{"id":632,"date":"2017-07-11T16:57:00","date_gmt":"2017-07-11T08:57:00","guid":{"rendered":"http:\/\/kylelv.com\/?p=632"},"modified":"2020-03-04T14:58:35","modified_gmt":"2020-03-04T06:58:35","slug":"bzoj-1941-sdoi2010hide-and-seek-k-d-tree","status":"publish","type":"post","link":"https:\/\/blog.kylelv.com\/?p=632","title":{"rendered":"bzoj 1941: [Sdoi2010]Hide and Seek &#8212; K-D tree"},"content":{"rendered":"\n<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-69fdef88365dc\" 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-69fdef88365dc\"  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=632\/#1941_Sdoi2010Hide_and_Seek\" title=\"1941: [Sdoi2010]Hide and Seek\">1941: [Sdoi2010]Hide and Seek<\/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=632\/#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=632\/#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=632\/#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=632\/#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=632\/#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=632\/#HINT\" title=\"HINT\">HINT<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.kylelv.com\/?p=632\/#Source\" title=\"Source\">Source<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"has-text-align-center wp-block-heading\"><span class=\"ez-toc-section\" id=\"1941_Sdoi2010Hide_and_Seek\"><\/span>1941: [Sdoi2010]Hide and Seek<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-text-align-center\">Time Limit:&nbsp;16 Sec&nbsp;&nbsp;Memory Limit:&nbsp;162 MB<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Description\"><\/span>Description<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5c0f\u732aiPig\u5728PKU\u521a\u4e0a\u5b8c\u4e86\u65e0\u804a\u7684\u732a\u6027\u4ee3\u6570\u8bfe\uff0c\u5929\u8d44\u806a\u6167\u7684iPig\u88ab\u8fd9\u95e8\u5bf9\u4ed6\u6765\u8bf4\u65e0\u6bd4\u7b80\u5355\u7684\u8bfe\u5f04\u5f97\u975e\u5e38\u5bc2\u5bde\uff0c\u4e3a\u4e86\u6d88\u9664\u5bc2\u5bde\u611f\uff0c\u4ed6\u51b3\u5b9a\u548c\u4ed6\u7684\u597d\u670b\u53cbgiPi\uff08\u9e21\u76ae\uff09\u73a9\u4e00\u4e2a\u66f4\u52a0\u5bc2\u5bde\u7684\u6e38\u620f&#8212;\u6349\u8ff7\u85cf\u3002 \u4f46\u662f\uff0c\u4ed6\u4eec\u89c9\u5f97\uff0c\u73a9\u666e\u901a\u7684\u6349\u8ff7\u85cf\u6ca1\u4ec0\u4e48\u610f\u601d\uff0c\u8fd8\u662f\u4e0d\u591f\u5bc2\u5bde\uff0c\u4e8e\u662f\uff0c\u4ed6\u4eec\u51b3\u5b9a\u73a9\u5bc2\u5bde\u65e0\u6bd4\u7684\u8783\u87f9\u7248\u6349\u8ff7\u85cf\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5c31\u662f\u8bf4\u4ed6\u4eec\u5728\u73a9\u6e38\u620f\u7684\u65f6\u5019\u53ea\u80fd\u6cbf\u6c34\u5e73\u6216\u5782\u76f4\u65b9\u5411\u8d70\u3002\u4e00\u756a\u5bc2\u5bde\u7684\u526a\u5200\u77f3\u5934\u5e03\u540e\uff0c\u4ed6\u4eec\u51b3\u5b9aiPig\u53bb\u6349giPi\u3002\u7531\u4e8e\u4ed6\u4eec\u90fd\u5f88\u719f\u6089PKU\u7684\u5730\u5f62\u4e86\uff0c\u6240\u4ee5giPi\u53ea\u4f1a\u8eb2\u5728PKU\u5185n\u4e2a\u9690\u79d8\u5730\u70b9\uff0c\u663e\u7136iPig\u4e5f\u53ea\u4f1a\u5728\u90a3n\u4e2a\u5730\u70b9\u5185\u627egiPi\u3002\u6e38\u620f\u4e00\u5f00\u59cb\uff0c\u4ed6\u4eec\u9009\u5b9a\u4e00\u4e2a\u5730\u70b9\uff0ciPig\u4fdd\u6301\u4e0d\u52a8\uff0c\u7136\u540egiPi\u752830\u79d2\u7684\u65f6\u95f4\u9003\u79bb\u73b0\u573a\uff08\u663e\u7136\uff0cgiPi\u4e0d\u4f1a\u5446\u5728\u539f\u5730\uff09\u3002\u7136\u540eiPig\u4f1a\u968f\u673a\u5730\u53bb\u627egiPi\uff0c\u76f4\u5230\u627e\u5230\u4e3a\u6b62\u3002\u7531\u4e8eiPig\u5f88\u61d2\uff0c\u6240\u4ee5\u4ed6\u5230\u603b\u662f\u8d70\u6700\u77ed\u7684\u8def\u5f84\uff0c\u800c\u4e14\uff0c\u4ed6\u9009\u62e9\u8d77\u59cb\u70b9\u4e0d\u662f\u968f\u4fbf\u9009\u7684\uff0c\u4ed6\u60f3\u627e\u4e00\u4e2a\u5730\u70b9\uff0c\u4f7f\u5f97\u8be5\u5730\u70b9\u5230\u6700\u8fdc\u7684\u5730\u70b9\u548c\u6700\u8fd1\u7684\u5730\u70b9\u7684\u8ddd\u79bb\u5dee\u6700\u5c0f\u3002iPig\u73b0\u5728\u60f3\u77e5\u9053\u8fd9\u4e2a\u8ddd\u79bb\u5dee\u6700\u5c0f\u662f\u591a\u5c11\u3002 \u7531\u4e8eiPig\u73b0\u5728\u624b\u4e0a\u6ca1\u6709\u7535\u8111\uff0c\u6240\u4ee5\u4e0d\u80fd\u7f16\u7a0b\u89e3\u51b3\u8fd9\u4e2a\u5982\u6b64\u7b80\u5355\u7684\u95ee\u9898\uff0c\u6240\u4ee5\u4ed6\u9a6c\u4e0a\u6253\u4e86\u4e2a\u7535\u8bdd\uff0c\u8981\u6c42\u4f60\u5e2e\u4ed6\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002iPig\u544a\u8bc9\u4e86\u4f60PKU\u7684n\u4e2a\u9690\u79d8\u5730\u70b9\u7684\u5750\u6807\uff0c\u8bf7\u4f60\u7f16\u7a0b\u6c42\u51faiPig\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Input\"><\/span>Input<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u7b2c\u4e00\u884c\u8f93\u5165\u4e00\u4e2a\u6574\u6570N \u7b2c2~N+1\u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570X\uff0cY\uff0c\u8868\u793a\u7b2ci\u4e2a\u5730\u70b9\u7684\u5750\u6807<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Output\"><\/span>Output<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u4e00\u4e2a\u6574\u6570\uff0c\u4e3a\u8ddd\u79bb\u5dee\u7684\u6700\u5c0f\u503c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sample_Input\"><\/span>Sample Input<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>4<br>0 0<br>1 0<br>0 1<br>1 1<br><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Sample_Output\"><\/span>Sample Output<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>1<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"HINT\"><\/span>HINT<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u5bf9\u4e8e30%\u7684\u6570\u636e,N&lt;=1000 \u5bf9\u4e8e100%\u7684\u6570\u636e\uff0cN&lt;=500000,0&lt;=X,Y&lt;=10^8 \u4fdd\u8bc1\u6570\u636e\u6ca1\u6709\u91cd\u70b9\u4fdd\u8bc1N&gt;=2<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Source\"><\/span>Source<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>#include&lt;map>\n#include&lt;cmath>\n#include&lt;queue>\n#include&lt;cstdio>\n#include&lt;cstring>\n#include&lt;iostream>\n#include&lt;algorithm>\nusing namespace std;\n#define inf 1000000007\n#define ll long long\n#define N 500010\ninline int rd()\n{\n    int x=0,f=1;char ch=getchar();\n    while(ch&lt;'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}\n    while(ch>='0'&amp;&amp;ch&lt;='9'){x=x*10+ch-'0';ch=getchar();}\n    return x*f;\n}\nstruct kdtr{int d&#91;2],mn&#91;2],mx&#91;2],ls,rs;}T&#91;N];\nint D,ans=inf,ansmx,ansmn,Q,rt;\nbool cmp(kdtr a,kdtr b){return a.d&#91;D]&lt;b.d&#91;D];}\nvoid ud(int p)\n{\n    int l=T&#91;p].ls,r=T&#91;p].rs;\n    for(int i=0;i&lt;2;++i)\n    {\n        if(l) T&#91;p].mx&#91;i]=max(T&#91;p].mx&#91;i],T&#91;l].mx&#91;i]),T&#91;p].mn&#91;i]=min(T&#91;p].mn&#91;i],T&#91;l].mn&#91;i]);\n        if(r) T&#91;p].mx&#91;i]=max(T&#91;p].mx&#91;i],T&#91;r].mx&#91;i]),T&#91;p].mn&#91;i]=min(T&#91;p].mn&#91;i],T&#91;r].mn&#91;i]);\n    }\n}\nvoid build(int &amp;p,int l,int r,int now)\n{\n    int mid=l+r>>1;D=now;\n    nth_element(T+l,T+mid,T+r+1,cmp);p=mid;\n    for(int i=0;i&lt;2;++i) T&#91;p].mx&#91;i]=T&#91;p].mn&#91;i]=T&#91;p].d&#91;i];\n    if(l&lt;mid) build(T&#91;p].ls,l,mid-1,now^1);\n    if(r>mid) build(T&#91;p].rs,mid+1,r,now^1);\n    ud(p);\n}\nvoid asmx(int &amp;x,int k){x=0;for(int i=0;i&lt;2;++i) x+=max(abs(T&#91;k].mx&#91;i]-T&#91;Q].d&#91;i]),abs(T&#91;k].mn&#91;i]-T&#91;Q].d&#91;i]));}\nvoid fdmx(int k,int now)\n{\n    int dis=abs(T&#91;k].d&#91;0]-T&#91;Q].d&#91;0])+abs(T&#91;k].d&#91;1]-T&#91;Q].d&#91;1]),dl=-1,dr=-1;\n    if(Q^k) ansmx=max(ansmx,dis);\n    if(T&#91;k].ls) asmx(dl,T&#91;k].ls);\n    if(T&#91;k].rs) asmx(dr,T&#91;k].rs);\n    if(dl>dr)\n    {\n        if(dl>ansmx) fdmx(T&#91;k].ls,now^1);\n        if(dr>ansmx) fdmx(T&#91;k].rs,now^1);\n    }\n    else\n    {\n        if(dr>ansmx) fdmx(T&#91;k].rs,now^1);\n        if(dl>ansmx) fdmx(T&#91;k].ls,now^1);\n    }\n}\nvoid asmn(int &amp;x,int k){x=0;for(int i=0;i&lt;2;++i) x+=max(0,T&#91;k].mn&#91;i]-T&#91;Q].d&#91;i])+max(0,T&#91;Q].d&#91;i]-T&#91;k].mx&#91;i]);}\nvoid fdmn(int k,int now)\n{\n    int dis=abs(T&#91;k].d&#91;0]-T&#91;Q].d&#91;0])+abs(T&#91;k].d&#91;1]-T&#91;Q].d&#91;1]),dl=inf,dr=inf;\n    if(Q^k) ansmn=min(ansmn,dis);\n    if(T&#91;k].ls) asmn(dl,T&#91;k].ls);\n    if(T&#91;k].rs) asmn(dr,T&#91;k].rs);\n    if(dl&lt;dr)\n    {\n        if(dl&lt;ansmn) fdmn(T&#91;k].ls,now^1);\n        if(dr&lt;ansmn) fdmn(T&#91;k].rs,now^1);\n    }\n    else\n    {\n        if(dr&lt;ansmn) fdmn(T&#91;k].rs,now^1);\n        if(dl&lt;ansmn) fdmn(T&#91;k].ls,now^1);\n    }\n}\nint n;\nint main()\n{\n    n=rd();\n    for(int i=1;i&lt;=n;++i)\n        T&#91;i].d&#91;0]=rd(),T&#91;i].d&#91;1]=rd();\n    build(rt,1,n,0);\n    for(int i=1;i&lt;=n;++i)\n    {\n        ansmx=-1;ansmn=inf;Q=i;\n        fdmx(rt,0);fdmn(rt,0);\n        ans=min(ans,ansmx-ansmn);\n    }\n    printf(\"%d\\n\",ans);\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>1941: [Sdoi2010]Hide and Seek Time Limit:&nbsp;16 Sec&#038;n [&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":[69,19],"class_list":["post-632","post","type-post","status-publish","format-standard","hentry","category-bzoj","tag-k-d-tree","tag-19"],"_links":{"self":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/632","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=632"}],"version-history":[{"count":1,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/632\/revisions"}],"predecessor-version":[{"id":633,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=\/wp\/v2\/posts\/632\/revisions\/633"}],"wp:attachment":[{"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.kylelv.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}