{"id":141,"date":"2025-01-12T12:46:36","date_gmt":"2025-01-12T04:46:36","guid":{"rendered":"http:\/\/150.230.63.147\/blog\/?p=141"},"modified":"2025-01-12T12:46:36","modified_gmt":"2025-01-12T04:46:36","slug":"c2-power-transmission-hard-edition-%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=141","title":{"rendered":"C2. Power Transmission (Hard Edition) \u89e3\u6790(\u601d\u7dad\u3001\u5e7e\u4f55)"},"content":{"rendered":"\n<div class=\"wp-block-jetpack-markdown\"><h1>Codeforce 1163 C2. Power Transmission (Hard Edition) \u89e3\u6790(\u601d\u7dad\u3001\u5e7e\u4f55)<\/h1>\n<p>\u4eca\u5929\u6211\u5011\u4f86\u770b\u770bCF1163C2<br>\n<a href=\"https:\/\/codeforces.com\/problemset\/problem\/1163\/C2\">\u984c\u76ee\u9023\u7d50<\/a><\/p>\n<blockquote>\n<p><strong>\u984c\u76ee<\/strong><br>\n\u7d66\u4e00\u5806\u9ede\uff0c\u6bcf\u5169\u500b\u9ede\u6703\u9020\u6210\u4e00\u500b<strong>\u76f4\u7dda<\/strong>\uff0c\u6c42\u6709\u591a\u5c11\u500b\u76f4\u7dda\u5c0d\u76f8\u4ea4\u3002<\/p>\n<\/blockquote>\n<h3>\u524d\u8a00<\/h3>\n<p>\u9019\u984c\u63d0\u4f9b\u4e86\u4e00\u500b\u8868\u9054\u76f4\u7dda\u7684\u65b9\u6cd5\u3002<\/p>\n<h3>\u60f3\u6cd5<\/h3>\n<p>\u9019\u984c\u7684\u96e3\u9ede\u5176\u5be6\u662f\u5728\u65bc\u5982\u4f55\u8868\u9054\u4e00\u689d\u76f4\u7dda\uff0c\u4e14\u8981\u8a8d\u70ba\u7528$map$\u4e0d\u6703\u8d85\u6642(\u6211\u4e5f\u4e0d\u61c2\u70ba\u4ec0\u9ebc\u6700\u591a\u6703\u6709$10^6$\u500b\u4e0d\u540c\u7684\u503c\u4f46\u662f\u4e0d\u5230$1$\u79d2\u5c31\u8dd1\u5b8c\u4e86)\u3002<br>\n\u8868\u9054\u4e00\u500b\u76f4\u7dda\uff0c\u6211\u5011\u5f9e\u4e00\u822c\u7684\u76f4\u7dda\u8868\u9054\u5f0f$y=ax+b$\u51fa\u767c\uff0c\u76ee\u524d$a,b$\u5f88\u6709\u53ef\u80fd\u4e0d\u662f\u6574\u6578\u3002\u6211\u5011\u628a\u6574\u500b\u8868\u9054\u5f0f\u4e58\u4e0a\u4e00\u500b$C$\uff0c\u8b8a\u6210$Cy=Cax+Cb$\uff0c\u6211\u5011\u628a$Ca=A,Cb=B$\uff0c\u4e5f\u5c31\u662f$A,B,C$\u662f\u6574\u6578\u3002<br>\n\u63a5\u8457\u4ee3\u5165\u5169\u9ede\uff0c\u5f97\u5230$\\frac{A}{C}=\\frac{y_2-y_1}{x_2-x_1}$\u3002\u63a5\u4e0b\u4f86\uff0c\u7531\u65bc\u6211\u5011\u5e0c\u671b\u5c0d\u65bc\u540c\u4e00\u689d\u76f4\u7dda\uff0c\u6211\u5011\u5f97\u5230\u7684$A,B,C$\u90fd\u662f\u5b8c\u5168\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u6211\u5011\u5148\u4ee4$g=gcd(\\frac{|\\Delta y|}{|\\Delta x|})$ where $\\Delta y=y_2-y_1,\\Delta x=x_2-x_1$\uff0c\u63a5\u8457$C=\\frac{\\Delta x}{g},A=\\frac{\\Delta y}{g}$\uff0c\u4e4b\u5f8c\u518d\u8a08\u7b97\u51fa$B=\\frac{x_1y_2-x_2y_1}{g}$\u3002<br>\n\u6700\u5f8c\u9084\u9700\u8981<\/p>\n<pre><code class=\"language-cpp=\">if(A&lt;0)A=-A,C=-C,B=-B;if(A==0 and C&lt;0)C=-C,B=-B;  \n<\/code><\/pre>\n<p>\u6211\u5011\u8981\u7528\u5169\u500b$map$\u5206\u5225\u7d00\u9304${A,C,B}$\u51fa\u73fe\u904e\u4e86\u6c92(\u7576\u540c\u6a23\u7684\u76f4\u7dda\u51fa\u73fe\u904e\u6642\u624d\u80fd\u5ffd\u7565)\uff0c\u548c\u7d00\u9304${A,C}$\u51fa\u73fe\u4e86\u5e7e\u6b21(\u7d00\u9304\u6bcf\u7a2e\u659c\u7387\u7684\u5e73\u884c\u7dda\u6bb5\u6709\u591a\u5c11\u500b)\u3002<\/p>\n<p>\u63a5\u8457\u53ea\u8981\u904d\u6b77\u6240\u6709\u51fa\u73fe\u904e\u7684\u659c\u7387\u628a\u7b54\u6848\u52a0\u4e0a\u5373\u53ef\u3002<\/p>\n<h3>\u7a0b\u5f0f\u78bc:<\/h3>\n<pre><code class=\"language-cpp=\">const int _n=1010;  \nint t,n,x,y,g,A,B,C,cnt;  \nPII pts[_n];  \nstruct L{  \n  int A,C,B;  \n  bool operator&lt;(const L&amp; rhs)const{  \n    if(A==rhs.A){  \n      if(B==rhs.B)return C&lt;rhs.C;  \n      return B&lt;rhs.B;  \n    }return A&lt;rhs.A;  \n  }  \n};  \nmap&lt;L,int&gt; mp;  \nmap&lt;PII,int&gt; mp2;  \nmain(void) {cin.tie(0);ios_base::sync_with_stdio(0);  \n  cin&gt;&gt;n;rep(i,1,n+1)cin&gt;&gt;pts[i].fi&gt;&gt;pts[i].se;  \n  rep(i,1,n)rep(j,i+1,n+1){  \n    x=pts[j].fi-pts[i].fi,y=pts[j].se-pts[i].se,g=__gcd(abs(x),abs(y));  \n    A=y\/g,C=x\/g,B=(pts[i].fi*pts[j].se-pts[j].fi*pts[i].se)\/g;  \n    if(A&lt;0)A=-A,C=-C,B=-B;if(A==0 and C&lt;0)C=-C,B=-B;  \n    if(!mp[{A,C,B}]){  \n      mp[{A,C,B}]++,mp2[{A,C}]++,cnt++;  \n    }  \n  }ll ans=0;  \n  for(auto it=mp2.begin();it!=mp2.end();it++){  \n    A=it-&gt;fi.fi,C=it-&gt;fi.se;  \n    ans+=1ll*mp2[{A,C}]*(cnt-mp2[{A,C}]);  \n  }cout&lt;&lt;ans\/2&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\/1163\/submission\/94083795\">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-141","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>C2. 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