{"id":948,"date":"2019-10-12T21:19:30","date_gmt":"2019-10-12T13:19:30","guid":{"rendered":"http:\/\/SmokeyDays.top\/wordpress\/?p=948"},"modified":"2019-10-12T21:30:35","modified_gmt":"2019-10-12T13:30:35","slug":"lp4027-noi2007-%e8%b4%a7%e5%b8%81%e5%85%91%e6%8d%a2","status":"publish","type":"post","link":"http:\/\/SmokeyDays.top\/wordpress\/2019\/10\/12\/lp4027-noi2007-%e8%b4%a7%e5%b8%81%e5%85%91%e6%8d%a2\/","title":{"rendered":"lp4027 NOI2007 \u8d27\u5e01\u5151\u6362"},"content":{"rendered":"\n

\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u6574\u4e2a\u884c\u4e3a\u4e00\u5b9a\u80fd\u88ab\u62c6\u5206\u4e3a\u5168\u4e70\u548c\u5168\u5356\u3002
\u7565\u5fae\u601d\u8003\u4e00\u4e0b\u5c31\u53ef\u4ee5\u8bc1\u660e\u8fd9\u4e2a\u5b9a\u7406\u3002\u5018\u82e5\u5148\u90e8\u5206\u4e70\u518d\u90e8\u5206\u4e70\uff0c\u518d\u5168\u5356\uff0c\u663e\u7136\u4e0d\u662f\u4f18\u7684\u3002\u56e0\u4e3a\u6211\u4eec\u603b\u53ef\u4ee5\u627e\u5230\u66f4\u4f18\u7684\u90e8\u5206\uff0c\u4f7f\u5f97\u5168\u4e70\u518d\u5168\u5356\u66f4\u4f18\uff1b\u540c\u7406\uff0c\u90e8\u5206\u5356\u518d\u90e8\u5206\u5356\u4e5f\u4e00\u5b9a\u4e0d\u4f1a\u66f4\u4f18\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5238\u662f\u5fc5\u987b\u6309\u6bd4\u4f8b\u5356\u51fa\u7684\u3002 \u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u628a\u6574\u4e2a\u51b3\u7b56\u62c6\u5206\u4e3a\u5f88\u591a\u4e2a\u5168\u4e70\u548c\u5168\u5356\u4ea4\u66ff\u51fa\u73b0\u7684\u70b9\uff0c\u7136\u540e\u5bf9\u8fd9\u4e9b\u70b9\u8fdb\u884cDP\u3002
\u6211\u4eec\u4e0d\u59a8\u8bb0\\(f_{i}\\)\u8868\u793a\u7b2ci\u4e2a\u70b9\u4e3a\u6b62\u6700\u591a\u7684\u94b1\u6570\u3002\u5018\u82e5\u7b2ci\u5929\u82b1\u4e86x\u6765\u8d2d\u4e70A\uff0c\u90a3\u4e48\u8d2d\u4e70\u7684\u6570\u91cf\u662fx\/A\uff0c\u90a3\u4e48\u8d2d\u4e70\u4e86B\u7684\u6570\u91cf\u662fx\/(A*Rate)\uff0c\u82b1\u8d39\u7684\u94b1\u662fxB\/(A*Rate)\u3002\u53ef\u4ee5\u89e3\u5f97\uff1a
$$x=\\frac{A*Rate*f_i}{RateA+B}$$
\u4e5f\u5c31\u662f\u8bf4\uff0c\u8d2d\u4e70\u7684A\u548cB\u5238\u7684\u6570\u91cf\u5206\u522b\u662f\uff1a
$$\\frac{Rate*f_i}{RateA+B},\\frac{f_i}{RateA+B}$$
\u90a3\u4e48\uff0c\u6211\u4eec\u4ecej\u8f6c\u79fb\u5230i\u7684\u65b9\u7a0b\u662f\uff1a
$$f_j=Max(\\frac{A_i*Rate_j*f_j}{Rate_jA_j+B_j}+\\frac{B_i*f_j}{Rate_jA_j+B_j})$$
\u6211\u4eec\u8003\u8651\u8fd9\u4e2a\u8f6c\u79fb\u5f0f\u8981\u5982\u4f55\u4f18\u5316\u3002 \u6211\u4eec\u5c1d\u8bd5\u5bf9\u8fd9\u4e2a\u5f0f\u5b50\u4f7f\u7528\u659c\u7387\u4f18\u5316\u3002\u7136\u800c\u4e00\u4e2a\u81f4\u547d\u7684\u95ee\u9898\u662f\uff0c\u659c\u7387\u4f18\u5316\u8981\u6c42\u6211\u4eec\u9700\u8981\u5c06\u65b9\u7a0b\u4e2di\u7684\u90e8\u5206\u548cj\u7684\u90e8\u5206\u72ec\u7acb\u5730\u653e\u5728x,y,k,b\u4e2d\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u8bbe\\(f_j=y\\)\u7684\u8ba1\u5212\u7834\u4ea7\u4e86\u3002 \u6211\u4eec\u4e0d\u59a8\u8bbe\uff1a
$$x=\\frac{Rate_i*f_i}{Rate_iA_i+B_i},y=\\frac{f_i}{Rate_iA_i+B_i}$$
\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a $$f_i=A_ix_j+B_iy_j$$
\u90a3\u4e48\uff0c\u5f53\u524d\u70b9\u4e4b\u524d\u7684\u6240\u6709\u70b9\u6784\u6210\u7684\u5c31\u662f\u5e73\u9762\u4e0a\u7684\u4e00\u4e9b\u70b9\uff0c\u7136\u540e\u6211\u4eec\u8981\u7528\u8fd9\u6761\u76f4\u7ebf\u53bb\u5207\u8fd9\u4e9b\u70b9\uff0c\u627e\u5230\u622a\u8ddd\u6700\u5927\u7684\u90a3\u4e2a\u3002
\u901a\u8fc7\u8fd9\u4e2a\u659c\u7387\u4f18\u5316\uff0c\u6211\u4eec\u628a\u95ee\u9898\u5982\u4e0b\u8f6c\u6362\uff1a\u6211\u4eec\u6709\u4e00\u4e2a\u4ec5\u5305\u542b\u7b2c\u4e00\u8c61\u9650\u7684\u5e73\u9762\uff0c\u6709\\(10^5\\)\u4e2a\u64cd\u4f5c\uff0c\u6bcf\u4e2a\u64cd\u4f5c\u53ef\u80fd\u662f\u52a0\u5165\u4e00\u4e2a\u70b9\uff0c\u6216\u67e5\u8be2\u300c\u7ecf\u8fc7\u4efb\u610f\u4e00\u70b9\u7684\u7ed9\u5b9a\u659c\u7387\u7684\u76f4\u7ebf\u7684\u6700\u5927\u622a\u8ddd\u300d\u3002 \u770b\u8d77\u6765\u8fd9\u4f3c\u4e4e\u9700\u8981\u53ef\u6301\u4e45\u5316\u51f8\u5305\u6216\u8005\u4e4b\u7c7b\u7684\u590d\u6742\u64cd\u4f5c\u3002\u4f46\u4ed4\u7ec6\u89c2\u5bdf\u6211\u4eec\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\u53ef\u79bb\u7ebf\u7684\u64cd\u4f5c\u3002
\u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u65f6\u95f4\u5206\u6cbb\uff0c\u7136\u540e\u5de6\u534a\u90e8\u5206\u5bf9x\u5750\u6807\u6392\u5e8f\u2014\u2014\u8fd9\u662f\u4e3a\u4e86\u7ef4\u62a4\u51f8\u5305\uff1b\u5bf9\u53f3\u534a\u90e8\u5206\u6309\u7167\u659c\u7387\u4ece\u5927\u5f80\u5c0f\u6392\u5e8f\u3002\u90a3\u4e48\u5bf9\u4e8e\u65b0\u52a0\u8fdb\u6765\u7684\u6bcf\u4e00\u4e2a\u76f4\u7ebf\uff0c\u90fd\u53ea\u6709\u53ef\u80fd\u627e\u5230\u51f8\u5305\u7684\u4e0b\u4e00\u4e2a\u70b9\u3002\u7528\u5355\u8c03\u6808\u5373\u53ef\u3002 \u56f4\u51f8\u58f3\u7684\u590d\u6742\u5ea6\u662fO(n)\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u66b4\u529b\u91cd\u6784\u3002\u7136\u540e\u53ef\u4ee5\u4e00\u8fb9\u5206\u6cbb\u4e00\u8fb9\u6392\u5e8f\u3002 \u590d\u6742\u5ea6O(nlogn)
\u6ce8\u610f\uff1a\u8981\u5224\u4e00\u4e0b\u5206\u6bcd\u4e0d\u80fd\u7b49\u4e8e\u6781\u5c0f\u6570\uff0c\u5426\u5219\u53ef\u80fd\u4f1a\u6302\u3002<\/p>\n\n\n\n

\u7565\u5fae\u601d\u8003\u4e00\u4e0b\u5c31\u53ef\u4ee5\u8bc1\u660e\u8fd9\u4e2a\u5b9a\u7406\u3002\u5018\u82e5\u5148\u90e8\u5206\u4e70\u518d\u90e8\u5206\u4e70\uff0c\u518d\u5168\u5356\uff0c\u663e\u7136\u4e0d\u662f\u4f18\u7684\u3002\u56e0\u4e3a\u6211\u4eec\u603b\u53ef\u4ee5\u627e\u5230\u66f4\u4f18\u7684\u90e8\u5206\uff0c\u4f7f\u5f97\u5168\u4e70\u518d\u5168\u5356\u66f4\u4f18\uff1b\u540c\u7406\uff0c\u90e8\u5206\u5356\u518d\u90e8\u5206\u5356\u4e5f\u4e00\u5b9a\u4e0d\u4f1a\u66f4\u4f18\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5238\u662f\u5fc5\u987b\u6309\u6bd4\u4f8b\u5356\u51fa\u7684\u3002 \u4e8e\u662f\uff0c\u6211\u4eec\u5c31\u628a\u6574\u4e2a\u51b3\u7b56\u62c6\u5206\u4e3a\u5f88\u591a\u4e2a\u5168\u4e70\u548c\u5168\u5356\u4ea4\u66ff\u51fa\u73b0\u7684\u70b9\uff0c\u7136\u540e\u5bf9\u8fd9\u4e9b\u70b9\u8fdb\u884cDP\u3002 \u6211\u4eec\u4e0d\u59a8\u8bb0\\(f_{i}\\)\u8868\u793a\u7b2ci\u4e2a\u70b9\u4e3a\u6b62\u6700\u591a\u7684\u94b1\u6570\u3002\u5018\u82e5\u7b2ci\u5929\u82b1\u4e86x\u6765\u8d2d\u4e70A\uff0c\u90a3\u4e48\u8d2d\u4e70\u7684\u6570\u91cf\u662fx\/A\uff0c\u90a3\u4e48\u8d2d\u4e70\u4e86B\u7684\u6570\u91cf\u662fx\/(A*Rate)\uff0c\u82b1\u8d39\u7684\u94b1\u662fxB\/(A*Rate)\u3002\u53ef\u4ee5\u89e3\u5f97\uff1a $$x=\\frac{A*Rate*f_i}{RateA+B}$$ \u4e5f\u5c31\u662f\u8bf4\uff0c\u8d2d\u4e70\u7684A\u548cB\u5238\u7684\u6570\u91cf\u5206\u522b\u662f\uff1a $$\\frac{Rate*f_i}{RateA+B},\\frac{f_i}{RateA+B}$$ \u90a3\u4e48\uff0c\u6211\u4eec\u4ecej\u8f6c\u79fb\u5230i\u7684\u65b9\u7a0b\u662f\uff1a $$f_j=Max(\\frac{A_i*Rate_j*f_j}{Rate_jA_j+B_j}+\\frac{B_i*f_j}{Rate_jA_j+B_j})$$ \u6211\u4eec\u8003\u8651\u8fd9\u4e2a\u8f6c\u79fb\u5f0f\u8981\u5982\u4f55\u4f18\u5316\u3002 \u6211\u4eec\u5c1d\u8bd5\u5bf9\u8fd9\u4e2a\u5f0f\u5b50\u4f7f\u7528\u659c\u7387\u4f18\u5316\u3002\u7136\u800c\u4e00\u4e2a\u81f4\u547d\u7684\u95ee\u9898\u662f\uff0c\u659c\u7387\u4f18\u5316\u8981\u6c42\u6211\u4eec\u9700\u8981\u5c06\u65b9\u7a0b\u4e2di\u7684\u90e8\u5206\u548cj\u7684\u90e8\u5206\u72ec\u7acb\u5730\u653e\u5728x,y,k,b\u4e2d\uff0c\u8fd9\u4f7f\u5f97\u6211\u4eec\u8bbe\\(f_j=y\\)\u7684\u8ba1\u5212\u7834\u4ea7\u4e86\u3002 \u6211\u4eec\u4e0d\u59a8\u8bbe\uff1a $$x=\\frac{Rate_i*f_i}{Rate_iA_i+B_i},y=\\frac{f_i}{Rate_iA_i+B_i}$$ \u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\uff1a $$f_i=A_ix_j+B_iy_j$$ \u90a3\u4e48\uff0c\u5f53\u524d\u70b9\u4e4b\u524d\u7684\u6240\u6709\u70b9\u6784\u6210\u7684\u5c31\u662f\u5e73\u9762\u4e0a\u7684\u4e00\u4e9b\u70b9\uff0c\u7136\u540e\u6211\u4eec\u8981\u7528\u8fd9\u6761\u76f4\u7ebf\u53bb\u5207\u8fd9\u4e9b\u70b9\uff0c\u627e\u5230\u622a\u8ddd\u6700\u5927\u7684\u90a3\u4e2a\u3002 \u901a\u8fc7\u8fd9\u4e2a\u659c\u7387\u4f18\u5316\uff0c\u6211\u4eec\u628a\u95ee\u9898\u5982\u4e0b\u8f6c\u6362\uff1a\u6211\u4eec\u6709\u4e00\u4e2a\u4ec5\u5305\u542b\u7b2c\u4e00\u8c61\u9650\u7684\u5e73\u9762\uff0c\u6709\\(10^5\\)\u4e2a\u64cd\u4f5c\uff0c\u6bcf\u4e2a\u64cd\u4f5c\u53ef\u80fd\u662f\u52a0\u5165\u4e00\u4e2a\u70b9\uff0c\u6216\u67e5\u8be2\u300c\u7ecf\u8fc7\u4efb\u610f\u4e00\u70b9\u7684\u7ed9\u5b9a\u659c\u7387\u7684\u76f4\u7ebf\u7684\u6700\u5927\u622a\u8ddd\u300d\u3002 \u770b\u8d77\u6765\u8fd9\u4f3c\u4e4e\u9700\u8981\u53ef\u6301\u4e45\u5316\u51f8\u5305\u6216\u8005\u4e4b\u7c7b\u7684\u590d\u6742\u64cd\u4f5c\u3002\u4f46\u4ed4\u7ec6\u89c2\u5bdf\u6211\u4eec\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\u53ef\u79bb\u7ebf\u7684\u64cd\u4f5c\u3002 \u56e0\u6b64\uff0c\u6211\u4eec\u5bf9\u65f6\u95f4\u5206\u6cbb\uff0c\u7136\u540e\u5de6\u534a\u90e8\u5206\u5bf9x\u5750\u6807\u6392\u5e8f\u2014\u2014\u8fd9\u662f\u4e3a\u4e86\u7ef4\u62a4\u51f8\u5305\uff1b\u5bf9\u53f3\u534a\u90e8\u5206\u6309\u7167\u659c\u7387\u4ece\u5927\u5f80\u5c0f\u6392\u5e8f\u3002\u90a3\u4e48\u5bf9\u4e8e\u65b0\u52a0\u8fdb\u6765\u7684\u6bcf\u4e00\u4e2a\u76f4\u7ebf\uff0c\u90fd\u53ea\u6709\u53ef\u80fd\u627e\u5230\u51f8\u5305\u7684\u4e0b\u4e00\u4e2a\u70b9\u3002\u7528\u5355\u8c03\u6808\u5373\u53ef\u3002 \u56f4\u51f8\u58f3\u7684\u590d\u6742\u5ea6\u662fO(n)\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u66b4\u529b\u91cd\u6784\u3002\u7136\u540e\u53ef\u4ee5\u4e00\u8fb9\u5206\u6cbb\u4e00\u8fb9\u6392\u5e8f\u3002 \u590d\u6742\u5ea6O(nlogn) \u6ce8\u610f\uff1a\u8981\u5224\u4e00\u4e0b\u5206\u6bcd\u4e0d\u80fd\u7b49\u4e8e\u6781\u5c0f\u6570\uff0c\u5426\u5219\u53ef\u80fd\u4f1a\u6302\u3002<\/p>\n\n\n\n

#include<iostream>\n#include<cstdio>\n#include<cstring>\n#include<algorithm>\n#include<queue>\n#include<vector>\n#include<cmath>\nusing namespace std;\n\nconst int N=100005;\nconst double eps=1E-10;\nconst double INF=1E10;\nstruct data{\n\tdouble a;double b;double r;int id;double x;double y;\n}a[N],b[N];\n\/\/\u659c\u7387\u4ece\u5927\u5f80\u5c0f\u6392\u5e8f\u3002 \ninline double cmp(const data &A,const data &B){\n\treturn A.a*B.b>B.a*A.b; \n}\nint n,st[N],tp=0;double m,f[N];\ninline double icpt(int P,double A,double B){\n\/\/\tprintf(\"icpt:%lf\\n\",a[P].x*A+a[P].y*B);\n\treturn a[P].x*A+a[P].y*B; \n}\ninline double slp(int A,int B){\n\tif(fabs(a[A].x-a[B].x)<eps){\n\t\treturn INF;\n\t}\n\treturn (a[A].y-a[B].y)\/(a[A].x-a[B].x);\n}\ninline void mg(int l,int r){\n\tint mid=(l+r)>>1;\n\tint I=l,J=mid+1,tp=l;\n\twhile(I<=mid&&J<=r){\n\t\tif(a[I].x<a[J].x){\n\t\t\tb[tp++]=a[I++];\n\t\t}else{\n\t\t\tb[tp++]=a[J++];\n\t\t}\n\t}\n\twhile(I<=mid){\n\t\tb[tp++]=a[I++];\n\t}\n\twhile(J<=r){\n\t\tb[tp++]=a[J++];\n\t}\n\tfor(int i=l;i<=r;++i){\n\t\ta[i]=b[i];\n\t}\n}\ninline void cdq(int l,int r){\n\tif(l==r){\n\t\tf[l]=max(f[l],f[l-1]);\n\t\ta[l].y=(double)f[l]\/(a[l].r*a[l].a+a[l].b);\n\t\ta[l].x=(double)a[l].r*a[l].y;\n\t\treturn;\n\t}\n\tint mid=(l+r)>>1;\n\tint I=l,J=mid+1;\n\tfor(int i=l;i<=r;++i){\n\t\tif(a[i].id<=mid){\n\t\t\tb[I++]=a[i];\n\t\t}else{\n\t\t\tb[J++]=a[i];\n\t\t}\n\t}\n\tfor(int i=l;i<=r;++i){\n\t\ta[i]=b[i];\n\t}\n\tcdq(l,mid);\n\ttp=0;\n\tfor(int i=l;i<=mid;++i){\n\t\twhile(tp>1&&slp(st[tp],i)+eps>slp(st[tp-1],st[tp])){\n\t\t\t--tp;\n\t\t}\n\t\tst[++tp]=i;\n\t}\n\/\/\tprintf(\"[%d,%d]\\n\",l,r);\n\/\/\tfor(int i=1;i<=tp;++i){\n\/\/\t\tprintf(\"%lf %lf\\n\",a[st[i]].x,a[st[i]].y);\n\/\/\t}\n\tfor(int i=mid+1;i<=r;++i){\n\t\twhile(tp>1&&slp(st[tp],st[tp-1])<=-a[i].a\/a[i].b+eps){\n\t\t\t--tp;\n\t\t}\n\t\tf[a[i].id]=max(f[a[i].id],icpt(st[tp],a[i].a,a[i].b));\n\/\/\t\tprintf(\"%d %lf\\n\",i,a[i].ans); \n\t}\n\tcdq(mid+1,r);\n\tmg(l,r);\n}\nvoid init(){\n\tscanf(\"%d%lf\",&n,&f[0]);\n\tfor(int i=1;i<=n;++i){\n\t\tscanf(\"%lf%lf%lf\",&a[i].a,&a[i].b,&a[i].r);\n\t\ta[i].id=i;\n\t}\n\tstd::sort(a+1,a+1+n,cmp);\n\tcdq(1,n);\n\/\/\tfor(int i=1;i<=n;++i){\n\/\/\t\tprintf(\"%d:%lf,%lf %lf %lf\\n\",a[i].id,a[i].x,a[i].y,-(double)a[i].a\/a[i].b,f[a[i].id]);\n\/\/\t}\n\tprintf(\"%.3lf\\n\",f[n]);\n}\nint main(){\n\tinit();\n\treturn 0;\n}\n\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u6211\u4eec\u89c2\u5bdf\u5230\uff0c\u6574\u4e2a\u884c\u4e3a\u4e00\u5b9a\u80fd\u88ab\u62c6\u5206\u4e3a\u5168\u4e70\u548c\u5168\u5356\u3002 \u7565\u5fae\u601d\u8003\u4e00\u4e0b\u5c31\u53ef\u4ee5\u8bc1\u660e\u8fd9\u4e2a\u5b9a\u7406\u3002\u5018\u82e5\u5148\u90e8\u5206\u4e70\u518d\u90e8\u5206\u4e70\uff0c\u518d\u5168\u5356\uff0c … <\/p>\n
\u7ee7\u7eed\u9605\u8bfb\u201clp4027 NOI2007 \u8d27\u5e01\u5151\u6362\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[50,34,88,6,5],"tags":[],"_links":{"self":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/948"}],"collection":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/comments?post=948"}],"version-history":[{"count":3,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/948\/revisions"}],"predecessor-version":[{"id":951,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/posts\/948\/revisions\/951"}],"wp:attachment":[{"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/media?parent=948"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/categories?post=948"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/SmokeyDays.top\/wordpress\/wp-json\/wp\/v2\/tags?post=948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}