u662f\u5224\u5b9a\u8d2a\u5fc3\u662f\u4e0d\u5bf9\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u8fd8\u9700\u8981\u6ee1\u8db3\u4e00\u4e2a\u6761\u4ef6\u4f7f\u5f97\u603b\u91cd\u91cf\u81f3\u5c11\u4e3aW<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a01\u80cc\u5305\u95ee\u9898<\/p>\n<p>\u53d6\u5230\u91cd\u91cf\u4e3a(&gt;=)w\uff0c\u4f7f\u5f97\u6743\u503c\u6700\u5927\uff0c\u80cc\u5305dp\u5224\u5b9a\u5373\u53ef<\/p>\n<pre class=\"lang:c++ decode:true \">#include&lt;map&gt;\r\n#include&lt;cmath&gt;\r\n#include&lt;queue&gt;\r\n#include&lt;cstdio&gt;\r\n#include&lt;string&gt;\r\n#include&lt;cstring&gt;\r\n#include&lt;iostream&gt;\r\n#include&lt;algorithm&gt;\r\nusing namespace std;\r\n#define inf 1000000007\r\n#define ll long long\r\n#define N 1010\r\n#define db double\r\n#define eps 1e-5\r\ninline int rd()\r\n{\r\n    int x=0,f=1;char ch=getchar();\r\n    while(ch&lt;'0'||ch&gt;'9'){if(ch=='-')f=-1;ch=getchar();}\r\n    while(ch&gt;='0'&amp;&amp;ch&lt;='9'){x=x*10+ch-'0';ch=getchar();}\r\n    return x*f;\r\n}\r\nint n,W,w[N],t[N];\r\nstruct qaz{int x;db v;}a[N];\r\nbool cmp(qaz a,qaz b){return a.v&gt;b.v;}\r\ndb f[N];\r\nbool ck(db x)\r\n{\r\n    for(int i=1;i&lt;=n;i++)\r\n    {\r\n        a[i].v=(db)t[i]-x*w[i];\r\n        a[i].x=w[i];\r\n    }\r\n    for(int i=1;i&lt;=W;i++) f[i]=-inf;\r\n    f[0]=0;\r\n    for(int i=1;i&lt;=n;i++)\r\n    {\r\n        for(int j=W;j&gt;=0;j--)\r\n        {\r\n            f[min(W,j+a[i].x)]=max(f[min(W,j+a[i].x)],f[j]+a[i].v);\r\n        }\r\n    }\r\n    return f[W]&gt;=0?1:0;\r\n}\r\nint main()\r\n{\r\n    n=rd();W=rd();\r\n    for(int i=1;i&lt;=n;i++) w[i]=rd(),t[i]=rd();\r\n    db l=0,r=1000,mid;\r\n    while(r-l&gt;eps)\r\n    {\r\n        mid=(l+r)\/2;\r\n        if(ck(mid)) l=mid;\r\n        else r=mid;\r\n    }\r\n    printf(\"%d\\n\",(int)(mid*1000));\r\n    return 0;\r\n}\r\n\/*\r\n3 15\r\n20 21\r\n10 11\r\n30 31\r\n\r\n*\/\r\n<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>5281: [Usaco2018 Open]Talent Show Time Limit:\u00a010 Sec\u00a0\u00a0M [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[61,5],"class_list":["post-538","post","type-post","status-publish","format-standard","hentry","category-bzoj","tag-61","tag-dp"],"_links":{"self":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=538"}],"version-history":[{"count":1,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/538\/revisions"}],"predecessor-version":[{"id":539,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/538\/revisions\/539"}],"wp:attachment":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=538"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=538"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}