{"id":376,"date":"2013-03-29T14:15:00","date_gmt":"2013-03-29T06:15:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/280"},"modified":"2013-03-29T14:15:00","modified_gmt":"2013-03-29T06:15:00","slug":"bzoj_2732_hnoi2012_archery_-_half-plane_ac","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=376","title":{"rendered":"BZOJ 2732([HNOI2012]\u5c04\u7bad-\u534a\u5e73\u9762\u4ea4)"},"content":{"rendered":"

<\/p>\n

2732: [HNOI2012]\u5c04\u7bad<\/h2>\n

Time Limit: <\/span>10 Sec  Memory Limit: <\/span>128 MB
\nSubmit: <\/span>186  Solved: <\/span>104
\n[Submit<\/a>][Status<\/a>][Discuss<\/a>]<\/center><\/p>\n

Description<\/h2>\n
\n

\u6cab\u6cab\u6700\u8fd1\u5728\u73a9\u4e00\u4e2a\u4e8c\u7ef4\u7684\u5c04\u7bad\u6e38\u620f\uff0c\u5982\u4e0b\u56fe 1 \u6240\u793a\uff0c\u8fd9\u4e2a\u6e38\u620f\u4e2d\u7684 x \u8f74\u5728\u5730\u9762\uff0c\u7b2c\u4e00\u8c61\u9650\u4e2d\u6709\u4e00\u4e9b\u7ad6\u76f4\u7ebf\u6bb5\u4f5c\u4e3a\u9776\u5b50\uff0c\u4efb\u610f\u4e24\u4e2a\u9776\u5b50\u90fd\u6ca1\u6709\u516c\u5171\u90e8\u5206\uff0c\u4e5f\u4e0d\u4f1a\u63a5\u89e6\u5750\u6807\u8f74\u3002\u6cab\u6cab\u63a7\u5236\u4e00\u4e2a\u4f4d\u4e8e(0,0)\u7684\u5f13\u7bad\u624b\uff0c\u53ef\u4ee5\u671d 0 \u81f3 90?\u4e2d\u7684\u4efb\u610f\u89d2\u5ea6\uff08\u4e0d\u5305\u62ec 0\u5ea6\u548c 90\u5ea6\uff09\uff0c\u4ee5\u4efb\u610f\u5927\u5c0f\u7684\u529b\u91cf\u5c04\u51fa\u5e26\u6709\u7a7f\u900f\u80fd\u529b\u7684\u5149\u4e4b\u7bad\u3002\u7531\u4e8e\u6e38\u620f\u4e2d\u6ca1\u6709\u7a7a\u6c14\u963b\u529b\uff0c\u5e76\u4e14\u5149\u4e4b\u7bad\u6ca1\u6709\u7bad\u8eab\uff0c\u7bad\u7684\u8f68\u8ff9\u4f1a\u662f\u4e00\u6761\u6807\u51c6\u7684\u629b\u7269\u7ebf\uff0c\u88ab\u8f68\u8ff9\u7a7f\u8fc7\u7684\u6240\u6709\u9776\u5b50\u90fd\u8ba4\u4e3a\u88ab\u6cab\u6cab\u5c04\u4e2d\u4e86\uff0c\u5305\u62ec\u90a3\u4e9b \u53ea\u6709\u7aef\u70b9\u88ab\u5c04\u4e2d\u7684\u9776\u5b50\u3002\u8fd9\u4e2a\u6e38\u620f\u6709\u591a\u79cd\u6a21\u5f0f\uff0c\u5176\u4e2d\u6cab\u6cab\u6700\u559c\u6b22\u7684\u662f\u95ef\u5173\u6a21\u5f0f\u3002\u5728\u95ef\u5173\u6a21\u5f0f\u4e2d\uff0c\u7b2c\u4e00\u5173\u53ea\u6709\u4e00\u4e2a\u9776
\n \u5b50\uff0c\u5c04\u4e2d\u8fd9\u4e2a\u9776\u5b50\u5373\u53ef\u8fdb\u5165\u7b2c\u4e8c\u5173\uff0c\u8fd9\u65f6\u5728\u7b2c\u4e00\u5173\u7684\u57fa\u7840\u4e0a\u4f1a\u51fa\u73b0\u53e6\u5916\u4e00\u4e2a\u9776\u5b50\uff0c\u82e5\u80fd\u591f\u4e00\u7bad \u53cc\u96d5\u5c04\u4e2d\u8fd9\u4e24\u4e2a\u9776\u5b50\u4fbf\u53ef\u8fdb\u5165\u7b2c\u4e09\u5173\uff0c\u8fd9\u65f6\u4f1a\u51fa\u73b0\u7b2c\u4e09\u4e2a\u9776\u5b50\u3002\u4f9d\u6b64\u7c7b\u63a8\uff0c\u6bcf\u8fc7\u4e00\u5173\u90fd\u4f1a\u65b0\u51fa \u73b0\u4e00\u4e2a\u9776\u5b50\uff0c\u5728\u7b2c K \u5173\u5fc5\u987b\u4e00\u7bad\u5c04\u4e2d\u524d K \u5173\u51fa\u73b0\u7684\u6240\u6709 K \u4e2a\u9776\u5b50\u624d\u80fd\u8fdb\u5165\u7b2c K+1 \u5173\uff0c\u5426\u5219\u6e38\u620f \u7ed3\u675f\u3002\u6cab\u6cab\u82b1\u4e86\u5f88\u591a\u65f6\u95f4\u5728\u8fd9\u4e2a\u6e38\u620f\u4e0a\uff0c\u5374\u6700\u591a\u53ea\u80fd\u73a9\u5230\u7b2c\u4e03\u5173\u201c\u4e03\u661f\u8fde\u73e0\u201d\uff0c\u8fd9\u8ba9\u5979\u975e\u5e38\u56f0\u60d1\u3002 \u4e8e\u662f\u5979\u8bbe\u6cd5\u83b7\u5f97\u4e86\u6bcf\u4e00\u5173\u51fa\u73b0\u7684\u9776\u5b50\u7684\u4f4d\u7f6e\uff0c\u60f3\u8ba9\u4f60\u544a\u8bc9\u5979\uff0c\u6700\u591a\u80fd\u901a\u8fc7\u591a\u5c11\u5173<\/span><\/p>\n<\/div>\n

Input<\/h2>\n
\n

\u8f93\u5165\u6587\u4ef6\u7b2c\u4e00\u884c\u662f\u4e00\u4e2a\u6b63\u6574\u6570N\uff0c\u8868\u793a\u4e00\u5171\u6709N\u5173\u3002\u63a5\u4e0b\u6765\u6709N\u884c\uff0c\u7b2ci+1\u884c\u662f\u7528\u7a7a格\u9694\u5f00\u7684\u4e09\u4e2a\u6b63\u6574\u6570xi\uff0cyi1\uff0cyi2(yi1<yi2 )\uff0c\u8868\u793a\u7b2ci\u5173\u51fa\u73b0\u7684\u9776\u5b50\u7684\u6a2a\u5750\u6807\u662fxi\uff0c\u7eb5\u5750\u6807\u7684\u8303\u56f4\u662f\u4eceyi1\u5230yi2 \u3002 
\n \u8f93\u5165\u4fdd\u8bc130%\u7684\u6570\u636e\u6ee1\u8db3N\u2264100\uff0c50%\u7684\u6570\u636e\u6ee1\u8db3N\u22645000\uff0c100%\u7684\u6570\u636e\u6ee1\u8db3N\u2264100000\u4e14\u7ed9 \u51fa\u7684\u6240\u6709\u5750\u6807\u4e0d\u8d85\u8fc7109 \u3002 
\n <\/span><\/p>\n<\/div>\n

Output<\/h2>\n
\n

\n\u4ec5\u5305\u542b\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a\u6700\u591a\u7684\u901a\u5173\u6570\u3002 <\/span>\n<\/p>\n<\/div>\n

Sample Input<\/h2>\n
\n5
\n

\n2 8 12

\n5 4 5

\n3 8 10

\n6 2 3

\n1 3 7

\n<\/span><\/div>\n

Sample Output<\/h2>\n
\n3

\n<\/span><\/div>\n

HINT<\/h2>\n
\n

\"\"<\/p>\n<\/p>\n<\/div>\n

\n<\/h2>\n
\u5148\u628a\u65b9\u7a0b\u5199\u51fa\u6765\uff0c\u6539\u4e00\u6539\u3002<\/span><\/div>\n
\u7136\u540e\u5728\u5750\u6807\u7cfb\u4e0a\u505a\u534a<\/span>\u5e73\u9762\u4ea4\u3002<\/span><\/div>\n
<\/span><\/p>\n
#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<cmath>\n#include<iostream>\n#include<algorithm>\n#include<functional>\n#define MAXN (100000+10)\n#define MAXCi (1000000000)\n#define eps 1e-15\n#define For(i,n) for(int i=1;i<=n;i++)\nusing namespace std;\nint n;\nstruct P\n{\n\tdouble x,y;\n\tP(){}\n\tP(double _x,double _y):x(_x),y(_y){}\n}p[MAXN*4];\nstruct V\n{\n\tdouble x,y;\n\tV(){}\n\tV(double _x,double _y):x(_x),y(_y){}\n\tV(P a,P b):x(b.x-a.x),y(b.y-a.y){}\n\tfriend double operator*(V a,V b){return a.x*b.y-a.y*b.x;}\n\tfriend V operator*(double a,V b){return V(a*b.x,a*b.y);}\n\tfriend P operator+(P a,V b){return P(a.x+b.x,a.y+b.y);}\n};\nstruct line\n{\n\tP p;\n\tV v;\n\tdouble ang;\n\tint i;\n\tline(){}\n\tline(double _x,double _y,double _a,double _b,int _i):p(P(_x,_y)),v(V(_a,_b)),i(_i){ang=atan2(v.y,v.x);}\n\tbool onleft(P A)\n\t{\n\t\treturn v*V(p,A)>=0;\n\t}\n\tbool operator<(const line& l) const\n\t{\n\t\treturn ang<l.ang;\n\t}\n\tfriend P getinter(line a,line b)\n\t{\n\t\t\/*\n\t\tV u=V(a.p,b.p);\n\t\tdouble t=(a.v*u)\/(b.v*a.v);\n\t\treturn b.p+(t*b.v);\n\t\tdouble s1=V(a.p,b.p+b.v)*a.v;\n\t\tdouble s2=a.v*V(a.p,b.p);\n\t\treturn b.p+(-s1\/(s1+s2))*b.v;\n\/\/\t\tV u=V(a.p,b.p);\n\t\t*\/\n\t\tV u=V(b.p,a.p);\n\t\tdouble t=(b.v*u)\/(a.v*b.v);\n\t\treturn a.p+t*a.v;\n\n\t}\n}que[MAXN*10],q[MAXN*4];\nint size=0;\nint half_intersection(line *l,int n)\n{\n\tint first=1,last=0;\n\tfor (int i=1;i<=size;i++)\n\t{\n\t\tif (l[i].i>n) continue;\n\t\tif (!last) {q[++last]=l[i];continue;}\n\t\twhile (first<last&&!l[i].onleft(p[last-1])) last--;\n\t\twhile (first<last&&!l[i].onleft(p[first])) first++;\n\t\tif (fabs(q[last].v*l[i].v)<=eps)\n\t\t{\n\t\t\tif (q[last].onleft(l[i].p)) q[last]=l[i];\n\t\t}\n\t\telse q[++last]=l[i];\n\t\tif (first<last) p[last-1]=getinter(q[last-1],q[last]);\n\t}\n\tbool flag=1;\n\twhile (flag)\n\t{\n\t\tflag=0;\n\t\twhile (first<last&&!q[first].onleft(p[last-1])) last--,flag=1;\n\t\twhile (first<last&&!q[last].onleft(p[first])) first++,flag=1;\n\t}\n\t\/*\n\tp[last]=getinter(q[last],q[first]);\n\tfor (int i=first;i<=last;i++)\n\t\tprintf("%lf %lfn",p[i].x,p[i].y);\n\tcout<<endl;\n\t*\/\n\treturn last-first>1;\n}\nvoid pri(line a,line b)\n{\n\tP c=getinter(a,b);\n\tprintf("%.lf %.lfn",c.x,c.y);\n}\nint main()\n{\n\tfreopen("archery.in","r",stdin);\n\tfreopen("archery.out","w",stdout);\n\tcin>>n;\n\tque[1]=line(0,0,0,1,0);\n\tque[2]=line(-1,0,1,0,0);\n\tque[3]=line(0,MAXCi,-1,0,0);\n\tque[4]=line(-MAXCi,MAXCi,0,-1,0);size=4;\n\/\/\tpri(que[3],que[4]);\n\/\/\tsize=0;\n\tfor (int i=1;i<=n;i++)\n\t{\n\t\tdouble x,l,r;\n\t\tscanf("%lf%lf%lf",&x,&l,&r);\n\t\tque[++size]=line(0,l\/x,1\/x,-1,i);\n\t\tque[++size]=line(0,r\/x,-1\/x,1,i);\n\t}\n\tsort(que+1,que+1+size);\n\/\/\tcout<<size<<endl;\n\/\/\tfor (int i=l;i<=r;i++) cout<<halsf_intersection(que,i)<<' ';\n\/\/\tcout<<half_intersection(que,50001);\n\tint l=0,r=n,Mid=0;\n\twhile (l<=r)\n\t{\n\t\tint mid=(l+r)>>1;\n\t\tif (half_intersection(que,mid)) {Mid=mid;l=mid+1;}else r=mid-1;\n\t}\n\tcout<<Mid<<endl;\n\treturn 0;\n}<\/pre>\n<\/div>\n
\n<\/div>\n","protected":false},"excerpt":{"rendered":"
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