{"id":30,"date":"2025-11-09T20:43:41","date_gmt":"2025-11-09T12:43:41","guid":{"rendered":"https:\/\/tblog.zeabur.app\/?p=30"},"modified":"2025-11-09T20:46:30","modified_gmt":"2025-11-09T12:46:30","slug":"%e9%a2%98%e8%a7%a3-uva10566-crossed-ladders","status":"publish","type":"post","link":"https:\/\/tblog.zeabur.app\/?p=30","title":{"rendered":"\u9898\u89e3 UVA10566 Crossed Ladders"},"content":{"rendered":"\n

\u9898\u76ee\u5927\u610f<\/h2>\n\n\n\n

\u7ed9\u51fa\u4e24\u628a\u68af\u5b50\u7684\u9ad8\u957f\u5ea6 $x$ \u548c $y$\uff0c\u4ee5\u53ca\u4ea4\u53c9\u70b9 $c$ \u7684\u9ad8\u5ea6\uff0c\u6c42\u9053\u8def\u7684\u5bbd\uff08\u5373\u4e24\u68af\u5b50\u5e95\u7aef\u4e4b\u95f4\u7684\u8ddd\u79bb\uff09\u3002<\/p>\n\n\n\n

\u89e3\u9898\u601d\u8def<\/h2>\n\n\n\n

\u6570\u5b66 + \u4e8c\u5206<\/h3>\n\n\n\n

\u53ef\u4ee5\u5229\u7528\u68af\u5b50\u7684\u957f\u5ea6\u548c\u68af\u5b50\u4e0e\u5730\u9762\u7684\u5939\u89d2\u6765\u6c42\u5f97\u9053\u8def\u7684\u5bbd\u3002<\/p>\n\n\n\n

\u8bbe\u68af\u5b50 $x$ \u4e0e $y$ \u4e0e\u5730\u9762\u7684\u5939\u89d2\u5206\u522b\u4e3a $\\alpha$ \u548c $\\beta$\uff0c\u9053\u8def\u7684\u5bbd\u8bbe\u4e3a $w$\uff0c\u68af\u5b50 $x$ \u7684\u5e95\u7aef\u4e0e\u4ea4\u53c9\u70b9\u5728\u5730\u9762\u7684\u6c34\u5e73\u6295\u5f71\u8ddd\u79bb\u4e3a $h$\u3002<\/p>\n\n\n\n

\"\"\/<\/div><\/figure>\n\n\n\n

\u5219\u6709 $\\sin(\\alpha)=\\frac{c}{x}$\uff0c$\\sin(\\beta)=\\frac{c}{y}$\uff0c$\\cos(\\alpha)=\\frac{w+h}{x}$\uff0c$\\cos(\\beta)=\\frac{w}{y}$\u3002<\/p>\n\n\n\n

\u89e3\u51fa $h$ \u4e3a\uff1a
$\\displaystyle h=y\\times\\cos(\\beta)=y\\times\\sqrt{1-\\sin^2(\\beta)}=y\\times\\sqrt{1-\\frac{c^2}{y^2}}=y\\times\\frac{\\sqrt{y^2-c^2}}{y}=\\sqrt{y^2-c^2}$
\u5e76\u8868\u793a\u9053\u8def\u5bbd $w$ \u4e3a\uff1a
$\\displaystyle w=x\\times\\cos(\\alpha)-h=x\\times\\sqrt{1-\\sin^2(\\alpha)}-h=x\\times\\sqrt{1-\\frac{c^2}{x^2}}-h=x\\times\\frac{\\sqrt{x^2-c^2}}{x}-h=\\sqrt{x^2-c^2}-h$
\u5c06 $h=\\sqrt{y^2-c^2}$ \u4ee3\u5165\uff0c\u5f97\uff1a
$\\displaystyle w=\\sqrt{x^2-c^2}-\\sqrt{y^2-c^2}$
\u4e0d\u96be\u770b\u51fa\uff0c\u8be5\u89e3\u6790\u5f0f\u5177\u6709\u5355\u8c03\u9012\u51cf\u6027\uff0c\u53c8\u7531\u4e8e\u6570\u636e\u4e3a\u5b9e\u6570\uff0c\u5219\u53ef\u4ee5\u4f7f\u7528\u5b9e\u6570\u4e8c\u5206\uff0c\u4e0d\u65ad\u903c\u8fd1\u6240\u9700\u7cbe\u5ea6\u3002<\/p>\n\n\n\n

\u4ee3\u7801<\/h2>\n\n\n\n
#include<bits\/stdc++.h>\n#include<ext\/pb_ds\/assoc_container.hpp>\n#include<ext\/pb_ds\/hash_policy.hpp>\n#define int long long\n#define endl \"\\n\" \nusing namespace __gnu_cxx;\nusing namespace __gnu_pbds;\nusing namespace std;\ndouble x,y,c;\ninline bool check(long double m)\/\/\u68c0\u67e5\u51fd\u6570\n{\n    long double h1=sqrt(x*x-m*m);\n    long double h2=sqrt(y*y-m*m);\n    return (h1*h2)<(h1*c+h2*c);\/\/\u8fd4\u56de\u7cbe\u5ea6\u504f\u5c0f\uff08true\uff09\u8fd8\u662f\u504f\u5927\uff08false\uff09\u3002\n}\nsigned main() \n{\n    while(cin>>x>>y>>c)\n    {\n        long double l=0,r=min(x,y);\/\/\u5de6\u53f3\u7aef\u70b9\n        long double m;\n        while(r-l>=1e-6)\/\/\u5b9e\u6570\u4e8c\u5206\n        {\n            m=(l+r)\/2;\/\/\u6ce8\u610f double \u7c7b\u578b\u4e0d\u80fd\u7528\u53f3\u79fb\u8fd0\u7b97\n            if(check(m))r=m;\n            else l=m;\n        }\n        cout<<fixed<<setprecision(3)<<l<<endl;\n    }\n    return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u9898\u76ee\u5927\u610f \u7ed9\u51fa\u4e24\u628a\u68af\u5b50\u7684\u9ad8\u957f\u5ea6 $x$ \u548c $y$\uff0c\u4ee5\u53ca\u4ea4\u53c9\u70b9 $c$ \u7684\u9ad8\u5ea6\uff0c\u6c42\u9053\u8def\u7684\u5bbd\uff08\u5373\u4e24\u68af\u5b50\u5e95\u7aef\u4e4b\u95f4\u7684 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[3],"class_list":["post-30","post","type-post","status-publish","format-standard","hentry","category-oi","tag-oi"],"featured_image_src":null,"author_info":{"display_name":"CaelumRadish_c","author_link":"https:\/\/tblog.zeabur.app\/?author=1"},"_links":{"self":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/30","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=30"}],"version-history":[{"count":2,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/30\/revisions"}],"predecessor-version":[{"id":34,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/30\/revisions\/34"}],"wp:attachment":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=30"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=30"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=30"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}