{"id":58,"date":"2025-01-11T23:03:11","date_gmt":"2025-01-11T15:03:11","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=58"},"modified":"2025-01-11T23:03:11","modified_gmt":"2025-01-11T15:03:11","slug":"a-peter-and-snow-blower-%e8%a7%a3%e6%9e%90%e6%80%9d%e7%b6%ad%e3%80%81%e5%b9%be%e4%bd%95","status":"publish","type":"post","link":"https:\/\/blog.seekrealthing.net\/blog\/?p=58","title":{"rendered":"A. Peter and Snow Blower \u89e3\u6790(\u601d\u7dad\u3001\u5e7e\u4f55)"},"content":{"rendered":"\n<div class=\"wp-block-jetpack-markdown\"><h1>Codeforce 613 A. Peter and Snow Blower \u89e3\u6790(\u601d\u7dad\u3001\u5e7e\u4f55)<\/h1>\n<p>\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF613A<br>\n<a href=\"https:\/\/codeforces.com\/problemset\/problem\/613\/A\">\u984c\u76ee\u9023\u7d50<\/a><\/p>\n<blockquote>\n<p><strong>\u984c\u76ee<\/strong><br>\n\u7d66\u4f60\u4e00\u500b\u9ede$P$\u548c$n$\u500b\u9ede\u5f62\u6210\u7684\u591a\u908a\u5f62(\u7167\u9806\u6216\u9006\u6642\u91dd\u9806\u5e8f\u7d66)\uff0c\u6c42\u9019\u500b\u591a\u908a\u5f62\u7e5e\u8457$P$\u8f49\u6700\u5f8c\u53ef\u4ee5\u9020\u6210\u7684\u9762\u7a4d\u3002(\u6709\u95dc\u6b63\u5f0f\u7684&quot;\u65cb\u8f49&quot;\u5b9a\u7fa9\u8acb\u770b\u539f\u984c)<\/p>\n<\/blockquote>\n<h3>\u524d\u8a00<\/h3>\n<p>\u5132\u5b58\u9ede\u7684\u5ea7\u6a19\u6642\u6c92\u60f3\u904e\u8981\u7528$pair&lt;long\\ long,long\\ long&gt;$\uff0c\u7d50\u679cdebug\u8d85\u4e45<\/p>\n<h3>\u60f3\u6cd5<\/h3>\n<p>\u9996\u5148\u8981\u6ce8\u610f\u5230:\u7531\u65bc\u984c\u76ee\u7684\u65cb\u8f49\u7684\u5b9a\u7fa9\u662f\u628a\u6bcf\u500b\u9ede\u90fd\u5c0d\u65bc\u9ede$P$\u53bb\u505a\u65cb\u8f49\uff0c\u6240\u4ee5\u6700\u5f8c\u7684\u5716\u5f62\u4e00\u5b9a\u662f\u5169\u500b\u540c\u5fc3\u5713\uff0c\u800c\u9762\u7a4d\u5c31\u662f\u5169\u500b\u5713\u4e2d\u9593\u7684\u9762\u7a4d\uff0c\u800c\u6211\u5011\u53ea\u9700\u8981\u7dad\u8b77\u6700\u9577\u7684\u534a\u5f91\u548c\u6700\u77ed\u7684\u534a\u5f91\u5c31\u597d\u3002<br>\n\u7531\u65bc\u984c\u76ee\u662f\u6309\u7167\u9806\u5e8f\u7d66\u591a\u908a\u5f62\u7684\u9ede\uff0c\u6240\u4ee5\u6211\u5011\u53ef\u4ee5\u628a\u6bcf\u689d\u908a\u55ae\u7368\u62ff\u51fa\u4f86\u8003\u616e\u548c$P$\u9ede\u7684\u6700\u77ed\u548c\u6700\u9577\u8ddd\u96e2\u3002<br>\n<img decoding=\"async\" src=\"https:\/\/i.imgur.com\/ycXLzEg.png\" alt=\"\"><br>\n<img decoding=\"async\" src=\"https:\/\/i.imgur.com\/DXevIvL.jpg\" alt=\"\"><br>\n\u5982\u4e0a\u5716\u6240\u793a\uff0c\u60f3\u8981\u5224\u65b7\u9ede$P$\u5230\u7dda\u6bb5$\\overline{SE}$\u7684\u6700\u77ed\u8ddd\u96e2\u7dda\u6bb5\u662f\u5426\u5728\u7dda\u6bb5$\\overline{SE}$\u4e0a\uff0c\u6211\u5011\u53ea\u9700\u8981\u5224\u65b7$\\overrightarrow{PM}$\u662f\u5426\u88ab$\\overrightarrow{PS},\\overrightarrow{PE}$\u6240\u5305\u4f4f\uff0c\u800c\u5176\u4e2d\u4e00\u7a2e\u65b9\u6cd5\u5c31\u662f\u5229\u7528\u5916\u7a4d(\u53c9\u7a4d\u3001cross product):<br>\n\u5982\u679c$\\overrightarrow{PM}$\u662f\u88ab\u5305\u4f4f\u7684\uff0c\u90a3\u9ebc$sgn(\\overrightarrow{PM}\\times\\overrightarrow{PS})=-sgn(\\overrightarrow{PM}\\times\\overrightarrow{PE})$<br>\n\u53cd\u4e4b\u5982\u679c$sgn(\\overrightarrow{PM}\\times\\overrightarrow{PS})=sgn(\\overrightarrow{PM}\\times\\overrightarrow{PE})$\uff0c\u90a3\u9ebc\u4ee3\u8868\u6c92\u6709\u88ab\u5305\u4f4f\u3002\u4ee5\u4e0a\u662f\u5229\u7528\u4e86\u5916\u7a4d\u7684\u6027\u8cea:$\\overrightarrow{AB}\\times\\overrightarrow{CD}=-\\overrightarrow{CD}\\times\\overrightarrow{AB}$\u5c0d\u65bc\u4efb\u4f55\u5411\u91cf$\\overrightarrow{AB},\\overrightarrow{CD}$\u3002<br>\n\u800c\u8981\u8a08\u7b97\u6700\u77ed\u8ddd\u96e2\uff0c\u6211\u5011\u6709\u5169\u7a2e\u65b9\u6cd5:<\/p>\n<ol>\n<li>\u5229\u7528\u5167\u7a4d\u662f\u6295\u5f71\u9577\u5ea6\u7684\u76f8\u4e58\u7684\u6027\u8cea\uff0c\u6211\u5011\u628a\u7dda\u6bb5\u7684\u6cd5\u5411\u91cf\u548c$\\overrightarrow{PE}$\u4f5c\u5167\u7a4d\uff0c\u518d\u9664\u4ee5\u6cd5\u5411\u91cf\u7684\u9577\u5ea6\uff0c\u5c31\u662f\u6700\u77ed\u8ddd\u96e2\u3002<\/li>\n<li>\u5229\u7528\u5916\u7a4d\u7684\u7d55\u5c0d\u503c\u662f\u5411\u91cf\u5011\u6240\u5c55\u51fa\u7684\u56db\u908a\u5f62\u9762\u7a4d\uff0c\u4e14\u7b49\u65bc\u5e95\u4e58\u4ee5\u9ad8\uff0c$|\\overrightarrow{PS}\\times\\overrightarrow{PE}|\/|\\overrightarrow{SE}|$\u5c31\u662f\u6700\u77ed\u8ddd\u96e2\u3002<\/li>\n<\/ol>\n<p>\u800c\u900f\u904e\u89c0\u5bdf\u53ef\u4ee5\u767c\u73fe\uff0c$P$\u9ede\u5230\u7dda\u6bb5\u7684\u9577\u5ea6\uff0c\u4e0d\u662f\u6700\u77ed\u8ddd\u96e2\uff0c\u90a3\u5c31\u662f\u7aef\u9ede\u3002\u6709\u4e86\u4ee5\u4e0a\u8cc7\u8a0a\uff0c\u6211\u5011\u5c31\u53ef\u4ee5\u5beb\u4e86\u3002<\/p>\n<h3>\u7a0b\u5f0f\u78bc:<\/h3>\n<pre><code class=\"language-cpp=\">const int _n=1e5+10;  \nint t,n,m;  \nPII p,prev,ps[_n];  \ndb minn=1e9,maxx=-1e9,pi=acos(-1);  \nbool sgn(db x){  \n  return x&gt;=0.0?0:1;  \n}  \ndb cp(PII u,PII v){  \n  return (db)(u.fi*v.se-u.se*v.fi);  \n}  \ndb len(PII u){  \n  return sqrt(u.fi*u.fi+u.se*u.se);  \n}  \nvoid f(PII x,PII y){  \n  PII tt2={y.fi-p.fi,y.se-p.se},tt3={x.fi-p.fi,x.se-p.se},tt1={-(tt3.se-tt2.se),tt3.fi-tt2.fi};  \n  db res1=len(tt2),res2=len(tt3),res3=abs((db)(tt1.fi*tt2.fi+tt1.se*tt2.se))\/len(tt1);  \n  bool z=1;if(sgn(cp(tt1,tt2))==sgn(cp(tt1,tt3)))z=0;  \n  if(z){  \n    minn=min(minn,min(res1,min(res2,res3)));  \n    maxx=max(maxx,max(res1,max(res2,res3)));  \n  }else{  \n    minn=min(minn,min(res1,res2));  \n    maxx=max(maxx,max(res1,res2));  \n  }  \n}  \nmain(void) {ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);  \n  \/\/\u9019\u908a\u7684PII\u5fc5\u9808\u662fpair&lt;ll,ll&gt;  \n  cin&gt;&gt;n&gt;&gt;p.fi&gt;&gt;p.se;rep(i,0,n)cin&gt;&gt;ps[i].fi&gt;&gt;ps[i].se; prev=ps[0];  \n  rep(i,1,n)f(prev,ps[i]),prev=ps[i];  \n  f(prev,ps[0]);  \n  cout&lt;&lt;setprecision(20)&lt;&lt;pi*(maxx*maxx-minn*minn)&lt;&lt;'\\n';  \n  return 0;  \n}  \n<\/code><\/pre>\n<p>\u6a19\u982d\u3001\u6a21\u677f\u8acb\u9edeSubmission\u770b<br>\n<a href=\"https:\/\/codeforces.com\/contest\/613\/submission\/91112005\">Submission<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[3],"tags":[10,9,22,8],"class_list":["post-58","post","type-post","status-publish","format-standard","hentry","category-ojcode","tag-codeforce","tag-ojcode","tag-22","tag-8"],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A. 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