{"id":353,"date":"2013-03-16T08:39:00","date_gmt":"2013-03-16T00:39:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/257"},"modified":"2013-03-16T08:39:00","modified_gmt":"2013-03-16T00:39:00","slug":"bzoj_1502_noi2005_under_the_lemon-simpson_points","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=353","title":{"rendered":"BZOJ 1502([NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811-Simpson\u79ef\u5206)"},"content":{"rendered":"<p><center style=\"font-family:arial,verdana,helvetica,sans-serif; font-size:14px\"><\/p>\n<h2 style=\"color:blue\">1502: [NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811<\/h2>\n<p><span class=\"green\">Time Limit:&nbsp;<\/span>5 Sec&nbsp;&nbsp;<span class=\"green\">Memory Limit:&nbsp;<\/span>64 MB<br \/>\n<span class=\"green\">Submit:&nbsp;<\/span>250&nbsp;&nbsp;<span class=\"green\">Solved:&nbsp;<\/span>148<br \/>\n[<a href=\"http:\/\/www.lydsy.com\/JudgeOnline\/submitpage.php?id=1502\" style=\"color:blue; text-decoration:none\">Submit<\/a>][<a href=\"http:\/\/www.lydsy.com\/JudgeOnline\/problemstatus.php?id=1502\" style=\"color:blue; text-decoration:none\">Status<\/a>][<a href=\"http:\/\/www.lydsy.com\/JudgeOnline\/bbs.php?id=1502\" style=\"color:blue; text-decoration:none\">Discuss<\/a>]<\/center><\/p>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">Description<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n\u674e\u54f2\u975e\u5e38\u975e\u5e38\u559c\u6b22\u67e0\u6aac\u6811,\u7279\u522b\u662f\u5728\u9759\u9759\u7684\u591c\u665a,\u5f53\u5929\u7a7a\u4e2d\u6709\u4e00\u5f2f\u660e\u6708\u6e29\u67d4\u5730\u7167\u4eae\u5730\u9762\u4e0a\u7684\u666f\u7269\u65f6,\u4ed6\u5fc5\u4f1a\u60a0\u95f2\u5730\u5750\u5728\u4ed6\u4eb2\u624b\u690d\u4e0b\u7684\u90a3\u68f5\u67e0\u6aac\u6811\u65c1,\u72ec\u81ea\u601d\u7d22\u7740\u4eba\u751f\u7684\u54f2\u7406\u3002<br \/>\n\u674e\u54f2\u662f\u4e00\u4e2a\u559c\u7231\u601d\u8003\u7684\u5b69\u5b50,\u5f53\u4ed6\u770b\u5230\u5728\u6708\u5149\u7684\u7167\u5c04\u4e0b\u67e0\u6aac\u6811\u6295\u5728\u5730\u9762\u4e0a\u7684\u5f71\u5b50\u662f\u5982\u6b64\u7684\u6e05\u6670,\u9a6c\u4e0a\u60f3\u5230\u4e86\u4e00\u4e2a\u95ee\u9898:\u6811\u5f71\u7684\u9762\u79ef\u662f\u591a\u5927\u5462?<br \/>\n\u674e\u54f2\u77e5\u9053,\u76f4\u63a5\u6d4b\u91cf\u9762\u79ef\u662f\u5f88\u96be\u7684,\u4ed6\u60f3\u7528\u51e0\u4f55\u7684\u65b9\u6cd5\u7b97,\u56e0\u4e3a\u4ed6\u5bf9\u8fd9\u68f5\u67e0\u6aac\u6811\u7684\u5f62\u72b6\u4e86\u89e3\u5f97\u975e\u5e38\u6e05\u695a,\u800c\u4e14\u60f3\u597d\u4e86\u7b80\u5316\u7684\u65b9\u6cd5\u3002<br \/>\n\u674e\u54f2\u5c06\u6574\u68f5\u67e0\u6aac\u6811\u5206\u6210\u4e86 n \u5c42,\u7531\u4e0b\u5411\u4e0a\u4f9d\u6b21\u5c06\u5c42\u7f16\u53f7\u4e3a 1,2,...,n\u3002\u4ece\u7b2c 1\u5230 n-1 \u5c42,\u6bcf\u5c42\u90fd\u662f\u4e00\u4e2a\u5706\u53f0\u578b,\u7b2c n \u5c42(\u6700\u4e0a\u9762\u4e00\u5c42)\u662f\u5706\u9525\u578b\u3002\u5bf9\u4e8e\u5706\u53f0\u578b,\u5176\u4e0a\u4e0b\u5e95\u9762\u90fd\u662f\u6c34\u5e73\u7684\u5706\u3002\u5bf9\u4e8e\u76f8\u90bb\u7684\u4e24\u4e2a\u5706\u53f0,\u4e0a\u5c42\u7684\u4e0b\u5e95\u9762\u548c\u4e0b\u5c42\u7684\u4e0a\u5e95\u9762\u91cd\u5408\u3002\u7b2c n \u5c42(\u6700\u4e0a\u9762\u4e00\u5c42)\u5706\u9525\u7684\u5e95\u9762\u5c31\u662f\u7b2c n-1 \u5c42\u5706\u53f0\u7684\u4e0a\u5e95\u9762\u3002\u6240\u6709\u7684\u5e95\u9762\u7684\u5706\u5fc3(\u5305\u62ec\u6811\u9876)\u5904\u5728\u540c\u4e00\u6761\u4e0e\u5730\u9762\u5782\u76f4\u7684\u76f4\u7ebf\u4e0a\u3002\u674e\u54f2\u77e5\u9053\u6bcf\u4e00\u5c42\u7684\u9ad8\u5ea6\u4e3ah1,h2,...,hn,\u7b2c 1 \u5c42\u5706\u53f0\u7684\u4e0b\u5e95\u9762\u8ddd\u5730\u9762\u7684\u9ad8\u5ea6\u4e3a h0,\u4ee5\u53ca\u6bcf\u5c42\u7684\u4e0b\u5e95\u9762\u7684\u5706\u7684\u534a\u5f84 r1,r2,...,rn\u3002\u674e\u54f2\u7528\u719f\u77e5\u7684\u65b9\u6cd5\u6d4b\u51fa\u4e86\u6708\u4eae\u7684\u5149\u7ebf\u4e0e\u5730\u9762\u7684\u5939\u89d2\u4e3a<br \/>\n alpha\u3002<\/div>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n<img decoding=\"async\" src=\"http:\/\/nike0good.jp1.rpvhost.net\/wp-content\/uploads\/csdn\/other_site\/img_my_1363393438_6587.png\" alt=\"\" \/><\/p>\n<\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">Input<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n\u6587\u4ef6\u7684\u7b2c1\u884c\u5305\u542b\u4e00\u4e2a\u6574\u6570n\u548c\u4e00\u4e2a\u5b9e\u6570alpha\uff0c\u8868\u793a\u67e0\u6aac\u6811\u7684\u5c42\u6570\u548c\u6708\u4eae\u7684\u5149\u7ebf\u4e0e\u5730\u9762\u5939\u89d2(\u5355\u4f4d\u4e3a\u5f27\u5ea6)\u3002 \u7b2c2\u884c\u5305\u542bn&#43;1\u4e2a\u5b9e\u6570h0,h1,h2,\u2026,hn\uff0c\u8868\u793a\u6811\u79bb\u5730\u7684\u9ad8\u5ea6\u548c\u6bcf\u5c42\u7684\u9ad8\u5ea6\u3002 \u7b2c3\u884c\u5305\u542bn\u4e2a\u5b9e\u6570r1,r2,\u2026,rn\uff0c\u8868\u793a\u67e0\u6aac\u6811\u6bcf\u5c42\u4e0b\u5e95\u9762\u7684\u5706\u7684\u534a\u5f84\u3002 \u4e0a\u8ff0\u8f93\u5165\u6587\u4ef6\u4e2d\u7684\u6570\u636e\uff0c\u540c\u4e00\u884c\u76f8\u90bb\u7684\u4e24\u4e2a\u6570\u4e4b\u95f4\u7528\u4e00\u4e2a\u7a7a&#26684;\u5206\u9694\u3002 \u8f93\u5165\u7684\u6240\u6709\u5b9e\u6570\u7684\u5c0f\u6570\u70b9\u540e\u53ef\u80fd\u5305\u542b1\u81f310\u4f4d\u6709\u6548\u6570\u5b57\u3002<\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">Output<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n\u8f93\u51fa1\u4e2a\u5b9e\u6570\uff0c\u8868\u793a\u6811\u5f71\u7684\u9762\u79ef\u3002\u56db\u820d\u4e94\u5165\u4fdd\u7559\u4e24\u4f4d\u5c0f\u6570\u3002<\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">Sample Input<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n<span class=\"sampledata\" style=\"font-family:monospace; white-space:pre; background-color:rgb(141,184,255); font-size:18px\">2 0.7853981633<br style=\"font-family:arial,verdana,helvetica,sans-serif!important\" \/><br \/>\n10.0 10.00 10.00<br style=\"font-family:arial,verdana,helvetica,sans-serif!important\" \/><br \/>\n4.00 5.00<br style=\"font-family:arial,verdana,helvetica,sans-serif!important\" \/><br \/>\n<\/span><\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">Sample Output<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n<span class=\"sampledata\" style=\"font-family:monospace; white-space:pre; background-color:rgb(141,184,255); font-size:18px\">171.97<br style=\"font-family:arial,verdana,helvetica,sans-serif!important\" \/><br \/>\n<\/span><\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">HINT<\/h2>\n<div class=\"content\" style=\"font-family:arial,verdana,helvetica,sans-serif; height:auto; background-color:rgb(228,240,248); margin:0px; padding:0px 20px; font-size:14px\">\n<p>1\u2264n\u2264500\uff0c0.3&lt;alpha&lt;\u03c0 2\uff0c0&lt;hi\u2264100\uff0c0&lt;ri\u2264100\u3002<br \/>\n&nbsp;10%\u7684\u6570\u636e\u4e2d\uff0cn=1\u3002<br \/>\n30%\u7684\u6570\u636e\u4e2d\uff0cn\u22642\u3002<br \/>\n60%\u7684\u6570\u636e\u4e2d\uff0cn\u226420\u3002<br \/>\n100%\u7684\u6570\u636e\u4e2d\uff0cn\u2264500\u3002\n<\/p>\n<\/div>\n<h2 style=\"font-family:arial,verdana,helvetica,sans-serif; color:blue\">\n<\/h2>\n<div><span style=\"font-size:14px\">\u8fd9\u9898\u662fSimpson\u6a21\u7248\u9898\u3002<\/span><\/div>\n<div><span style=\"font-size:14px\">\u6709\u4e00\u4e2a\u5173\u952e\u662f\u5706\u7684\u516c\u5207\u7ebf\u7684\u6c42\u6cd5\u3002<\/span><\/div>\n<div><span style=\"font-size:14px\">\u9996\u5148\u5ef6\u957f\u5706\u7684\u5207\u7ebf\u6c42l\uff0c\u518d\u6c42\u03b8\uff0c\u6700\u540e\u7528\u76f8&#20284;\u4e09\u89d2\u5f62\u3002<\/span><\/div>\n<div><span style=\"font-size:14px\"><br \/>\n<\/span><\/div>\n<div><span style=\"font-size:14px\"><br \/>\n<\/span><\/div>\n<div><span style=\"font-size:14px\"><\/span><\/p>\n<pre name=\"code\" class=\"cpp\">#include&lt;cstdio&gt;\n#include&lt;cstdlib&gt;\n#include&lt;cstring&gt;\n#include&lt;cmath&gt;\n#include&lt;iostream&gt;\n#include&lt;algorithm&gt;\n#include&lt;functional&gt;\nusing namespace std;\n#define MAXN (500+10)\n#define eps 1e-8\ndouble h[MAXN],s[MAXN],r[MAXN],alpha,l1=0,r1=0;\ndouble sqr(double x){return x*x;}\nint n,size=0;\nstruct S\n{\n\tdouble x,y,p,q;\n}c[MAXN];\ndouble f(double l)\n{\n\tdouble t=0.0;\n\tfor (int i=0;i&lt;n;i++)\n\t{\n\t\tif (fabs(s[i]-l)&lt;r[i]) t=max(t,sqrt(sqr(r[i])-sqr(s[i]-l)));\n\t}\n\tfor (int i=1;i&lt;=size;i++)\n\t{\n\t\tif (c[i].x&lt;l&amp;&amp;l&lt;c[i].p)\tt=max(t,c[i].y+(c[i].q-c[i].y)*(l-c[i].x)\/(c[i].p-c[i].x));\n\t}\n\treturn t;\n\n}\ndouble simpson(double l,double r,double fl,double fmid,double fr)\n{\n\treturn (fl+4*fmid+fr)*(r-l)\/6;\n}\ndouble rsimpson(double l,double r,double fl,double fmid,double fr)\n{\n\tdouble m=(l+r)\/2;\n\tdouble p=f((l+m)\/2),q=f((m+r)\/2);\n\tdouble x=simpson(l,r,fl,fmid,fr),y=simpson(l,m,fl,p,fmid),z=simpson(m,r,fmid,q,fr);\n\tif (fabs(x-y-z)&lt;eps)\n\t\treturn y+z;\n\treturn rsimpson(l,m,fl,p,fmid)+rsimpson(m,r,fmid,q,fr);\n}\nint main()\n{\n\tscanf(&quot;%d%lf&quot;,&amp;n,&amp;alpha);\n\talpha=1\/tan(alpha);\n\tfor (int i=0;i&lt;=n;i++)\n\t{\n\t\tscanf(&quot;%lf&quot;,&amp;h[i]);\n\t\tif (i) h[i]+=h[i-1];\n\t\ts[i]=h[i]*alpha;\n\t}\n\tfor (int i=0;i&lt;n;i++)\n\t{\n\t\tscanf(&quot;%lf&quot;,&amp;r[i]);\n\t\tl1=min(l1,s[i]-r[i]);\n\t\tr1=max(r1,s[i]+r[i]);\n\t}\n\tr[n]=0;\n\tfor (int i=0;i&lt;n;i++)\n\t{\n\t\tdouble d=s[i+1]-s[i];\n\t\tif (d&gt;fabs(r[i]-r[i+1]))\n\t\t{\n\t\t\tc[++size].x=s[i]-r[i]*(r[i+1]-r[i])\/d;\n\t\t\tc[size].y=sqrt(sqr(r[i])-sqr(c[size].x-s[i]));\n\t\t\tc[size].p=s[i+1]-r[i+1]*(r[i+1]-r[i])\/d;\n\t\t\tc[size].q=sqrt(sqr(r[i+1])-sqr(c[size].p-s[i+1]));\n\t\t}\n\t}\n\tr1=max(r1,s[n]);\n\tprintf(&quot;%.2lf&quot;,2*rsimpson(l1,r1,0,f((l1+r1)\/2),0));\n\treturn 0;\n}<\/pre>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>1502: [NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811 Time Limit:&nbsp;5 Sec&nbsp;&nbsp; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[46],"class_list":["post-353","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-simpson_integration"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>BZOJ 1502([NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811-Simpson\u79ef\u5206) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=353\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"BZOJ 1502([NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811-Simpson\u79ef\u5206) - nike0good\" \/>\n<meta property=\"og:description\" content=\"1502: [NOI2005]\u6708\u4e0b\u67e0\u6aac\u6811 Time Limit:&nbsp;5 Sec&nbsp;&nbsp; [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/nike0good.com\/?p=353\" \/>\n<meta property=\"og:site_name\" content=\"nike0good\" \/>\n<meta property=\"article:published_time\" content=\"2013-03-16T00:39:00+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/nike0good.jp1.rpvhost.net\/wp-content\/uploads\/csdn\/other_site\/img_my_1363393438_6587.png\" \/>\n<meta name=\"author\" content=\"nike0good\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"nike0good\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=353#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/nike0good.com\\\/?p=353\"},\"author\":{\"name\":\"nike0good\",\"@id\":\"https:\\\/\\\/nike0good.com\\\/#\\\/schema\\\/person\\\/4defa38da89de87e400861e73396baad\"},\"headline\":\"BZOJ 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