{"id":655,"date":"2016-05-21T19:00:15","date_gmt":"2016-05-21T19:00:15","guid":{"rendered":"http:\/\/blogs.softwareclue.com\/?p=655"},"modified":"2016-05-21T19:00:15","modified_gmt":"2016-05-21T19:00:15","slug":"%e8%ae%a1%e7%ae%97%e5%87%a0%e4%bd%95%e5%b8%b8%e7%94%a8%e7%ae%97%e6%b3%95%ef%bc%8cacm%e7%ab%9e%e8%b5%9b%e5%bf%85%e5%a4%87","status":"publish","type":"post","link":"http:\/\/blog.softwareclues.com\/zh\/%e8%ae%a1%e7%ae%97%e5%87%a0%e4%bd%95%e5%b8%b8%e7%94%a8%e7%ae%97%e6%b3%95%ef%bc%8cacm%e7%ab%9e%e8%b5%9b%e5%bf%85%e5%a4%87","title":{"rendered":"\u8ba1\u7b97\u51e0\u4f55\u5e38\u7528\u7b97\u6cd5\uff0cACM\u7ade\u8d5b\u5fc5\u5907~"},"content":{"rendered":"

\u6765\u81ea<\/strong>2010\u5e74\u767e\u5ea6\u6587\u5e93<\/strong><\/p>\n

\u539f\u4f5c\u8005\u4e0d\u8be6<\/strong><\/p><\/blockquote>\n

1\u3001\u77e2\u91cf\u51cf\u6cd5<\/strong><\/p>\n

\u8bbe\u4e8c\u7ef4\u77e2\u91cf P = \uff08x1,y1\uff09 \uff0cQ = (x2,y2)
\n\u5219\u77e2\u91cf\u51cf\u6cd5\u5b9a\u4e49\u4e3a\uff1a P – Q = ( x1 – x2 , y1 – y2 )
\n\u663e\u7136\u6709\u6027\u8d28 P – Q = – ( Q – P )
\n\u5982\u4e0d\u52a0\u8bf4\u660e\uff0c\u4e0b\u9762\u6240\u6709\u7684\u70b9\u90fd\u770b\u4f5c\u77e2\u91cf\uff0c\u4e24\u70b9\u7684\u51cf\u6cd5\u5c31\u662f\u77e2\u91cf\u76f8\u51cf\uff1b<\/p>\n

2\u3001\u77e2\u91cf\u53c9\u79ef<\/strong><\/p>\n

\u8bbe\u77e2\u91cfP = \uff08x1,y1\uff09 \uff0cQ = (x2,y2)
\n\u5219\u77e2\u91cf\u53c9\u79ef\u5b9a\u4e49\u4e3a\uff1a P \u00d7 Q = x1*y2 – x2*y1 \u00a0 \u5f97\u5230\u7684\u662f\u4e00\u4e2a\u6807\u91cf
\n\u663e\u7136\u6709\u6027\u8d28 P \u00d7 Q = – ( Q \u00d7 P ) \u00a0 P \u00d7 ( – Q ) = – ( P \u00d7 Q )
\n\u5982\u4e0d\u52a0\u8bf4\u660e\uff0c\u4e0b\u9762\u6240\u6709\u7684\u70b9\u90fd\u770b\u4f5c\u77e2\u91cf\uff0c\u70b9\u7684\u4e58\u6cd5\u770b\u4f5c\u77e2\u91cf\u53c9\u79ef\uff1b
\n\u53c9\u4e58\u7684\u91cd\u8981\u6027\u8d28\uff1a
\n> \u82e5 P \u00d7 Q > 0 , \u5219P \u5728Q\u7684\u987a\u65f6\u9488\u65b9\u5411
\n> \u82e5 P \u00d7 Q < 0 , \u5219P \u5728Q\u7684\u9006\u65f6\u9488\u65b9\u5411
\n> \u82e5 P \u00d7 Q = 0 , \u5219P \u4e0eQ\u5171\u7ebf\uff0c\u4f46\u53ef\u80fd\u540c\u5411\u4e5f\u53ef\u80fd\u53cd\u5411<\/p>\n

3\u3001\u5224\u65ad\u70b9\u5728\u7ebf\u6bb5\u4e0a<\/strong><\/p>\n

\u8bbe\u70b9\u4e3aQ\uff0c\u7ebf\u6bb5\u4e3aP1P2 \uff0c\u5224\u65ad\u70b9Q\u5728\u8be5\u7ebf\u6bb5\u4e0a\u7684\u4f9d\u636e\u662f\uff1a
\n( Q – P1 ) \u00d7 ( P2 – P1 ) = 0 \u4e14 Q \u5728\u4ee5 P1\uff0cP2\u4e3a\u5bf9\u89d2\u9876\u70b9\u7684\u77e9\u5f62\u5185<\/p>\n

4\u3001\u5224\u65ad\u4e24\u7ebf\u6bb5\u662f\u5426\u76f8\u4ea4<\/strong><\/p>\n

\u6211\u4eec\u5206\u4e24\u6b65\u786e\u5b9a\u4e24\u6761\u7ebf\u6bb5\u662f\u5426\u76f8\u4ea4\uff1a<\/p>\n

(1)\u5feb\u901f\u6392\u65a5\u8bd5\u9a8c<\/strong>
\n\u8bbe\u4ee5\u7ebf\u6bb5 P1P2 \u4e3a\u5bf9\u89d2\u7ebf\u7684\u77e9\u5f62\u4e3aR\uff0c \u8bbe\u4ee5\u7ebf\u6bb5 Q1Q2 \u4e3a\u5bf9\u89d2\u7ebf\u7684\u77e9\u5f62\u4e3aT\uff0c\u5982\u679cR\u548cT\u4e0d\u76f8
\n\u4ea4\uff0c\u663e\u7136\u4e24\u7ebf\u6bb5\u4e0d\u4f1a\u76f8\u4ea4\uff1b<\/p>\n

(2)\u8de8\u7acb\u8bd5\u9a8c<\/strong>
\n\u5982\u679c\u4e24\u7ebf\u6bb5\u76f8\u4ea4\uff0c\u5219\u4e24\u7ebf\u6bb5\u5fc5\u7136\u76f8\u4e92\u8de8\u7acb\u5bf9\u65b9\uff0c\u5982\u56fe1\u6240\u793a\u3002\u5728\u56fe1\u4e2d\uff0cP1P2\u8de8\u7acbQ1Q2 \uff0c\u5219
\n\u77e2\u91cf ( P1 – Q1 ) \u548c( P2 – Q1 )\u4f4d\u4e8e\u77e2\u91cf( Q2 – Q1 ) \u7684\u4e24\u4fa7\uff0c\u5373
\n( P1 – Q1 ) \u00d7 ( Q2 – Q1 ) * ( P2 – Q1 ) \u00d7 ( Q2 – Q1 ) < 0
\n\u4e0a\u5f0f\u53ef\u6539\u5199\u6210<\/p>\n

( P1 – Q1 ) \u00d7 ( Q2 – Q1 ) * ( Q2 – Q1 ) \u00d7 ( P2 – Q1 ) > 0
\n\u5f53 ( P1 – Q1 ) \u00d7 ( Q2 – Q1 ) = 0 \u65f6\uff0c\u8bf4\u660e \u00a0 ( P1 – Q1 ) \u548c ( Q2 – Q1 )\u5171\u7ebf\uff0c<\/p>\n

\u4f46\u662f\u56e0\u4e3a\u5df2\u7ecf\u901a\u8fc7\u5feb\u901f\u6392\u65a5\u8bd5\u9a8c\uff0c\u6240\u4ee5 P1 \u4e00\u5b9a\u5728\u7ebf\u6bb5 Q1Q2\u4e0a\uff1b\u540c\u7406\uff0c( Q2 – Q1 ) \u00d7(
\nP2 – Q1 ) = 0 \u8bf4\u660e P2 \u4e00\u5b9a\u5728\u7ebf\u6bb5 Q1Q2\u4e0a\u3002<\/p>\n

\u6240\u4ee5\u5224\u65adP1P2\u8de8\u7acbQ1Q2\u7684\u4f9d\u636e\u662f\uff1a
\n( P1 – Q1 ) \u00d7 ( Q2 – Q1 ) * ( Q2 – Q1 ) \u00d7 ( P2 – Q1 ) \u2265 0
\n\u540c\u7406\u5224\u65adQ1Q2\u8de8\u7acbP1P2\u7684\u4f9d\u636e\u662f\uff1a
\n( Q1 – P1 ) \u00d7 ( P2 – P1 ) * ( P2 – P1 ) \u00d7 ( Q2 – P1 ) \u2265 0
\n\u81f3\u6b64\u5df2\u7ecf\u5b8c\u5168\u89e3\u51b3\u5224\u65ad\u7ebf\u6bb5\u662f\u5426\u76f8\u4ea4\u7684\u95ee\u9898\u3002<\/p>\n

5\u3001\u5224\u65ad\u7ebf\u6bb5\u548c\u76f4\u7ebf\u662f\u5426\u76f8\u4ea4<\/strong><\/p>\n

\u5982\u679c\u7ebf\u6bb5 P1P2\u548c\u76f4\u7ebfQ1Q2\u76f8\u4ea4\uff0c\u5219P1P2\u8de8\u7acbQ1Q2\uff0c\u5373\uff1a
\n( P1 – Q1 ) \u00d7 ( Q2 – Q1 ) * ( Q2 – Q1 ) \u00d7 ( P2 – Q1 ) \u2265 0<\/p>\n

6\u3001\u5224\u65ad\u77e9\u5f62\u662f\u5426\u5305\u542b\u70b9<\/strong><\/p>\n

\u53ea\u8981\u5224\u65ad\u8be5\u70b9\u7684\u6a2a\u5750\u6807\u548c\u7eb5\u5750\u6807\u662f\u5426\u5939\u5728\u77e9\u5f62\u7684\u5de6\u53f3\u8fb9\u548c\u4e0a\u4e0b\u8fb9\u4e4b\u95f4\u3002
\n\u5224\u65ad\u7ebf\u6bb5\u3001\u6298\u7ebf\u3001\u591a\u8fb9\u5f62\u662f\u5426\u5728\u77e9\u5f62\u4e2d
\n\u56e0\u4e3a\u77e9\u5f62\u662f\u4e2a\u51f8\u96c6\uff0c\u6240\u4ee5\u53ea\u8981\u5224\u65ad\u6240\u6709\u7aef\u70b9\u662f\u5426\u90fd\u5728\u77e9\u5f62\u4e2d\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n

6\u3001\u5224\u65ad\u77e9\u5f62\u662f\u5426\u5728\u77e9\u5f62\u4e2d<\/strong><\/p>\n

\u53ea\u8981\u6bd4\u8f83\u5de6\u53f3\u8fb9\u754c\u548c\u4e0a\u4e0b\u8fb9\u754c\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n

7\u3001\u5224\u65ad\u5706\u662f\u5426\u5728\u77e9\u5f62\u4e2d<\/strong><\/p>\n

\u5706\u5728\u77e9\u5f62\u4e2d\u7684\u5145\u8981\u6761\u4ef6\u662f\uff1a\u5706\u5fc3\u5728\u77e9\u5f62\u4e2d\u4e14\u5706\u7684\u534a\u5f84\u5c0f\u4e8e\u7b49\u4e8e\u5706\u5fc3\u5230\u77e9\u5f62\u56db\u8fb9\u7684\u8ddd\u79bb\u7684\u6700
\n\u5c0f\u503c\u3002<\/p>\n

8\u3001\u5224\u65ad\u70b9\u662f\u5426\u5728\u591a\u8fb9\u5f62\u4e2d<\/strong><\/p>\n

\u4ee5\u70b9P\u4e3a\u7aef\u70b9\uff0c\u5411\u5de6\u65b9\u4f5c\u5c04\u7ebfL\uff0c\u7531\u4e8e\u591a\u8fb9\u5f62\u662f\u6709\u754c\u7684\uff0c\u6240\u4ee5\u5c04\u7ebfL\u7684\u5de6\u7aef\u4e00\u5b9a\u5728\u591a\u8fb9\u5f62\u5916\uff0c
\n\u8003\u8651\u6cbf\u7740L\u4ece\u65e0\u7a77\u8fdc\u5904\u5f00\u59cb\u81ea\u5de6\u5411\u53f3\u79fb\u52a8\uff0c\u9047\u5230\u548c\u591a\u8fb9\u5f62\u7684\u7b2c\u4e00\u4e2a\u4ea4\u70b9\u7684\u65f6\u5019\uff0c\u8fdb\u5165\u5230\u4e86\u591a
\n\u8fb9\u5f62\u7684\u5185\u90e8\uff0c\u9047\u5230\u7b2c\u4e8c\u4e2a\u4ea4\u70b9\u7684\u65f6\u5019\uff0c\u79bb\u5f00\u4e86\u591a\u8fb9\u5f62\uff0c\u2026\u2026\u6240\u4ee5\u5f88\u5bb9\u6613\u770b\u51fa\u5f53L\u548c\u591a\u8fb9\u5f62\u7684
\n\u4ea4\u70b9\u6570\u76eeC\u662f\u5947\u6570\u7684\u65f6\u5019\uff0cP\u5728\u591a\u8fb9\u5f62\u5185\uff0c\u662f\u5076\u6570\u7684\u8bddP\u5728\u591a\u8fb9\u5f62\u5916\u3002
\n\u4f46\u662f\u6709\u4e9b\u7279\u6b8a\u60c5\u51b5\u8981\u52a0\u4ee5\u8003\u8651\u3002\u5982\u679cL\u548c\u591a\u8fb9\u5f62\u7684\u9876\u70b9\u76f8\u4ea4\uff0c\u6709\u4e9b\u60c5\u51b5\u4e0b\u4ea4\u70b9\u53ea\u80fd\u8ba1\u7b97\u4e00\u4e2a
\n\uff0c\u6709\u4e9b\u60c5\u51b5\u4e0b\u4ea4\u70b9\u4e0d\u5e94\u88ab\u8ba1\u7b97\uff08\u4f60\u81ea\u5df1\u753b\u4e2a\u56fe\u5c31\u660e\u767d\u4e86\uff09\uff1b\u5982\u679cL\u548c\u591a\u8fb9\u5f62\u7684\u4e00\u6761\u8fb9\u91cd\u5408\uff0c
\n\u8fd9\u6761\u8fb9\u5e94\u8be5\u88ab\u5ffd\u7565\u4e0d\u8ba1\u3002\u4e3a\u4e86\u7edf\u4e00\u8d77\u89c1\uff0c\u6211\u4eec\u5728\u8ba1\u7b97\u5c04\u7ebfL\u548c\u591a\u8fb9\u5f62\u7684\u4ea4\u70b9\u7684\u65f6\u5019\uff0c1\u3002\u5bf9
\n\u4e8e\u591a\u8fb9\u5f62\u7684\u6c34\u5e73\u8fb9\u4e0d\u4f5c\u8003\u8651\uff1b2\u3002\u5bf9\u4e8e\u591a\u8fb9\u5f62\u7684\u9876\u70b9\u548cL\u76f8\u4ea4\u7684\u60c5\u51b5\uff0c\u5982\u679c\u8be5\u9876\u70b9\u662f\u5176\u6240\u5c5e
\n\u7684\u8fb9\u4e0a\u7eb5\u5750\u6807\u8f83\u5927\u7684\u9876\u70b9\uff0c\u5219\u8ba1\u6570\uff0c\u5426\u5219\u5ffd\u7565\uff1b3\u3002\u5bf9\u4e8eP\u5728\u591a\u8fb9\u5f62\u8fb9\u4e0a\u7684\u60c5\u5f62\uff0c\u76f4\u63a5\u53ef\u5224
\n\u65adP\u5c5e\u4e8e\u591a\u8fb9\u884c\u3002\u7531\u6b64\u5f97\u51fa\u7b97\u6cd5\u7684\u4f2a\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n

1\u3001count \u2190 0;
\n2\u3001\u4ee5P\u4e3a\u7aef\u70b9\uff0c\u4f5c\u4ece\u53f3\u5411\u5de6\u7684\u5c04\u7ebfL;
\n3\u3001for \u591a\u8fb9\u5f62\u7684\u6bcf\u6761\u8fb9s
\n4\u3001do if P\u5728\u8fb9s\u4e0a
\n5\u3001then return true;
\n6\u3001if s\u4e0d\u662f\u6c34\u5e73\u7684
\n7\u3001then if s\u7684\u4e00\u4e2a\u7aef\u70b9\u5728L\u4e0a\u4e14\u8be5\u7aef\u70b9\u662fs\u4e24\u7aef\u70b9\u4e2d\u7eb5\u5750\u6807\u8f83\u5927\u7684\u7aef\u70b9
\n9\u3001then count \u2190 count+1
\n10\u3001else if s\u548cL\u76f8\u4ea4
\n11\u3001then count \u2190 count+1;
\n12i\u3001f count mod 2 = 1
\n13\u3001then return true
\n14\u3001else return false;<\/p>\n

\u5176\u4e2d\u505a\u5c04\u7ebfL\u7684\u65b9\u6cd5\u662f\uff1a\u8bbeP’\u7684\u7eb5\u5750\u6807\u548cP\u76f8\u540c\uff0c\u6a2a\u5750\u6807\u4e3a\u6b63\u65e0\u7a77\u5927\uff08\u5f88\u5927\u7684\u4e00\u4e2a\u6b63\u6570\uff09\uff0c
\n\u5219P\u548cP’\u5c31\u786e\u5b9a\u4e86\u5c04\u7ebfL\u3002\u8fd9\u4e2a\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u4e3aO(n)\u3002<\/p>\n

9\u3001\u5224\u65ad\u7ebf\u6bb5\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185<\/strong><\/p>\n

\u7ebf\u6bb5\u5728\u591a\u8fb9\u5f62\u5185\u7684\u4e00\u4e2a\u5fc5\u8981\u6761\u4ef6\u662f\u7ebf\u6bb5\u7684\u4e24\u4e2a\u7aef\u70b9\u90fd\u5728\u591a\u8fb9\u5f62\u5185\uff1b
\n\u5982\u679c\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u67d0\u6761\u8fb9\u5185\u4ea4\uff08\u4e24\u7ebf\u6bb5\u5185\u4ea4\u662f\u6307\u4e24\u7ebf\u6bb5\u76f8\u4ea4\u4e14\u4ea4\u70b9\u4e0d\u5728\u4e24\u7ebf\u6bb5\u7684\u7aef\u70b9\uff09
\n\uff0c\u56e0\u4e3a\u591a\u8fb9\u5f62\u7684\u8fb9\u7684\u5de6\u53f3\u4e24\u4fa7\u5206\u5c5e\u591a\u8fb9\u5f62\u5185\u5916\u4e0d\u540c\u90e8\u5206\uff0c\u6240\u4ee5\u7ebf\u6bb5\u4e00\u5b9a\u4f1a\u6709\u4e00\u90e8\u5206\u5728\u591a\u8fb9
\n\u5f62\u5916\u3002\u4e8e\u662f\u6211\u4eec\u5f97\u5230\u7ebf\u6bb5\u5728\u591a\u8fb9\u5f62\u5185\u7684\u7b2c\u4e8c\u4e2a\u5fc5\u8981\u6761\u4ef6\uff1a\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u6240\u6709\u8fb9\u90fd\u4e0d\u5185\u4ea4
\n\uff1b
\n\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u4ea4\u4e8e\u7ebf\u6bb5\u7684\u4e24\u7aef\u70b9\u5e76\u4e0d\u4f1a\u5f71\u54cd\u7ebf\u6bb5\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185\uff1b\u4f46\u662f\u5982\u679c\u591a\u8fb9\u5f62\u7684\u67d0\u4e2a
\n\u9876\u70b9\u548c\u7ebf\u6bb5\u76f8\u4ea4\uff0c\u8fd8\u5fc5\u987b\u5224\u65ad\u4e24\u76f8\u90bb\u4ea4\u70b9\u4e4b\u95f4\u7684\u7ebf\u6bb5\u662f\u5426\u5305\u542b\u4e0e\u591a\u8fb9\u5f62\u5185\u90e8\u3002\u56e0\u6b64\u6211\u4eec\u53ef
\n\u4ee5\u5148\u6c42\u51fa\u6240\u6709\u548c\u7ebf\u6bb5\u76f8\u4ea4\u7684\u591a\u8fb9\u5f62\u7684\u9876\u70b9\uff0c\u7136\u540e\u6309\u7167X-Y\u5750\u6807\u6392\u5e8f\uff0c\u8fd9\u6837\u76f8\u90bb\u7684\u4e24\u4e2a\u70b9\u5c31\u662f
\n\u5728\u7ebf\u6bb5\u4e0a\u76f8\u90bb\u7684\u4e24\u4ea4\u70b9\uff0c\u5982\u679c\u4efb\u610f\u76f8\u90bb\u4e24\u70b9\u7684\u4e2d\u70b9\u4e5f\u5728\u591a\u8fb9\u5f62\u5185\uff0c\u5219\u8be5\u7ebf\u6bb5\u4e00\u5b9a\u5728\u591a\u8fb9\u5f62
\n\u5185\u3002\u8bc1\u660e\u5982\u4e0b\uff1a
\n\u547d\u98981\uff1a<\/strong>
\n\u5982\u679c\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u4e24\u76f8\u90bb\u4ea4\u70b9P1 \uff0cP2\u7684\u4e2d\u70b9P’ \u4e5f\u5728\u591a\u8fb9\u5f62\u5185\uff0c\u5219P1, P2\u4e4b\u95f4\u7684\u6240\u6709\u70b9
\n\u90fd\u5728\u591a\u8fb9\u5f62\u5185\u3002
\n\u8bc1\u660e\uff1a<\/strong>
\n\u5047\u8bbeP1,P2\u4e4b\u95f4\u542b\u6709\u4e0d\u5728\u591a\u8fb9\u5f62\u5185\u7684\u70b9\uff0c\u4e0d\u59a8\u8bbe\u8be5\u70b9\u4e3aQ\uff0c\u5728P1, P’\u4e4b\u95f4\uff0c\u56e0\u4e3a\u591a\u8fb9\u5f62\u662f\u95ed
\n\u5408\u66f2\u7ebf\uff0c\u6240\u4ee5\u5176\u5185\u5916\u90e8\u4e4b\u95f4\u6709\u754c\uff0c\u800cP1\u5c5e\u4e8e\u591a\u8fb9\u884c\u5185\u90e8\uff0cQ\u5c5e\u4e8e\u591a\u8fb9\u6027\u5916\u90e8\uff0cP’\u5c5e\u4e8e\u591a\u8fb9\u6027
\n\u5185\u90e8\uff0cP1-Q-P’\u5b8c\u5168\u8fde\u7eed\uff0c\u6240\u4ee5P1Q\u548cQP’\u4e00\u5b9a\u8de8\u8d8a\u591a\u8fb9\u5f62\u7684\u8fb9\u754c\uff0c\u56e0\u6b64\u5728P1,P’\u4e4b\u95f4\u81f3\u5c11\u8fd8
\n\u6709\u4e24\u4e2a\u8be5\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u4ea4\u70b9\uff0c\u8fd9\u548cP1P2\u662f\u76f8\u90bb\u4e24\u4ea4\u70b9\u77db\u76fe\uff0c\u6545\u547d\u9898\u6210\u7acb\u3002\u8bc1\u6bd5
\n\u7531\u547d\u98981\u76f4\u63a5\u53ef\u5f97\u51fa\u63a8\u8bba\uff1a
\n\u63a8\u8bba2\uff1a<\/strong>
\n\u8bbe\u591a\u8fb9\u5f62\u548c\u7ebf\u6bb5PQ\u7684\u4ea4\u70b9\u4f9d\u6b21\u4e3aP1,P2,\u2026\u2026Pn\uff0c\u5176\u4e2dPi\u548cPi+1\u662f\u76f8\u90bb\u4e24\u4ea4\u70b9\uff0c\u7ebf\u6bb5PQ\u5728\u591a
\n\u8fb9\u5f62\u5185\u7684\u5145\u8981\u6761\u4ef6\u662f\uff1aP\uff0cQ\u5728\u591a\u8fb9\u5f62\u5185\u4e14\u5bf9\u4e8ei =1, 2,\u2026\u2026, n-1\uff0cPi ,Pi+1\u7684\u4e2d\u70b9\u4e5f\u5728\u591a
\n\u8fb9\u5f62\u5185\u3002<\/p>\n

\u5728\u5b9e\u9645\u7f16\u7a0b\u4e2d\uff0c\u6ca1\u6709\u5fc5\u8981\u8ba1\u7b97\u6240\u6709\u7684\u4ea4\u70b9\uff0c\u9996\u5148\u5e94\u5224\u65ad\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u8fb9\u662f\u5426\u5185\u4ea4\uff0c\u5018\u82e5
\n\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u67d0\u6761\u8fb9\u5185\u4ea4\u5219\u7ebf\u6bb5\u4e00\u5b9a\u5728\u591a\u8fb9\u5f62\u5916\uff1b\u5982\u679c\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u6bcf\u4e00\u6761\u8fb9\u90fd\u4e0d\u5185
\n\u4ea4\uff0c\u5219\u7ebf\u6bb5\u548c\u591a\u8fb9\u5f62\u7684\u4ea4\u70b9\u4e00\u5b9a\u662f\u7ebf\u6bb5\u7684\u7aef\u70b9\u6216\u8005\u591a\u8fb9\u5f62\u7684\u9876\u70b9\uff0c\u53ea\u8981\u5224\u65ad\u70b9\u662f\u5426\u5728\u7ebf\u6bb5
\n\u4e0a\u5c31\u53ef\u4ee5\u4e86\u3002
\n\u81f3\u6b64\u6211\u4eec\u5f97\u51fa\u7b97\u6cd5\u5982\u4e0b\uff1a
\n1\u3001f \u7ebf\u7aefPQ\u7684\u7aef\u70b9\u4e0d\u90fd\u5728\u591a\u8fb9\u5f62\u5185
\n2\u3001hen return false;
\n3\u3001\u70b9\u96c6pointSet\u521d\u59cb\u5316\u4e3a\u7a7a;
\n4\u3001for \u591a\u8fb9\u5f62\u7684\u6bcf\u6761\u8fb9s
\n5\u3001do if \u7ebf\u6bb5\u7684\u67d0\u4e2a\u7aef\u70b9\u5728s\u4e0a
\n6\u3001then \u5c06\u8be5\u7aef\u70b9\u52a0\u5165pointSet;
\n7\u3001else if s\u7684\u67d0\u4e2a\u7aef\u70b9\u5728\u7ebf\u6bb5PQ\u4e0a
\n8\u3001then \u5c06\u8be5\u7aef\u70b9\u52a0\u5165pointSet;
\n9\u3001else if s\u548c\u7ebf\u6bb5PQ\u76f8\u4ea4 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \/\/ \u8fd9\u65f6\u5019\u53ef\u4ee5\u80af\u5b9a\u662f\u5185\u4ea4
\n10\u3001\u00a0then return false;
\n11\u3001\u5c06pointSet\u4e2d\u7684\u70b9\u6309\u7167X-Y\u5750\u6807\u6392\u5e8f\uff0cX\u5750\u6807\u5c0f\u7684\u6392\u5728\u524d\u9762\uff0c\u5bf9\u4e8eX\u5750\u6807\u76f8\u540c\u7684\u70b9\uff0cY\u5750
\n\u6807\u5c0f\u7684\u6392\u5728\u524d\u9762\uff1b
\n12\u3001for pointSet\u4e2d\u6bcf\u4e24\u4e2a\u76f8\u90bb\u70b9 pointSet[i] , pointSet[ i+1]
\n13\u3001do if pointSet[i] , pointSet[ i+1] \u7684\u4e2d\u70b9\u4e0d\u5728\u591a\u8fb9\u5f62\u4e2d
\n14\u3001then return false;
\n15\u3001return true;<\/p>\n

\u8fd9\u4e2a\u7b97\u6cd5\u7684\u590d\u6742\u5ea6\u4e5f\u662fO(n)\u3002\u5176\u4e2d\u7684\u6392\u5e8f\u56e0\u4e3a\u4ea4\u70b9\u6570\u76ee\u80af\u5b9a\u8fdc\u5c0f\u4e8e\u591a\u8fb9\u5f62\u7684\u9876\u70b9\u6570\u76een\uff0c\u6240
\n\u4ee5\u6700\u591a\u662f\u5e38\u6570\u7ea7\u7684\u590d\u6742\u5ea6\uff0c\u51e0\u4e4e\u53ef\u4ee5\u5ffd\u7565\u4e0d\u8ba1\u3002<\/p>\n

10\u3001\u5224\u65ad\u6298\u7ebf\u5728\u591a\u8fb9\u5f62\u5185<\/strong><\/p>\n

\u53ea\u8981\u5224\u65ad\u6298\u7ebf\u7684\u6bcf\u6761\u7ebf\u6bb5\u662f\u5426\u90fd\u5728\u591a\u8fb9\u5f62\u5185\u5373\u53ef\u3002\u8bbe\u6298\u7ebf\u6709m\u6761\u7ebf\u6bb5\uff0c\u591a\u8fb9\u5f62\u6709n\u4e2a\u9876\u70b9\uff0c
\n\u5219\u590d\u6742\u5ea6\u4e3aO(m*n)\u3002<\/p>\n

11\u3001\u5224\u65ad\u591a\u8fb9\u5f62\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185<\/strong>
\n\u53ea\u8981\u5224\u65ad\u591a\u8fb9\u5f62\u7684\u6bcf\u6761\u8fb9\u662f\u5426\u90fd\u5728\u591a\u8fb9\u5f62\u5185\u5373\u53ef\u3002\u5224\u65ad\u4e00\u4e2a\u6709m\u4e2a\u9876\u70b9\u7684\u591a\u8fb9\u5f62\u662f\u5426\u5728\u4e00\u4e2a
\n\u6709n\u4e2a\u9876\u70b9\u7684\u591a\u8fb9\u5f62\u5185\u590d\u6742\u5ea6\u4e3aO(m*n)\u3002<\/p>\n

12\u3001\u5224\u65ad\u77e9\u5f62\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185<\/strong><\/p>\n

\u5c06\u77e9\u5f62\u8f6c\u5316\u4e3a\u591a\u8fb9\u5f62\uff0c\u7136\u540e\u518d\u5224\u65ad\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185\u3002<\/p>\n

13\u3001\u5224\u65ad\u5706\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185<\/strong><\/p>\n

\u53ea\u8981\u8ba1\u7b97\u5706\u5fc3\u5230\u591a\u8fb9\u5f62\u7684\u6bcf\u6761\u8fb9\u7684\u6700\u77ed\u8ddd\u79bb\uff0c\u5982\u679c\u8be5\u8ddd\u79bb\u5927\u4e8e\u7b49\u4e8e\u5706\u534a\u5f84\u5219\u8be5\u5706\u5728\u591a\u8fb9\u5f62
\n\u5185\u3002\u8ba1\u7b97\u5706\u5fc3\u5230\u591a\u8fb9\u5f62\u6bcf\u6761\u8fb9\u6700\u77ed\u8ddd\u79bb\u7684\u7b97\u6cd5\u5728\u540e\u6587\u9610\u8ff0\u3002<\/p>\n

14\u3001\u5224\u65ad\u70b9\u662f\u5426\u5728\u5706\u5185<\/strong><\/p>\n

\u8ba1\u7b97\u5706\u5fc3\u5230\u8be5\u70b9\u7684\u8ddd\u79bb\uff0c\u5982\u679c\u5c0f\u4e8e\u7b49\u4e8e\u534a\u5f84\u5219\u8be5\u70b9\u5728\u5706\u5185\u3002<\/p>\n

15\u3001\u5224\u65ad\u7ebf\u6bb5\u3001\u6298\u7ebf\u3001\u77e9\u5f62\u3001\u591a\u8fb9\u5f62\u662f\u5426\u5728\u5706\u5185<\/strong><\/p>\n

\u56e0\u4e3a\u5706\u662f\u51f8\u96c6\uff0c\u6240\u4ee5\u53ea\u8981\u5224\u65ad\u662f\u5426\u6bcf\u4e2a\u9876\u70b9\u90fd\u5728\u5706\u5185\u5373\u53ef\u3002<\/p>\n

16\u3001\u5224\u65ad\u5706\u662f\u5426\u5728\u5706\u5185<\/strong><\/p>\n

\u8bbe\u4e24\u5706\u4e3aO1,O2\uff0c\u534a\u5f84\u5206\u522b\u4e3ar1, r2\uff0c\u8981\u5224\u65adO2\u662f\u5426\u5728O1\u5185\u3002\u5148\u6bd4\u8f83r1\uff0cr2\u7684\u5927\u5c0f\uff0c\u5982\u679cr
\n1<r2\u5219O2\u4e0d\u53ef\u80fd\u5728O1\u5185\uff1b\u5426\u5219\u5982\u679c\u4e24\u5706\u5fc3\u7684\u8ddd\u79bb\u5927\u4e8er1 – r2 \uff0c\u5219O2\u4e0d\u5728O1\u5185\uff1b\u5426\u5219O2\u5728
\nO1\u5185\u3002<\/p>\n

17\u3001\u8ba1\u7b97\u70b9\u5230\u7ebf\u6bb5\u7684\u6700\u8fd1\u70b9<\/strong><\/p>\n

\u5982\u679c\u8be5\u7ebf\u6bb5\u5e73\u884c\u4e8eX\u8f74\uff08Y\u8f74\uff09\uff0c\u5219\u8fc7\u70b9point\u4f5c\u8be5\u7ebf\u6bb5\u6240\u5728\u76f4\u7ebf\u7684\u5782\u7ebf\uff0c\u5782\u8db3\u5f88\u5bb9\u6613\u6c42\u5f97\uff0c
\n\u7136\u540e\u8ba1\u7b97\u51fa\u5782\u8db3\uff0c\u5982\u679c\u5782\u8db3\u5728\u7ebf\u6bb5\u4e0a\u5219\u8fd4\u56de\u5782\u8db3\uff0c\u5426\u5219\u8fd4\u56de\u79bb\u5782\u8db3\u8fd1\u7684\u7aef\u70b9\uff1b
\n\u5982\u679c\u8be5\u7ebf\u6bb5\u4e0d\u5e73\u884c\u4e8eX\u8f74\u4e5f\u4e0d\u5e73\u884c\u4e8eY\u8f74\uff0c\u5219\u659c\u7387\u5b58\u5728\u4e14\u4e0d\u4e3a0\u3002\u8bbe\u7ebf\u6bb5\u7684\u4e24\u7aef\u70b9\u4e3apt1\u548cpt
\n2\uff0c\u659c\u7387\u4e3a\uff1a
\nk = ( pt2.y – pt1. y ) \/ (pt2.x – pt1.x );
\n\u8be5\u76f4\u7ebf\u65b9\u7a0b\u4e3a\uff1a
\ny = k* ( x – pt1.x) + pt1.y
\n\u5176\u5782\u7ebf\u7684\u659c\u7387\u4e3a – 1 \/ k\uff0c
\n\u5782\u7ebf\u65b9\u7a0b\u4e3a\uff1a
\ny = (-1\/k) * (x – point.x) + point.y
\n\u8054\u7acb\u4e24\u76f4\u7ebf\u65b9\u7a0b\u89e3\u5f97\uff1a
\nx = ( k^2 * pt1.x + k * (point.y – pt1.y ) + point.x ) \/ ( k^2 + 1)
\ny = k * ( x – pt1.x) + pt1.y;
\n\u7136\u540e\u518d\u5224\u65ad\u5782\u8db3\u662f\u5426\u5728\u7ebf\u6bb5\u4e0a\uff0c\u5982\u679c\u5728\u7ebf\u6bb5\u4e0a\u5219\u8fd4\u56de\u5782\u8db3\uff1b\u5982\u679c\u4e0d\u5728\u5219\u8ba1\u7b97\u4e24\u7aef\u70b9\u5230\u5782\u8db3
\n\u7684\u8ddd\u79bb\uff0c\u9009\u62e9\u8ddd\u79bb\u5782\u8db3\u8f83\u8fd1\u7684\u7aef\u70b9\u8fd4\u56de\u3002<\/p>\n

18\u3001\u8ba1\u7b97\u70b9\u5230\u6298\u7ebf\u3001\u77e9\u5f62\u3001\u591a\u8fb9\u5f62\u7684\u6700\u8fd1\u70b9<\/strong><\/p>\n

\u53ea\u8981\u5206\u522b\u8ba1\u7b97\u70b9\u5230\u6bcf\u6761\u7ebf\u6bb5\u7684\u6700\u8fd1\u70b9\uff0c\u8bb0\u5f55\u6700\u8fd1\u8ddd\u79bb\uff0c\u53d6\u5176\u4e2d\u6700\u8fd1\u8ddd\u79bb\u6700\u5c0f\u7684\u70b9\u5373\u53ef\u3002<\/p>\n

19\u3001\u8ba1\u7b97\u70b9\u5230\u5706\u7684\u6700\u8fd1\u8ddd\u79bb<\/strong>
\n\u5982\u679c\u8be5\u70b9\u5728\u5706\u5fc3\uff0c\u5219\u8fd4\u56deUNDEFINED
\n\u8fde\u63a5\u70b9P\u548c\u5706\u5fc3O\uff0c\u5982\u679cPO\u5e73\u884c\u4e8eX\u8f74\uff0c\u5219\u6839\u636eP\u5728O\u7684\u5de6\u8fb9\u8fd8\u662f\u53f3\u8fb9\u8ba1\u7b97\u51fa\u6700\u8fd1\u70b9\u7684\u6a2a\u5750\u6807\u4e3a
\ncenterPoint.x – radius \u6216 centerPoint.x + radius\uff0c \u5982\u56fe4 (a)\u6240\u793a\uff1b\u5982\u679c\u5982\u679cPO\u5e73
\n\u884c\u4e8eY\u8f74\uff0c\u5219\u6839\u636eP\u5728O\u7684\u4e0a\u8fb9\u8fd8\u662f\u4e0b\u8fb9\u8ba1\u7b97\u51fa\u6700\u8fd1\u70b9\u7684\u7eb5\u5750\u6807\u4e3a centerPoint.y -+radius
\n\u6216 centerPoint.y – radius\uff0c \u5982\u56fe4 (b)\u6240\u793a\u3002
\n\u5982\u679cPO\u4e0d\u5e73\u884c\u4e8eX\u8f74\u548cY\u8f74\uff0c\u5219PO\u7684\u659c\u7387\u5b58\u5728\u4e14\u4e0d\u4e3a0\uff0c\u5982\u56fe4(c)\u6240\u793a\u3002\u8fd9\u65f6\u76f4\u7ebfPO\u659c\u7387\u4e3a<\/p>\n

k = \uff08 P.y – O.y \uff09\/ ( P.x – O.x )
\n\u76f4\u7ebfPO\u7684\u65b9\u7a0b\u4e3a\uff1a
\ny = k * ( x – P.x) + P.y
\n\u8bbe\u5706\u65b9\u7a0b\u4e3a:
\n(x – O.x ) ^2 + ( y – O.y ) ^2 = r ^2\uff0c
\n\u8054\u7acb\u4e24\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u89e3\u51fa\u76f4\u7ebfPO\u548c\u5706\u7684\u4ea4\u70b9\uff0c\u53d6\u5176\u4e2d\u79bbP\u70b9\u8f83\u8fd1\u7684\u4ea4\u70b9\u5373\u53ef\u3002<\/p>\n

20\u3001\u8ba1\u7b97\u4e24\u6761\u5171\u7ebf\u7684\u7ebf\u6bb5\u7684\u4ea4\u70b9<\/strong><\/p>\n

\u5bf9\u4e8e\u4e24\u6761\u5171\u7ebf\u7684\u7ebf\u6bb5\uff0c\u5b83\u4eec\u4e4b\u95f4\u7684\u4f4d\u7f6e\u5173\u7cfb\u6709\u56fe5\u6240\u793a\u7684\u51e0\u79cd\u60c5\u51b5\u3002
\n\u56fe5(a)\u4e2d\u4e24\u6761\u7ebf\u6bb5\u6ca1\u6709\u4ea4\u70b9\uff1b\u56fe5 (b) \u548c (d) \u4e2d\u4e24\u6761\u7ebf\u6bb5\u6709\u65e0\u7a77\u7126\u70b9\uff1b\u56fe5 (c) \u4e2d\u4e24\u6761\u7ebf
\n\u6bb5\u6709\u4e00\u4e2a\u4ea4\u70b9\u3002\u8bbeline1\u662f\u4e24\u6761\u7ebf\u6bb5\u4e2d\u8f83\u957f\u7684\u4e00\u6761\uff0cline2\u662f\u8f83\u77ed\u7684\u4e00\u6761\uff0c\u5982\u679cline1\u5305\u542b\u4e86
\nline2\u7684\u4e24\u4e2a\u7aef\u70b9\uff0c\u5219\u662f\u56fe5(d)\u7684\u60c5\u51b5\uff0c\u4e24\u7ebf\u6bb5\u6709\u65e0\u7a77\u4ea4\u70b9\uff1b\u5982\u679cline1\u53ea\u5305\u542bline2\u7684\u4e00\u4e2a
\n\u7aef\u70b9\uff0c\u90a3\u4e48\u5982\u679cline1\u7684\u67d0\u4e2a\u7aef\u70b9\u7b49\u4e8e\u88abline1\u5305\u542b\u7684line2\u7684\u90a3\u4e2a\u7aef\u70b9\uff0c\u5219\u662f\u56fe5(c)\u7684\u60c5\u51b5
\n\uff0c\u8fd9\u65f6\u4e24\u7ebf\u6bb5\u53ea\u6709\u4e00\u4e2a\u4ea4\u70b9\uff0c\u5426\u5219\u5c31\u662f\u56fe5(c)\u7684\u60c5\u51b5\uff0c\u4e24\u7ebf\u6bb5\u4e5f\u662f\u6709\u65e0\u7a77\u7684\u4ea4\u70b9\uff1b\u5982\u679cli
\nne1\u4e0d\u5305\u542bline2\u7684\u4efb\u4f55\u7aef\u70b9\uff0c\u5219\u662f\u56fe5(a)\u7684\u60c5\u51b5\uff0c\u8fd9\u65f6\u4e24\u7ebf\u6bb5\u6ca1\u6709\u4ea4\u70b9\u3002<\/p>\n

21\u3001\u8ba1\u7b97\u7ebf\u6bb5\u6216\u76f4\u7ebf\u4e0e\u7ebf\u6bb5\u7684\u4ea4\u70b9<\/strong>
\n\u8bbe\u4e00\u6761\u7ebf\u6bb5\u4e3aL0 = P1P2\uff0c\u53e6\u4e00\u6761\u7ebf\u6bb5\u6216\u76f4\u7ebf\u4e3aL1 = Q1Q2 \uff0c\u8981\u8ba1\u7b97\u7684\u5c31\u662fL0\u548cL1\u7684\u4ea4\u70b9\u3002<\/p>\n

1\u3001\u9996\u5148\u5224\u65adL0\u548cL1\u662f\u5426\u76f8\u4ea4\uff08\u65b9\u6cd5\u5df2\u5728\u524d\u6587\u8ba8\u8bba\u8fc7\uff09\uff0c\u5982\u679c\u4e0d\u76f8\u4ea4\u5219\u6ca1\u6709\u4ea4\u70b9\uff0c\u5426\u5219\u8bf4
\n\u660eL0\u548cL1\u4e00\u5b9a\u6709\u4ea4\u70b9\uff0c\u4e0b\u9762\u5c31\u5c06L0\u548cL1\u90fd\u770b\u4f5c\u76f4\u7ebf\u6765\u8003\u8651\u3002
\n2\u3001\u5982\u679cP1\u548cP2\u6a2a\u5750\u6807\u76f8\u540c\uff0c\u5373L0\u5e73\u884c\u4e8eY\u8f74
\na) \u82e5L1\u4e5f\u5e73\u884c\u4e8eY\u8f74\uff0c
\ni. \u82e5P1\u7684\u7eb5\u5750\u6807\u548cQ1\u7684\u7eb5\u5750\u6807\u76f8\u540c\uff0c\u8bf4\u660eL0\u548cL1\u5171\u7ebf\uff0c\u5047\u5982L1\u662f\u76f4\u7ebf\u7684\u8bdd\u4ed6\u4eec\u6709\u65e0\u7a77\u7684\u4ea4
\n\u70b9\uff0c\u5047\u5982L1\u662f\u7ebf\u6bb5\u7684\u8bdd\u53ef\u7528”\u8ba1\u7b97\u4e24\u6761\u5171\u7ebf\u7ebf\u6bb5\u7684\u4ea4\u70b9”\u7684\u7b97\u6cd5\u6c42\u4ed6\u4eec\u7684\u4ea4\u70b9\uff08\u8be5\u65b9\u6cd5\u5728\u524d
\n\u6587\u5df2\u8ba8\u8bba\u8fc7\uff09\uff1b
\nii. \u5426\u5219\u8bf4\u660eL0\u548cL1\u5e73\u884c\uff0c\u4ed6\u4eec\u6ca1\u6709\u4ea4\u70b9\uff1b
\nb) \u82e5L1\u4e0d\u5e73\u884c\u4e8eY\u8f74\uff0c\u5219\u4ea4\u70b9\u6a2a\u5750\u6807\u4e3aP1\u7684\u6a2a\u5750\u6807\uff0c\u4ee3\u5165\u5230L1\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4ea4
\n\u70b9\u7eb5\u5750\u6807\uff1b
\n3\u3001\u5982\u679cP1\u548cP2\u6a2a\u5750\u6807\u4e0d\u540c\uff0c\u4f46\u662fQ1\u548cQ2\u6a2a\u5750\u6807\u76f8\u540c\uff0c\u5373L1\u5e73\u884c\u4e8eY\u8f74\uff0c\u5219\u4ea4\u70b9\u6a2a\u5750\u6807\u4e3aQ
\n1\u7684\u6a2a\u5750\u6807\uff0c\u4ee3\u5165\u5230L0\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4ea4\u70b9\u7eb5\u5750\u6807\uff1b
\n4\u3001\u5982\u679cP1\u548cP2\u7eb5\u5750\u6807\u76f8\u540c\uff0c\u5373L0\u5e73\u884c\u4e8eX\u8f74
\na) \u82e5L1\u4e5f\u5e73\u884c\u4e8eX\u8f74\uff0c
\ni. \u82e5P1\u7684\u6a2a\u5750\u6807\u548cQ1\u7684\u6a2a\u5750\u6807\u76f8\u540c\uff0c\u8bf4\u660eL0\u548cL1\u5171\u7ebf\uff0c\u5047\u5982L1\u662f\u76f4\u7ebf\u7684\u8bdd\u4ed6\u4eec\u6709\u65e0\u7a77\u7684\u4ea4
\n\u70b9\uff0c\u5047\u5982L1\u662f\u7ebf\u6bb5\u7684\u8bdd\u53ef\u7528”\u8ba1\u7b97\u4e24\u6761\u5171\u7ebf\u7ebf\u6bb5\u7684\u4ea4\u70b9”\u7684\u7b97\u6cd5\u6c42\u4ed6\u4eec\u7684\u4ea4\u70b9\uff08\u8be5\u65b9\u6cd5\u5728\u524d
\n\u6587\u5df2\u8ba8\u8bba\u8fc7\uff09\uff1b
\nii. \u5426\u5219\u8bf4\u660eL0\u548cL1\u5e73\u884c\uff0c\u4ed6\u4eec\u6ca1\u6709\u4ea4\u70b9\uff1b
\nb) \u82e5L1\u4e0d\u5e73\u884c\u4e8eX\u8f74\uff0c\u5219\u4ea4\u70b9\u7eb5\u5750\u6807\u4e3aP1\u7684\u7eb5\u5750\u6807\uff0c\u4ee3\u5165\u5230L1\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4ea4
\n\u70b9\u6a2a\u5750\u6807\uff1b
\n5\u3001\u5982\u679cP1\u548cP2\u7eb5\u5750\u6807\u4e0d\u540c\uff0c\u4f46\u662fQ1\u548cQ2\u7eb5\u5750\u6807\u76f8\u540c\uff0c\u5373L1\u5e73\u884c\u4e8eX\u8f74\uff0c\u5219\u4ea4\u70b9\u7eb5\u5750\u6807\u4e3aQ
\n1\u7684\u7eb5\u5750\u6807\uff0c\u4ee3\u5165\u5230L0\u7684\u76f4\u7ebf\u65b9\u7a0b\u4e2d\u53ef\u4ee5\u8ba1\u7b97\u51fa\u4ea4\u70b9\u6a2a\u5750\u6807\uff1b
\n6\u3001\u5269\u4e0b\u7684\u60c5\u51b5\u5c31\u662fL1\u548cL0\u7684\u659c\u7387\u5747\u5b58\u5728\u4e14\u4e0d\u4e3a0\u7684\u60c5\u51b5
\na) \u8ba1\u7b97\u51faL0\u7684\u659c\u7387K0\uff0cL1\u7684\u659c\u7387K1 \uff1b
\nb) \u5982\u679cK1 = K2
\ni. \u5982\u679cQ1\u5728L0\u4e0a\uff0c\u5219\u8bf4\u660eL0\u548cL1\u5171\u7ebf\uff0c\u5047\u5982L1\u662f\u76f4\u7ebf\u7684\u8bdd\u6709\u65e0\u7a77\u4ea4\u70b9\uff0c\u5047\u5982L1\u662f\u7ebf\u6bb5\u7684\u8bdd
\n\u53ef\u7528”\u8ba1\u7b97\u4e24\u6761\u5171\u7ebf\u7ebf\u6bb5\u7684\u4ea4\u70b9”\u7684\u7b97\u6cd5\u6c42\u4ed6\u4eec\u7684\u4ea4\u70b9\uff08\u8be5\u65b9\u6cd5\u5728\u524d\u6587\u5df2\u8ba8\u8bba\u8fc7\uff09\uff1b
\nii. \u5982\u679cQ1\u4e0d\u5728L0\u4e0a\uff0c\u5219\u8bf4\u660eL0\u548cL1\u5e73\u884c\uff0c\u4ed6\u4eec\u6ca1\u6709\u4ea4\u70b9\u3002
\nc) \u8054\u7acb\u4e24\u76f4\u7ebf\u7684\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u89e3\u51fa\u4ea4\u70b9\u6765<\/p>\n

\u8bf4\u660e\uff1a<\/strong>\u8fd9\u4e2a\u7b97\u6cd5\u5e76\u4e0d\u590d\u6742\uff0c\u4f46\u662f\u8981\u5206\u60c5\u51b5\u8ba8\u8bba\u6e05\u695a\uff0c\u5c24\u5176\u662f\u5f53\u4e24\u6761\u7ebf\u6bb5\u5171\u7ebf\u7684\u60c5\u51b5\u9700\u8981\u5355
\n\u72ec\u8003\u8651\uff0c\u6240\u4ee5\u5728\u524d\u6587\u5c06\u6c42\u4e24\u6761\u5171\u7ebf\u7ebf\u6bb5\u7684\u7b97\u6cd5\u5355\u72ec\u5199\u51fa\u6765\u3002\u53e6\u5916\uff0c\u4e00\u5f00\u59cb\u5c31\u5148\u5229\u7528\u77e2\u91cf\u53c9
\n\u4e58\u5224\u65ad\u7ebf\u6bb5\u4e0e\u7ebf\u6bb5\uff08\u6216\u76f4\u7ebf\uff09\u662f\u5426\u76f8\u4ea4\uff0c\u5982\u679c\u7ed3\u679c\u662f\u76f8\u4ea4\uff0c\u90a3\u4e48\u5728\u540e\u9762\u5c31\u53ef\u4ee5\u5c06\u7ebf\u6bb5\u5168\u90e8
\n\u770b\u4f5c\u76f4\u7ebf\u6765\u8003\u8651\u3002<\/p>\n

22\u3001\u6c42\u7ebf\u6bb5\u6216\u76f4\u7ebf\u4e0e\u6298\u7ebf\u3001\u77e9\u5f62\u3001\u591a\u8fb9\u5f62\u7684\u4ea4\u70b9<\/strong><\/p>\n

\u5206\u522b\u6c42\u4e0e\u6bcf\u6761\u8fb9\u7684\u4ea4\u70b9\u5373\u53ef\u3002<\/p>\n

23\u3001\u6c42\u7ebf\u6bb5\u6216\u76f4\u7ebf\u4e0e\u5706\u7684\u4ea4\u70b9<\/strong><\/p>\n

\u8bbe\u5706\u5fc3\u4e3aO\uff0c\u5706\u534a\u5f84\u4e3ar\uff0c\u76f4\u7ebf\uff08\u6216\u7ebf\u6bb5\uff09L\u4e0a\u7684\u4e24\u70b9\u4e3aP1,P2\u3002
\n1\u3001\u5982\u679cL\u662f\u7ebf\u6bb5\u4e14P1\uff0cP2\u90fd\u5305\u542b\u5728\u5706O\u5185\uff0c\u5219\u6ca1\u6709\u4ea4\u70b9\uff1b\u5426\u5219\u8fdb\u884c\u4e0b\u4e00\u6b65
\n2\u3001\u5982\u679cL\u5e73\u884c\u4e8eY\u8f74\uff0c
\na) \u8ba1\u7b97\u5706\u5fc3\u5230L\u7684\u8ddd\u79bbdis
\nb) \u5982\u679cdis > r \u5219L\u548c\u5706\u6ca1\u6709\u4ea4\u70b9\uff1b
\nc) \u5229\u7528\u52fe\u80a1\u5b9a\u7406\uff0c\u53ef\u4ee5\u6c42\u51fa\u4e24\u4ea4\u70b9\u5750\u6807\uff0c\u5982\u56fe6(a)\u6240\u793a\uff1b\u4f46\u8981\u6ce8\u610f\u8003\u8651L\u548c\u5706\u7684\u76f8\u5207\u60c5\u51b5
\n3\u3001\u5982\u679cL\u5e73\u884c\u4e8eX\u8f74\uff0c\u505a\u6cd5\u4e0eL\u5e73\u884c\u4e8eY\u8f74\u7684\u60c5\u51b5\u7c7b\u4f3c\uff1b
\n4\u3001\u5982\u679cL\u65e2\u4e0d\u5e73\u884cX\u8f74\u4e5f\u4e0d\u5e73\u884cY\u8f74\uff0c\u53ef\u4ee5\u6c42\u51faL\u7684\u659c\u7387K\uff0c\u7136\u540e\u5217\u51faL\u7684\u70b9\u659c\u5f0f\u65b9\u7a0b\uff0c\u548c\u5706\u65b9\u7a0b\u8054\u7acb\u5373\u53ef\u6c42\u89e3\u51faL\u548c\u5706\u7684\u4e24\u4e2a\u4ea4\u70b9\uff1b
\n5\u3001\u5982\u679cL\u662f\u7ebf\u6bb5\uff0c\u5bf9\u4e8e2\uff0c3\uff0c4\u4e2d\u6c42\u51fa\u7684\u4ea4\u70b9\u8fd8\u8981\u5206\u522b\u5224\u65ad\u662f\u5426\u5c5e\u4e8e\u8be5\u7ebf\u6bb5\u7684\u8303\u56f4\u5185\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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