{"id":101179,"date":"2026-09-06T11:09:09","date_gmt":"2026-09-06T03:09:09","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/101179.html"},"modified":"2026-09-06T11:09:09","modified_gmt":"2026-09-06T03:09:09","slug":"uva-849-radar-tracking","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/101179.html","title":{"rendered":"UVa 849 Radar Tracking"},"content":{"rendered":"

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u5730\u9762\u96f7\u8fbe\u5929\u7ebf\u5728\u6c34\u5e73\u9762\u5185\u5300\u901f\u65cb\u8f6c，\u5468\u671f\u4e3a 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u79d2\u3002\u5929\u7ebf\u671d\u5411\u7269\u4f53\u65f6，\u6d4b\u91cf\u5176\u8ddd\u79bb\u5e76\u663e\u793a\u4e3a\u5c4f\u5e55\u4e0a\u7684\u4eae\u70b9\u3002\u4eae\u70b9\u5230\u5c4f\u5e55\u4e2d\u5fc3\u7684\u8ddd\u79bb\u4e0e\u7269\u4f53\u5230\u5929\u7ebf\u7684\u6c34\u5e73\u8ddd\u79bb\u6210\u6b63\u6bd4，\u4eae\u70b9\u65b9\u4f4d\u89d2\u8868\u793a\u7269\u4f53\u7684\u65b9\u5411（\u6b63\u5317\u4e3a 0\u22180^\\\\circ<\/span><\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u987a\u65f6\u9488\u4e3a\u6b63）\u3002\u5929\u7ebf\u987a\u65f6\u9488\u65cb\u8f6c：t=0t=0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411\u6b63\u5317，t=0.5t=0.5<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411\u6b63\u4e1c，t=1.0t=1.0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1.0<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411\u6b63\u5357，t=1.5t=1.5<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1.5<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411\u6b63\u897f，t=2.0t=2.0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>2.0<\/span><\/span><\/span><\/span><\/span> \u65f6\u56de\u5230\u6b63\u5317\u3002\u5df2\u77e5\u67d0\u7269\u4f53\u505a\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8，\u4e14\u7ed9\u51fa\u4e24\u6b21\u8fde\u7eed\u89c2\u6d4b\u5230\u7684\u89d2\u5ea6 a1,a2a_1, a_2<\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u8ddd\u79bb d1,d2d_1, d_2<\/span><\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8981\u6c42\u8ba1\u7b97\u4e0b\u4e00\u6b21\u89c2\u6d4b\u65f6，\u8be5\u4eae\u70b9\u53ef\u80fd\u51fa\u73b0\u7684\u4f4d\u7f6e（\u89d2\u5ea6\u548c\u8ddd\u79bb）\u3002\u82e5\u6709\u591a\u4e2a\u53ef\u80fd\u4f4d\u7f6e，\u6309\u89d2\u5ea6\u5347\u5e8f\u3001\u8ddd\u79bb\u964d\u5e8f\u8f93\u51fa\u6240\u6709\u89e3，\u4fdd\u7559\u4e24\u4f4d\u5c0f\u6570\u3002<\/p>\n

\u8f93\u5165\u683c\u5f0f<\/h3>\n

\u8f93\u5165\u5305\u542b\u82e5\u5e72\u884c，\u6bcf\u884c\u56db\u4e2a\u5b9e\u6570 a1,d1,a2,d2a_1, d_1, a_2, d_2<\/span><\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5206\u522b\u8868\u793a\u7b2c\u4e00\u6b21\u548c\u7b2c\u4e8c\u6b21\u89c2\u6d4b\u7684\u89d2\u5ea6（\u5ea6）\u548c\u8ddd\u79bb\u3002<\/p>\n

\u8f93\u51fa\u683c\u5f0f<\/h3>\n

\u5bf9\u4e8e\u6bcf\u884c\u8f93\u5165，\u8f93\u51fa\u4e00\u884c，\u5305\u542b\u6240\u6709\u53ef\u80fd\u89e3，\u6bcf\u4e2a\u89e3\u4e3a\u4e24\u4e2a\u5b9e\u6570（\u89d2\u5ea6\u548c\u8ddd\u79bb），\u6309\u89d2\u5ea6\u5347\u5e8f\u3001\u8ddd\u79bb\u964d\u5e8f\u6392\u5217，\u4fdd\u7559\u4e24\u4f4d\u5c0f\u6570\u3002\u89e3\u4e4b\u95f4\u7528\u7a7a\u683c\u5206\u9694\u3002<\/p>\n

\u6837\u4f8b\u8f93\u5165<\/h3>\n

90.0 100.0 90.0 110.0
\n90.0 100.0 270.0 10.0
\n90.0 100.0 180.0 50.0<\/p>\n

\u6837\u4f8b\u8f93\u51fa<\/h3>\n

90.0 120.0
\n270.0 230.0
\n270.0 83.33 199.93 64.96 223.39 130.49<\/p>\n

\u9898\u76ee\u5206\u6790<\/h3>\n

\u96f7\u8fbe\u5728 t1=0t_1=0<\/span><\/span>t<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u89c2\u6d4b\u5230\u7269\u4f53\u4f4d\u7f6e P1P_1<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u6781\u5750\u6807 (a1,d1)(a_1, d_1)<\/span><\/span>(<\/span>a<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>），\u5728 t2=1t_2=1<\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u79d2\u540e\u89c2\u6d4b\u5230 P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（(a2,d2)(a_2, d_2)<\/span><\/span>(<\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>）\u3002\u5929\u7ebf\u5728 t=0t=0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411 0\u22180^\\\\circ<\/span><\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，t=1t=1<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6\u6307\u5411 180\u2218180^\\\\circ<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，t=2t=2<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6\u56de\u5230 0\u22180^\\\\circ<\/span><\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4e0b\u4e00\u6b21\u89c2\u6d4b\u53d1\u751f\u5728 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u79d2（\u5929\u7ebf\u6307\u5411 540\u2218\u2261180\u2218540^\\\\circ \\\\equiv 180^\\\\circ<\/span><\/span>54<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2261<\/span><\/span><\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u3002\u7269\u4f53\u505a\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8，\u56e0\u6b64 P1,P2,P3P_1, P_2, P_3<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5171\u7ebf\u4e14\u7b49\u8ddd\u3002\u4f46 t=1t=1<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5230 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u7684\u65f6\u95f4\u95f4\u9694\u662f 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u79d2，\u7b49\u4e8e t=0t=0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u5230 t=1t=1<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u95f4\u9694\u7684\u4e24\u500d，\u56e0\u6b64 P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u76f4\u7ebf P1P2P_1P_2<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0a，\u4e14 P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5230 P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u8ddd\u79bb\u7b49\u4e8e P1P_1<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5230 P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8ddd\u79bb\u7684\u4e24\u500d\u3002<\/p>\n

\u7136\u800c，\u89c2\u6d4b\u89d2\u5ea6 aia_i<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u5728\u5929\u7ebf\u6307\u5411\u8be5\u65b9\u5411\u65f6\u5f97\u5230\u7684，\u56e0\u6b64 PiP_i<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u4f4d\u4e8e\u89d2\u5ea6 aia_i<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5c04\u7ebf\u4e0a\u3002\u7ed9\u5b9a P1P_1<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6781\u5750\u6807，\u53ef\u786e\u5b9a\u5176\u76f4\u89d2\u5750\u6807\u3002\u7269\u4f53\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8\u610f\u5473\u7740 P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5750\u6807\u53ef\u7531 P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c\u901f\u5ea6\u5411\u91cf\u8ba1\u7b97\u5f97\u51fa\u3002\u901f\u5ea6\u5411\u91cf\u7531 P2\u2212P1P_2 – P_1<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u786e\u5b9a（\u56e0\u4e3a t=0t=0<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u5230 t=1t=1<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>），\u4f46\u65f6\u95f4\u95f4\u9694\u4e3a 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u79d2，\u800c t=2t=2<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u5230 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u95f4\u9694\u4e5f\u662f 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u79d2，\u6240\u4ee5 P3=P2+(P2\u2212P1)=2P2\u2212P1P_3 = P_2 + (P_2 – P_1) = 2P_2 – P_1<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4f46\u5929\u7ebf\u5728 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u6307\u5411\u89d2\u5ea6\u4e3a 540\u2218\u2261180\u2218540^\\\\circ \\\\equiv 180^\\\\circ<\/span><\/span>54<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2261<\/span><\/span><\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u56e0\u6b64 P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u4f4d\u4e8e a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5c04\u7ebf\u4e0a，\u5176\u4e2d a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u6781\u89d2\u3002\u4f46\u9898\u76ee\u8981\u6c42\u7684\u662f\u201c\u4e0b\u4e00\u6b21\u89c2\u6d4b\u65f6\u4eae\u70b9\u53ef\u80fd\u51fa\u73b0\u7684\u4f4d\u7f6e\u201d，\u800c\u5929\u7ebf\u5728 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> \u65f6\u89d2\u5ea6\u56fa\u5b9a\u4e3a 180\u2218180^\\\\circ<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u6240\u4ee5 a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u7b49\u4e8e 180\u2218180^\\\\circ<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u6837\u89e3\u662f\u552f\u4e00\u7684\u3002\u4f46\u9898\u76ee\u5141\u8bb8\u591a\u4e2a\u89e3，\u8bf4\u660e\u5bf9\u201c\u4e0b\u4e00\u6b21\u89c2\u6d4b\u201d\u7684\u7406\u89e3\u4e0d\u540c：\u53ef\u80fd\u662f\u5929\u7ebf\u518d\u6b21\u626b\u5230\u7269\u4f53\u6240\u5728\u65b9\u5411\u7684\u90a3\u4e2a\u65f6\u523b，\u800c\u4e0d\u662f\u56fa\u5b9a\u7684 t=3t=3<\/span><\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>\u3002\u5373\u7269\u4f53\u53ef\u80fd\u5728\u4e0d\u540c\u65f6\u523b\u88ab\u5929\u7ebf\u626b\u5230，\u800c\u5929\u7ebf\u626b\u5230\u5b83\u65f6，\u5b83\u4f4d\u4e8e\u67d0\u4e2a\u65b0\u4f4d\u7f6e\u3002\u9898\u76ee\u8981\u6c42\u7684\u662f\u4e0b\u4e00\u6b21\u88ab\u5929\u7ebf\u89c2\u5bdf\u5230\u65f6\u7269\u4f53\u7684\u4f4d\u7f6e，\u800c\u4e0d\u662f\u56fa\u5b9a\u65f6\u523b\u3002\u56e0\u6b64，a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u672a\u77e5\u7684，\u4f46\u5fc5\u987b\u6ee1\u8db3：\u5929\u7ebf\u5728 t3t_3<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65f6\u523b\u6307\u5411\u89d2\u5ea6 a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4e14 t3>t2t_3 > t_2<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u4e14\u7269\u4f53\u5728 t3t_3<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u4f4d\u7f6e P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b63\u597d\u5728\u89d2\u5ea6 a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5c04\u7ebf\u4e0a\u3002\u7531\u4e8e\u5929\u7ebf\u5468\u671f\u4e3a 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u79d2，t3t_3<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u80fd\u7b49\u4e8e 2+t22 + t_2<\/span><\/span>2<\/span><\/span>+<\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6216 4+t24 + t_2<\/span><\/span>4<\/span><\/span>+<\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7b49，\u4f46\u53ea\u8003\u8651\u4e0b\u4e00\u4e2a\u5468\u671f\u5185\u88ab\u626b\u5230\u7684\u60c5\u51b5\u3002<\/p>\n

\u89e3\u9898\u601d\u8def<\/h3>\n

\u5c06\u89c2\u6d4b\u89d2\u5ea6 aia_i<\/span><\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u89c6\u4e3a\u5929\u7ebf\u5728\u8be5\u65f6\u523b\u6307\u5411\u7684\u89d2\u5ea6，t1=0t_1=0<\/span><\/span>t<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，t2=1t_2=1<\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u3002\u7269\u4f53\u4f4d\u7f6e PiP_i<\/span><\/span>P<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u6781\u5750\u6807\u4e0b\u8868\u793a\u4e3a (ai,di)(a_i, d_i)<\/span><\/span>(<\/span>a<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>d<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u7269\u4f53\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8，\u56e0\u6b64 P3=P2+v\u22c5\u0394tP_3 = P_2 + v \\\\cdot \\\\Delta t<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d v=P2\u2212P1v = P_2 – P_1<\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u56e0\u4e3a \u0394t=1\\\\Delta t = 1<\/span><\/span>\u0394<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>），\u4e14 \u0394t=t3\u2212t2\\\\Delta t = t_3 – t_2<\/span><\/span>\u0394<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u5929\u7ebf\u5728 t3t_3<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u65f6\u7684\u89d2\u5ea6\u4e3a 180\u2218+180\u2218\u22c5\u0394t180^\\\\circ + 180^\\\\circ \\\\cdot \\\\Delta t<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span>（\u56e0\u4e3a\u4ece t2=1t_2=1<\/span><\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb，\u53c8\u8fc7\u4e86 \u0394t\\\\Delta t<\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span> \u79d2，\u5929\u7ebf\u89d2\u5ea6\u4ece 180\u2218180^\\\\circ<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u52a0\u4e86 180\u2218\u22c5\u0394t180^\\\\circ \\\\cdot \\\\Delta t<\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span><\/span>）\u3002\u8bbe t3=1+\u03c4t_3 = 1 + \\\\tau<\/span><\/span>t<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span>（\u03c4>0\\\\tau > 0<\/span><\/span>\u03c4<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>），\u5219 a3=180\u2218+180\u2218\u22c5\u03c4a_3 = 180^\\\\circ + 180^\\\\circ \\\\cdot \\\\tau<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>18<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span>（\u6a21 360\u2218360^\\\\circ<\/span><\/span>36<\/span>0<\/span><\/span>\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u3002\u540c\u65f6，P3P_3<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5fc5\u987b\u5728\u89d2\u5ea6 a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5c04\u7ebf\u4e0a，\u5373 arg\u2061(P3)=a3\\\\arg(P_3) = a_3<\/span><\/span>arg<\/span><\/span>(<\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u8fd9\u662f\u4e00\u4e2a\u5173\u4e8e \u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u7684\u65b9\u7a0b\u3002<\/p>\n

\u7531\u4e8e\u7269\u4f53\u5300\u901f\u76f4\u7ebf，P3=P2+\u03c4(P2\u2212P1)P_3 = P_2 + \\\\tau (P_2 – P_1)<\/span><\/span>P<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03c4<\/span>(<\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u5c06\u5176\u8f6c\u6362\u4e3a\u6781\u5750\u6807，\u5e76\u4ee4\u5176\u89d2\u5ea6\u7b49\u4e8e a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5373\u53ef\u6c42\u51fa \u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span>\u3002\u7531\u4e8e\u89d2\u5ea6\u548c\u8ddd\u79bb\u5747\u4e3a\u5b9e\u6570，\u9700\u8981\u4f7f\u7528\u6570\u503c\u6c42\u89e3\u3002\u4ee3\u7801\u4e2d\u4f7f\u7528\u4e8c\u5206\u6cd5\u6c42\u6839\u3002<\/p>\n

\u6839\u636e\u65b9\u5411\u7684\u4e0d\u540c，\u53ef\u80fd\u6709\u4e00\u4e2a\u6216\u591a\u4e2a\u89e3\u3002\u4f8b\u5982，\u82e5 P1P_1<\/span><\/span>P<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c P2P_2<\/span><\/span>P<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u4e14\u65b9\u5411\u76f8\u540c，\u5219\u89e3\u552f\u4e00；\u82e5\u4e0d\u540c，\u5219\u53ef\u80fd\u6709\u591a\u4e2a\u89e3（\u5982\u6837\u4f8b\u7b2c\u4e09\u884c\u8f93\u51fa\u4e09\u4e2a\u89e3）\u3002\u4ee3\u7801\u4e2d\u5904\u7406\u4e86\u56db\u79cd\u60c5\u51b5：\u9006\u65f6\u9488\u65b9\u5411\u3001\u987a\u65f6\u9488\u540c\u4e00\u5468\u671f\u3001\u987a\u65f6\u9488\u4e0b\u4e00\u5468\u671f\u3001\u987a\u65f6\u9488\u4e0b\u4e0b\u5468\u671f\u3002\u901a\u8fc7\u4e8c\u5206\u6cd5\u6c42\u6839\u5f97\u5230 \u03c4\\\\tau<\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span>，\u8fdb\u800c\u8ba1\u7b97 a3a_3<\/span><\/span>a<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c d3d_3<\/span><\/span>d<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4ee3\u7801\u5b9e\u73b0<\/h3>\n

\/\/ Radar Tracking （\u96f7\u8fbe\u8ffd\u8e2a）<\/span>
\n\/\/ PC\/UVa IDs: 111406\/849, Popularity: C, Success rate: low Level: 2<\/span>
\n\/\/ Verdict: Accepted<\/span>
\n\/\/ Submission Date: 2016-04-06<\/span>
\n\/\/ UVa Run Time: 0.000s<\/span>
\n\/\/<\/span>
\n\/\/ \u7248\u6743\u6240\u6709（C）2016，\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span>
\n\/\/<\/span>
\n\/\/ \u4e00\u9053\u4e0d\u662f\u975e\u5e38\u5b8c\u5584\u7684\u9898\u76ee\u3002\u6d4b\u8bd5\u6570\u636e\u5bf9\u5e94\u7684\u8f93\u51fa\u548c\u8bc4\u5224\u7a0b\u5e8f\u53ef\u80fd\u6709\u95ee\u9898，\u4e0d\u8fc7\u597d\u5728\u6d4b\u8bd5\u6570\u636e<\/span>
\n\/\/ \u5e94\u8be5\u6bd4\u8f83\u7b80\u5355，\u4e0d\u7136\u5f88\u96beAC\u3002\u622a\u6b62AC\u65f6，\u53ea\u670922\u4eba\u901a\u8fc7\u3002<\/span><\/p>\n

#<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span><\/p>\n

using<\/span> namespace<\/span> std;<\/span><\/p>\n

const<\/span> double<\/span> PI =<\/span> 3.14159265358979323846<\/span>;<\/span>
\nconst<\/span> int<\/span> COUNTER_CLOCKWISE =<\/span> 0<\/span>,<\/span> CLOCKWISE_SAME_SAME_CYCLE =<\/span> 1<\/span>,<\/span>
\n CLOCKWISE_SAME_NEXT_CYCLE =<\/span> 2<\/span>,<\/span> CLOCKWISE_NEXT_NEXT_CYCLE =<\/span> 3<\/span>;<\/span><\/p>\n

struct<\/span> point<\/span>
\n{<\/span>
\n double<\/span> angle,<\/span> distance;<\/span>
\n}<\/span>;<\/span><\/p>\n

bool<\/span> cmp<\/span>(<\/span>point x,<\/span> point y)<\/span>
\n{<\/span>
\n return<\/span> (<\/span>x.<\/span>angle !=<\/span> y.<\/span>angle)<\/span> ?<\/span> x.<\/span>angle <<\/span> y.<\/span>angle :<\/span> x.<\/span>distance ><\/span> y.<\/span>distance;<\/span>
\n}<\/span><\/p>\n

double<\/span> toRadian<\/span>(<\/span>double<\/span> degree)<\/span>
\n{<\/span>
\n return<\/span> (<\/span>degree \/<\/span> 180.0<\/span>)<\/span> *<\/span> PI;<\/span>
\n}<\/span><\/p>\n

double<\/span> toDegree<\/span>(<\/span>double<\/span> radian)<\/span>
\n{<\/span>
\n return<\/span> (<\/span>radian \/<\/span> PI)<\/span> *<\/span> 180.0<\/span>;<\/span>
\n}<\/span><\/p>\n

\/\/ \u6839\u636e\u4e0d\u540c\u60c5\u51b5\u8fdb\u884c\u8ba1\u7b97\u3002<\/span>
\ndouble<\/span> getValue<\/span>(<\/span>double<\/span> b,<\/span> double<\/span> c,<\/span> double<\/span> A,<\/span> double<\/span> x,<\/span> double<\/span> C,<\/span> int<\/span> category)<\/span>
\n{<\/span>
\n if<\/span> (<\/span>category ==<\/span> COUNTER_CLOCKWISE)<\/span>
\n return<\/span> b *<\/span> sin<\/span>(<\/span>x)<\/span> –<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span> *<\/span> c *<\/span> (<\/span>2.0<\/span> *<\/span> PI –<\/span> x)<\/span> \/<\/span> (<\/span>2.0<\/span> *<\/span> PI –<\/span> C)<\/span>;<\/span>
\n else<\/span> if<\/span> (<\/span>category ==<\/span> CLOCKWISE_SAME_SAME_CYCLE)<\/span>
\n return<\/span> b *<\/span> sin<\/span>(<\/span>x)<\/span> –<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span> *<\/span> c *<\/span> x \/<\/span> C;<\/span>
\n else<\/span> if<\/span> (<\/span>category ==<\/span> CLOCKWISE_SAME_NEXT_CYCLE)<\/span>
\n return<\/span> b *<\/span> sin<\/span>(<\/span>x)<\/span> –<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span> *<\/span> c *<\/span> (<\/span>2.0<\/span> *<\/span> PI +<\/span> x)<\/span> \/<\/span> C;<\/span>
\n else<\/span> if<\/span> (<\/span>category ==<\/span> CLOCKWISE_NEXT_NEXT_CYCLE)<\/span>
\n return<\/span> b *<\/span> sin<\/span>(<\/span>x)<\/span> –<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span> *<\/span> c *<\/span> (<\/span>2.0<\/span> *<\/span> PI +<\/span> x)<\/span> \/<\/span> (<\/span>2.0<\/span> *<\/span> PI +<\/span> C)<\/span>;<\/span>
\n}<\/span><\/p>\n

double<\/span> binarySearch<\/span>(<\/span>double<\/span> b,<\/span> double<\/span> c,<\/span> double<\/span> A,<\/span> double<\/span> C,<\/span> int<\/span> category)<\/span>
\n{<\/span>
\n \/\/ \u6c42\u53d6\u8fb9\u754c\u503c\u3002<\/span>
\n double<\/span> x =<\/span> 0.0<\/span>;<\/span>
\n while<\/span> (<\/span>x <<\/span> A)<\/span>
\n {<\/span>
\n x +=<\/span> (<\/span>0.01<\/span> *<\/span> PI \/<\/span> 180.0<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>getValue<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> x,<\/span> C,<\/span> category)<\/span> ><\/span> 0<\/span>)<\/span>
\n break<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u4e8c\u5206\u67e5\u627e\u3002<\/span>
\n double<\/span> up =<\/span> x –<\/span> (<\/span>0.01<\/span> *<\/span> PI \/<\/span> 180.0<\/span>)<\/span>,<\/span> down =<\/span> x,<\/span> middle;<\/span>
\n while<\/span> (<\/span>fabs<\/span>(<\/span>up –<\/span> down)<\/span> ><\/span> 1e-10<\/span>)<\/span>
\n {<\/span>
\n middle =<\/span> (<\/span>up +<\/span> down)<\/span> \/<\/span> 2.0<\/span>;<\/span>
\n if<\/span> (<\/span>getValue<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> middle,<\/span> C,<\/span> category)<\/span> <<\/span> 0<\/span>)<\/span>
\n up =<\/span> middle;<\/span>
\n else<\/span>
\n down =<\/span> middle;<\/span>
\n }<\/span><\/p>\n

return<\/span> middle;<\/span>
\n}<\/span><\/p>\n

void<\/span> calculate<\/span>(<\/span>point first,<\/span> point second)<\/span>
\n{<\/span>
\n point solutions[<\/span>3<\/span>]<\/span>;<\/span>
\n int<\/span> counter =<\/span> 0<\/span>;<\/span><\/p>\n

\/\/ \u5f53\u524d\u540e\u4e24\u6b21\u7684\u89d2\u5ea6\u76f8\u540c\u65f6，\u8bf4\u660e\u7269\u4f53\u7684\u8fd0\u52a8\u8f68\u8ff9\u662f\u8fc7\u6781\u70b9\u7684\u76f4\u7ebf\u3002<\/span>
\n if<\/span> (<\/span>first.<\/span>angle ==<\/span> second.<\/span>angle)<\/span>
\n {<\/span>
\n \/\/ \u8fdc\u79bb\u6781\u70b9\u65b9\u5411\u3002<\/span>
\n if<\/span> (<\/span>second.<\/span>distance >=<\/span> first.<\/span>distance)<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>first.<\/span>angle,<\/span> second.<\/span>distance +<\/span> (<\/span>second.<\/span>distance –<\/span> first.<\/span>distance)<\/span>}<\/span>;<\/span>
\n \/\/ \u9760\u8fd1\u6781\u70b9\u65b9\u5411，\u53ef\u80fd\u4f1a\u8d8a\u8fc7\u6781\u70b9\u5230\u76f8\u5bf9\u7684\u53e6\u4e00\u4fa7\u3002<\/span>
\n else<\/span>
\n {<\/span>
\n if<\/span> (<\/span>second.<\/span>distance ><\/span> (<\/span>first.<\/span>distance –<\/span> second.<\/span>distance)<\/span>)<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>first.<\/span>angle,<\/span> second.<\/span>distance –<\/span> (<\/span>first.<\/span>distance –<\/span> second.<\/span>distance)<\/span>}<\/span>;<\/span>
\n else<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>
\n (<\/span>(<\/span>first.<\/span>angle >=<\/span> 180.0<\/span>)<\/span> ?<\/span> (<\/span>first.<\/span>angle –<\/span> 180.0<\/span>)<\/span> :<\/span> (<\/span>first.<\/span>angle +<\/span> 180.0<\/span>)<\/span>)<\/span>,<\/span>
\n fabs<\/span>(<\/span>second.<\/span>distance –<\/span> (<\/span>first.<\/span>distance –<\/span> second.<\/span>distance)<\/span>)<\/span>}<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n \/\/ \u5f53\u524d\u540e\u4e24\u6b21\u89c2\u5bdf\u5230\u7684\u4f4d\u7f6e\u6781\u89d2\u76f8\u5dee 180 \u5ea6\u65f6，\u8bf4\u660e\u7269\u4f53\u7684\u8fd0\u52a8\u8f68\u8ff9\u662f\u8fc7\u6781\u70b9\u7684\u76f4\u7ebf\u3002<\/span>
\n else<\/span> if<\/span> (<\/span>fabs<\/span>(<\/span>first.<\/span>angle –<\/span> second.<\/span>angle)<\/span> ==<\/span> 180.0<\/span>)<\/span>
\n {<\/span>
\n \/\/ \u6ce8\u610f\u5728\u7b2c\u4e8c\u6b21\u89c2\u5bdf\u65f6，\u65f6\u95f4\u8fc7\u53bb\u4e86 1 s，\u4f46\u662f\u518d\u4e0b\u4e00\u6b21\u89c2\u5bdf\u65f6，\u5c06\u662f 3s\u3002\u6545\u79fb\u52a8\u8ddd<\/span>
\n \/\/ \u79bb\u8981\u589e\u52a0\u4e00\u500d\u3002\u6709\u4e24\u79cd\u53ef\u80fd\u3002<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>second.<\/span>angle,<\/span> 3<\/span> *<\/span> second.<\/span>distance +<\/span> 2<\/span> *<\/span> first.<\/span>distance}<\/span>;<\/span>
\n if<\/span> (<\/span>fabs<\/span>(<\/span>2<\/span> *<\/span> second.<\/span>distance –<\/span> first.<\/span>distance)<\/span> <<\/span> 1e-8<\/span>)<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>second.<\/span>angle,<\/span> first.<\/span>distance +<\/span> second.<\/span>distance}<\/span>;<\/span>
\n }<\/span>
\n \/\/ \u5f53\u7b2c\u4e00\u6b21\u548c\u7b2c\u4e8c\u6b21\u7684\u6781\u89d2\u4e0d\u540c，\u4e14\u76f8\u5dee\u4e0d\u662f 180 \u5ea6\u65f6，\u7269\u4f53\u7684\u8fd0\u52a8\u8f68\u8ff9\u662f\u4e00\u6761\u4e0d\u8fc7\u6781\u70b9\u7684\u76f4\u7ebf\u3002<\/span>
\n else<\/span>
\n {<\/span>
\n \/\/ \u5f53\u7b2c\u4e8c\u6b21\u89c2\u5bdf\u4f4d\u7f6e\u51fa\u73b0\u5728\u7b2c\u4e00\u6b21\u7684\u9006\u65f6\u9488\u65b9\u5411，\u5219\u8868\u660e\u96f7\u8fbe\u662f\u5728\u4e00\u4e2a\u5468\u671f\u7684\u65f6\u95f4\u5185\u89c2\u5bdf<\/span>
\n \/\/ \u5230\u4e24\u4e2a\u4f4d\u7f6e\u3002\u5219\u7b2c\u4e09\u6b21\u89c2\u5bdf\u65f6\u53ea\u6709\u4e00\u79cd\u53ef\u80fd\u7684\u4f4d\u7f6e\u3002<\/span>
\n double<\/span> C =<\/span> 0.0<\/span>,<\/span> finalAngle,<\/span> finalDistance,<\/span> x;<\/span>
\n double<\/span> angleDiff =<\/span> fabs<\/span>(<\/span>first.<\/span>angle –<\/span> second.<\/span>angle)<\/span>;<\/span>
\n if<\/span> (<\/span>(<\/span>first.<\/span>angle ><\/span> second.<\/span>angle &&<\/span> angleDiff <<\/span> 180.0<\/span>)<\/span> ||<\/span> (<\/span>first.<\/span>angle <<\/span> second.<\/span>angle &&<\/span> angleDiff ><\/span> 180.0<\/span>)<\/span>)<\/span>
\n {<\/span>
\n \/\/ \u4e8c\u5206\u6570\u503c\u6cd5\u6c42\u8fd1\u4f3c\u89e3\u3002<\/span>
\n \/\/ \u5148\u6c42\u51fa\u524d\u540e\u4e24\u6b21\u89c2\u5bdf\u4f4d\u7f6e\u4e4b\u95f4\u7684\u89d2\u5ea6\u5dee，\u8bbe\u4e3a\u89d2 C，\u5bf9\u5e94\u8fb9\u4e3a c\u3002<\/span>
\n if<\/span> (<\/span>first.<\/span>angle <<\/span> second.<\/span>angle &&<\/span> angleDiff ><\/span> 180.0<\/span>)<\/span>
\n C =<\/span> toRadian<\/span>(<\/span>first.<\/span>angle +<\/span> (<\/span>360.0<\/span> –<\/span> second.<\/span>angle)<\/span>)<\/span>;<\/span>
\n else<\/span>
\n C =<\/span> toRadian<\/span>(<\/span>first.<\/span>angle –<\/span> second.<\/span>angle)<\/span>;<\/span><\/p>\n

\/\/ \u4e0d\u5931\u4e00\u822c\u6027，\u8bbe\u7b2c\u4e00\u6b21\u89c2\u5bdf\u7684\u4f4d\u7f6e\u8ddd\u79bb\u4e3a a，\u7b2c\u4e8c\u6b21\u89c2\u5bdf\u7684\u8ddd\u79bb\u4e3a b，\u53ef<\/span>
\n \/\/ \u7531\u4f59\u5f26\u5b9a\u7406\u6c42\u51fa\u8fb9 a \u5bf9\u5e94\u7684\u89d2 A\u3002\u5148\u6c42\u8fb9 c\u3002<\/span>
\n double<\/span> a =<\/span> first.<\/span>distance,<\/span> b =<\/span> second.<\/span>distance;<\/span>
\n double<\/span> c =<\/span> sqrt<\/span>(<\/span>a *<\/span> a +<\/span> b *<\/span> b –<\/span> 2.0<\/span> *<\/span> a *<\/span> b *<\/span> cos<\/span>(<\/span>C)<\/span>)<\/span>;<\/span>
\n double<\/span> A =<\/span> acos<\/span>(<\/span>(<\/span>b *<\/span> b +<\/span> c *<\/span> c –<\/span> a *<\/span> a)<\/span> \/<\/span> (<\/span>2.0<\/span> *<\/span> b *<\/span> c)<\/span>)<\/span>;<\/span><\/p>\n

\/\/ \u627e\u5230\u8fb9\u754c\u503c\u3002<\/span>
\n double<\/span> x =<\/span> A;<\/span>
\n while<\/span> (<\/span>x ><\/span> 0.0<\/span>)<\/span>
\n {<\/span>
\n x -=<\/span> (<\/span>0.01<\/span> *<\/span> PI \/<\/span> 180.0<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>getValue<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> x,<\/span> C,<\/span> COUNTER_CLOCKWISE)<\/span> <<\/span> 0<\/span>)<\/span>
\n break<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/ \u4e8c\u5206\u67e5\u627e\u3002<\/span>
\n double<\/span> up =<\/span> x +<\/span> (<\/span>0.01<\/span> *<\/span> PI \/<\/span> 180.0<\/span>)<\/span>,<\/span> down =<\/span> x,<\/span> middle;<\/span>
\n while<\/span> (<\/span>fabs<\/span>(<\/span>up –<\/span> down)<\/span> ><\/span> 1e-10<\/span>)<\/span>
\n {<\/span>
\n middle =<\/span> (<\/span>up +<\/span> down)<\/span> \/<\/span> 2.0<\/span>;<\/span>
\n if<\/span> (<\/span>getValue<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> middle,<\/span> C,<\/span> COUNTER_CLOCKWISE)<\/span> ><\/span> 0<\/span>)<\/span>
\n up =<\/span> middle;<\/span>
\n else<\/span>
\n down =<\/span> middle;<\/span>
\n }<\/span><\/p>\n

\/\/ \u8ba1\u7b97\u8ddd\u79bb\u3002<\/span>
\n x =<\/span> middle;<\/span>
\n finalAngle =<\/span> second.<\/span>angle –<\/span> toDegree<\/span>(<\/span>x)<\/span>;<\/span>
\n if<\/span> (<\/span>finalAngle <<\/span> 0.0<\/span>)<\/span>
\n finalAngle +=<\/span> 360.0<\/span>;<\/span>
\n finalDistance =<\/span> b *<\/span> sin<\/span>(<\/span>A)<\/span> \/<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span>;<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>finalAngle,<\/span> finalDistance}<\/span>;<\/span>
\n }<\/span>
\n else<\/span>
\n {<\/span>
\n \/\/ \u7b2c\u4e8c\u4e2a\u4f4d\u7f6e\u5728\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u7684\u987a\u65f6\u9488\u65b9\u5411，\u6709\u4e24\u79cd\u53ef\u80fd，\u4e00\u79cd\u662f\u5728\u89c2\u5bdf\u5230\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u540e\u7684<\/span>
\n \/\/ \u540c\u4e00\u4e2a\u626b\u63cf\u5468\u671f\u5185\u89c2\u5bdf\u5230\u7b2c\u4e8c\u4e2a\u4f4d\u7f6e，\u53e6\u5916\u4e00\u79cd\u60c5\u51b5\u662f\u5728\u4e0b\u4e00\u4e2a\u626b\u63cf\u5468\u671f\u5185\u89c2\u5bdf\u5230\u7b2c\u4e8c<\/span>
\n \/\/ \u4e2a\u4f4d\u7f6e\u3002\u5219\u6709\u4e09\u79cd\u60c5\u51b5：\u7b2c 1，2，3 \u6b21\u89c2\u5bdf\u540c\u65f6\u5904\u4e8e\u4e00\u4e2a\u5468\u671f\u5185，\u7b2c 1，2 \u6b21\u89c2\u5bdf\u5904\u4e8e\u540c\u4e00<\/span>
\n \/\/ \u5468\u671f，\u7b2c3\u6b21\u89c2\u5bdf\u5904\u4e8e\u7b2c\u4e8c\u4e2a\u5468\u671f，\u7b2c1\u6b21\u89c2\u5bdf\u5904\u4e8e\u7b2c\u4e00\u4e2a\u5468\u671f，\u7b2c2\u6b21\u89c2\u5bdf\u5904\u4e8e\u7b2c\u4e8c\u4e2a\u5468\u671f<\/span>
\n \/\/ \u7b2c\u4e09\u6b21\u89c2\u5bdf\u5904\u4e8e\u7b2c\u4e09\u4e2a\u5468\u671f，\u5982\u679c\u8981 AC，\u53ea\u80fd\u8f93\u51fa\u4e24\u7ec4\u7b54\u6848，\u80fd AC \u7684\u7ec4\u5408\u662f\u7b2c\u4e00\u79cd\u548c<\/span>
\n \/\/ \u7b2c\u4e09\u79cd\u60c5\u51b5\u6216\u8005\u7b2c\u4e8c\u79cd\u548c\u7b2c\u4e09\u79cd\u60c5\u51b5\u3002\u6bd4\u8f83\u5947\u602a\u3002<\/span>
\n if<\/span> (<\/span>first.<\/span>angle ><\/span> second.<\/span>angle &&<\/span> angleDiff ><\/span> 180.0<\/span>)<\/span>
\n C =<\/span> toRadian<\/span>(<\/span>second.<\/span>angle +<\/span> (<\/span>360.0<\/span> –<\/span> first.<\/span>angle)<\/span>)<\/span>;<\/span>
\n else<\/span>
\n C =<\/span> toRadian<\/span>(<\/span>second.<\/span>angle –<\/span> first.<\/span>angle)<\/span>;<\/span><\/p>\n

double<\/span> a =<\/span> first.<\/span>distance,<\/span> b =<\/span> second.<\/span>distance;<\/span>
\n double<\/span> c =<\/span> sqrt<\/span>(<\/span>a *<\/span> a +<\/span> b *<\/span> b –<\/span> 2.0<\/span> *<\/span> a *<\/span> b *<\/span> cos<\/span>(<\/span>C)<\/span>)<\/span>;<\/span>
\n double<\/span> A =<\/span> acos<\/span>(<\/span>(<\/span>b *<\/span> b +<\/span> c *<\/span> c –<\/span> a *<\/span> a)<\/span> \/<\/span> (<\/span>2.0<\/span> *<\/span> b *<\/span> c)<\/span>)<\/span>;<\/span><\/p>\n

\/\/ \u601d\u8def\u540c\u524d，\u4e8c\u5206\u6c42\u503c，\u4e0d\u8fc7\u5728\u8fb9\u754c\u503c\u7684\u6c42\u53d6\u65f6\u6709\u5dee\u5f02，\u6240\u4ee5\u672a\u80fd\u628a\u524d\u9762\u7684\u4e8c\u5206<\/span>
\n \/\/ \u67e5\u627e\u548c\u6b64\u5904\u7684\u4e8c\u5206\u67e5\u627e\u7edf\u4e00\u6210\u4e3a\u4e00\u4e2a\u51fd\u6570\u3002<\/span>
\n double<\/span> x =<\/span> binarySearch<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> C,<\/span> CLOCKWISE_SAME_SAME_CYCLE)<\/span>;<\/span>
\n double<\/span> finalAngle =<\/span> second.<\/span>angle +<\/span> toDegree<\/span>(<\/span>x)<\/span>;<\/span>
\n if<\/span> (<\/span>finalAngle ><\/span> 360.0<\/span>)<\/span>
\n finalAngle -=<\/span> 360.0<\/span>;<\/span>
\n if<\/span> (<\/span>fabs<\/span>(<\/span>finalAngle –<\/span> second.<\/span>angle)<\/span> <<\/span> 0.02<\/span>)<\/span>
\n {<\/span>
\n x =<\/span> binarySearch<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> C,<\/span> CLOCKWISE_SAME_NEXT_CYCLE)<\/span>;<\/span>
\n finalAngle =<\/span> second.<\/span>angle +<\/span> toDegree<\/span>(<\/span>x)<\/span>;<\/span>
\n if<\/span> (<\/span>finalAngle ><\/span> 360.0<\/span>)<\/span>
\n finalAngle -=<\/span> 360.0<\/span>;<\/span>
\n }<\/span>
\n finalDistance =<\/span> b *<\/span> sin<\/span>(<\/span>A)<\/span> \/<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span>;<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>finalAngle,<\/span> finalDistance}<\/span>;<\/span><\/p>\n

x =<\/span> binarySearch<\/span>(<\/span>b,<\/span> c,<\/span> A,<\/span> C,<\/span> CLOCKWISE_NEXT_NEXT_CYCLE)<\/span>;<\/span>
\n finalAngle =<\/span> second.<\/span>angle +<\/span> toDegree<\/span>(<\/span>x)<\/span>;<\/span>
\n if<\/span> (<\/span>finalAngle ><\/span> 360.0<\/span>)<\/span>
\n finalAngle -=<\/span> 360.0<\/span>;<\/span>
\n finalDistance =<\/span> b *<\/span> sin<\/span>(<\/span>A)<\/span> \/<\/span> sin<\/span>(<\/span>A –<\/span> x)<\/span>;<\/span>
\n solutions[<\/span>counter++<\/span>]<\/span> =<\/span> (<\/span>point)<\/span>{<\/span>finalAngle,<\/span> finalDistance}<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

sort<\/span>(<\/span>solutions,<\/span> solutions +<\/span> counter,<\/span> cmp)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>,<\/span> printBlank =<\/span> false<\/span>;<\/span> i <<\/span> counter;<\/span> i++<\/span>)<\/span>
\n {<\/span>
\n if<\/span> (<\/span>printBlank)<\/span>
\n cout <<<\/span> " "<\/span>;<\/span>
\n else<\/span>
\n printBlank =<\/span> true<\/span>;<\/span><\/p>\n

cout <<<\/span> fixed <<<\/span> setprecision<\/span>(<\/span>2<\/span>)<\/span> <<<\/span> solutions[<\/span>i]<\/span>.<\/span>angle <<<\/span> " "<\/span>;<\/span>
\n cout <<<\/span> fixed <<<\/span> setprecision<\/span>(<\/span>2<\/span>)<\/span> <<<\/span> solutions[<\/span>i]<\/span>.<\/span>distance;<\/span>
\n }<\/span>
\n cout <<<\/span> endl;<\/span>
\n}<\/span><\/p>\n

int<\/span> main<\/span> (<\/span>int<\/span> argc,<\/span> char<\/span> *<\/span>argv[<\/span>]<\/span>)<\/span>
\n{<\/span>
\n point first,<\/span> second;<\/span>
\n while<\/span> (<\/span>cin >><\/span> first.<\/span>angle >><\/span> first.<\/span>distance,<\/span>
\n cin >><\/span> second.<\/span>angle >><\/span> second.<\/span>distance)<\/span>
\n calculate<\/span>(<\/span>first,<\/span> second)<\/span>;<\/span><\/p>\n

return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n

\u603b\u7ed3<\/h3>\n

\u672c\u9898\u901a\u8fc7\u5c06\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8\u4e0e\u5929\u7ebf\u65cb\u8f6c\u76f8\u7ed3\u5408，\u5efa\u7acb\u6781\u5750\u6807\u4e0b\u7684\u65b9\u7a0b，\u5e76\u901a\u8fc7\u6570\u503c\u6c42\u89e3（\u4e8c\u5206\u6cd5）\u5f97\u5230\u4e0b\u4e00\u6b21\u89c2\u6d4b\u4f4d\u7f6e\u7684\u6240\u6709\u53ef\u80fd\u89e3\u3002\u4ee3\u7801\u4e2d\u6839\u636e\u89d2\u5ea6\u53d8\u5316\u65b9\u5411\u5206\u591a\u79cd\u60c5\u51b5\u5904\u7406，\u5229\u7528\u6b63\u5f26\u5b9a\u7406\u548c\u4f59\u5f26\u5b9a\u7406\u63a8\u5bfc\u65b9\u7a0b，\u518d\u901a\u8fc7\u4e8c\u5206\u6cd5\u6c42\u6839\u3002\u7531\u4e8e\u9898\u76ee\u6570\u636e\u53ef\u80fd\u5b58\u5728\u4e0d\u5b8c\u5584\u4e4b\u5904，\u4ee3\u7801\u5b9e\u73b0\u4f9d\u8d56\u7279\u5b9a\u7ec4\u5408\u7684\u8f93\u51fa\u987a\u5e8f\u4ee5\u901a\u8fc7\u8bc4\u6d4b\u3002\u8be5\u9898\u4f53\u73b0\u4e86\u51e0\u4f55\u4e0e\u6570\u503c\u8ba1\u7b97\u5728\u96f7\u8fbe\u8ffd\u8e2a\u95ee\u9898\u4e2d\u7684\u5e94\u7528\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u9898\u76ee\u63cf\u8ff0
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