{"msg":"第三节 图论应用","code":200,"data":{"currentIndex":null,"examId":null,"examTime":null,"questionList":[{"id":"796239510743568385","title":"已知某山区六个乡镇C1，C2,…，C6之间的公路距离（公里数）如下表:<br><img alt=\"\" width=\"545\" height=\"160\" src=\"https://image.chaiding.com/ruankao/26b8474fcb25312095072516b1db62b9.jpg?x-oss-process=style/ruankaodaren\"><br>其中符号“∞“表示两个乡镇之间没有直通公路。乡镇C1到C3虽然没有直通公路， 但可以经过其他乡镇达到，根据上表，可以算出C1到C3最短的路程为（57）公里。","analyze":"本题考查图论应用基础知识。<br>根据题中给出的6个乡镇间的公路距离表，可以绘制距离图如下：<br><img alt=\"\" width=\"394\" height=\"152\" src=\"https://image.chaiding.com/ruankao/f4ba0f36e73c8f484ec93a13ac82a8df.jpg?x-oss-process=style/ruankaodaren\"><br>结点①、②、…、⑥分别表示这6个乡镇，结点之间的连线表示有公路直接通达， 连线上的数字表示公里数。从图可以看出，乡镇①到③没有直通公路，但可以通过其他乡镇达到。显然，路径①-⑤-④-③总的里程数45公里是最短的。","multi":0,"questionType":1,"answer":"C","chooseItem":["796239511712452609"],"itemList":[{"id":"796239511649538049","questionId":"796239510743568385","content":" 35","answer":0,"chooseValue":"A"},{"id":"796239511683092481","questionId":"796239510743568385","content":" 40","answer":0,"chooseValue":"B"},{"id":"796239511712452609","questionId":"796239510743568385","content":" 45","answer":1,"chooseValue":"C"},{"id":"796239511746007041","questionId":"796239510743568385","content":" 50","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796239502606618625","title":"已知A、B、……、I 九人比赛结果排名（没有并列名次）的部分情况如下图：<br><img alt=\"\" width=\"127\" height=\"105\" src=\"https://image.chaiding.com/ruankao/5809247bda709315ac5ee4b8f7a26c0e.jpg?x-oss-process=style/ruankaodaren\"><br>图中的箭头表示“排名前于”，例如D—>A表示D排名前于A。<br>根据上图中表示的部分排名情况，可以推断，第3名可能是（55）。","analyze":"本题考查应用数学基础知识。<br>根据题中的箭头图画出如下的网络图：<br><img alt=\"\" width=\"281\" height=\"128\" src=\"https://image.chaiding.com/ruankao/7b43ce7e0591d2c80684fa7dddfe6345.jpg?x-oss-process=style/ruankaodaren\"><br>从上图看出，D排名在其他所有人之前，所以D —定是第1名。由于只有ESA仅排在D之后，因此第2名只可能是E或A (G之前有D、E、H)。<br>如果E是第2名，则第3名可能是H、F或A(B之前有DEA, B不可能是第3名）；如果A是第2名，则第3名必是E (B之前有DEA, B不可能是第3名）；<br>因此，第3名只可能是A、E、F或H。","multi":0,"questionType":1,"answer":"A","chooseItem":["796239503533559809"],"itemList":[{"id":"796239503533559809","questionId":"796239502606618625","content":" A、E、F 或 H","answer":1,"chooseValue":"A"},{"id":"796239503583891457","questionId":"796239502606618625","content":" B、F 或 H","answer":0,"chooseValue":"B"},{"id":"796239503613251585","questionId":"796239502606618625","content":" F 或 H","answer":0,"chooseValue":"C"},{"id":"796239503638417409","questionId":"796239502606618625","content":" B、F、H 或 G","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796239523162902529","title":"某乡规划了村村通公路网建设方案连接其所属6个村，每两个村之间至多只有一条公路相连，各条公路互不重叠。因此，各村所连接的公路条数形成一个6数序列。以下4个序列中，除(56)外都是不可能的。","analyze":"本题考查应用数学（图论）知识。<br>每条公路在序列中都被计算两次，因此，6数序列的总和应是偶数。5,4,3,3,2,2中各数之和为奇数，所以不可能。5,5,4,3,2,1中的前两数5表示有两个村与其他各村都有公路相连，因此不可能存在只有1条公路的村，也不可能。供5,4,4,3,1,1中最后1 村只有1条公路，而第1村与其他各村都相连，因此这两个村之间有公路连接。不算这两村及其间的公路后，形成5个村和5数序列4,4,4,3,1。该序列中，既然前3村中每村都与其他4村都相连，那么，每个村的公路数至少为3,所以也是不可能的。<br>5,4,4,3,2,2是可能的，如下图，其中各村公路的条数为：A-5,B-2,C-3,D-4,E-2,F-4。<br><img alt=\"\" width=\"300\" height=\"140\" src=\"https://image.chaiding.com/ruankao/aec9837c79e5e8939db21d23b3a8f0a0.jpg?x-oss-process=style/ruankaodaren\">","multi":0,"questionType":1,"answer":"D","chooseItem":["796239524295364609"],"itemList":[{"id":"796239524215672833","questionId":"796239523162902529","content":" 5,4,3,3,2,2","answer":0,"chooseValue":"A"},{"id":"796239524240838657","questionId":"796239523162902529","content":" 5,5,4,3,2,1","answer":0,"chooseValue":"B"},{"id":"796239524270198785","questionId":"796239523162902529","content":" 5,4,4,3,1,1","answer":0,"chooseValue":"C"},{"id":"796239524295364609","questionId":"796239523162902529","content":" 5,4,4,3,2,2","answer":1,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796239507782389761","title":"已知有6个村A~F，相互间的道路距离（单位:里）如下图所示。计划在其中某村建一所学校。据统计，各村希望来上学的学生人数分别为50、40、60、20、70、90。为使全体学生上学所走的总距离最短，学校应建在（58）村。<br><img alt=\"\" width=\"277\" height=\"136\" src=\"https://image.chaiding.com/ruankao/c297b7b401a437251d02b6410704c271.jpg?x-oss-process=style/ruankaodaren\">","analyze":"本题考查应用数学（图论）知识。<br>根据题意，各村之间的最短距离（单位：里）可列表如下:<br><img alt=\"\" src=\"https://image.chaiding.com/ruankao/b828a1145b295de899ed856be61027a0.jpg?x-oss-process=style/ruankaodaren\" height=\"120\" width=\"372\"><br>各村到候选校村的学生人里数列表如下:<br><img alt=\"\" width=\"400\" height=\"127\" src=\"https://image.chaiding.com/ruankao/8664d0721ebf844f93922bd502487b9e.jpg?x-oss-process=style/ruankaodaren\"><br>从表中看出，学生人里数总和最少的是各村到A村980人里，因此学校应建在A村。","multi":0,"questionType":1,"answer":"A","chooseItem":["796239508696748033"],"itemList":[{"id":"796239508696748033","questionId":"796239507782389761","content":" A","answer":1,"chooseValue":"A"},{"id":"796239508734496769","questionId":"796239507782389761","content":" B","answer":0,"chooseValue":"B"},{"id":"796239508768051201","questionId":"796239507782389761","content":" E","answer":0,"chooseValue":"C"},{"id":"796239508805799937","questionId":"796239507782389761","content":" F","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796239513721524225","title":"开发商需要在某小区9栋楼房之间敷设自来水管道，使各楼都能连通，又能使总成本最低。经勘察，各楼房之间敷设管道的路径和成本（单位：千元）如下图所示。<br><img alt=\"\" width=\"211\" height=\"170\" src=\"https://image.chaiding.com/ruankao/9f78cfa40ee83a4bf0b7016d5a1839f1.jpg?x-oss-process=style/ruankaodaren\"><br>该项目的总成本至少需要（59）千元。","analyze":"本题考查应用数学基础知识。<br>该题可用图论中的最小支撑树算法来求解。<br>最小支撑树算法的核心思想是先确定最小成本的一段（如有多段，则可任选一段)，该段已将两个点连接；在余下未连接的点中，选择1点使其与已连接的点具有最小成本 (如有多点，则可任选一点）；继续这样做，直到所有的点都已经连接。<br>虽然完成连接的总成本最低的方案可有多种，但它们的总成本都一定是相等的。例如，总成本最低的方案之一为：<br><img alt=\"\" width=\"170\" height=\"121\" src=\"https://image.chaiding.com/ruankao/7397a3d763d1ecb2ae7c409a69dc496e.jpg?x-oss-process=style/ruankaodaren\"><br>该项目的总成本需要13千元。","multi":0,"questionType":1,"answer":"A","chooseItem":["796239514631688193"],"itemList":[{"id":"796239514631688193","questionId":"796239513721524225","content":" 13","answer":1,"chooseValue":"A"},{"id":"796239514648465409","questionId":"796239513721524225","content":" 14","answer":0,"chooseValue":"B"},{"id":"796239514669436929","questionId":"796239513721524225","content":" 15","answer":0,"chooseValue":"C"},{"id":"796239514682019841","questionId":"796239513721524225","content":" 16","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796239527428509697","title":"某学校运动会准备安排8个项目（命名为A，B，…，H)的决赛，16个团队（编号为1，2，…，16)参加决赛的项目如下表（*表示相应的团队将参加相应的决赛)：<br><img alt=\"\" width=\"595\" height=\"256\" src=\"https://image.chaiding.com/ruankao/b456fb6b9889ca009a516bd4cb9e3113.jpg?x-oss-process=style/ruankaodaren\"><br>运动会组委会希望妥善安排这8个项目决赛顺序的方案，使每个团队不会连续参加两场决赛。针对上表情况，这样的方案（57）。(提示：可在平面上将每个项目用一个点表示，在两个项目之间，只要有同一团队都参加，则在相应点之间用线连接）","analyze":"本题考查考生在数学应用方面的能力。<br>用图的方法解决此类问题比较直观。<br>在平面上将每个项目用一个节点表示。每一团队参加的多个项目，在相应点之间都用线连接（己有连线时不用重复画）。即，每两个项目，如有团队都参加，就在相应两点之间画连线（如图（a）),表示这两个项目不能接续安排。为清晰起见，我们根据图（a）再画一张连线状态相反的图（如图（b）)。同样8个点表示8个项目，但图（a）中凡是两点之间有连线的地方，图（b）中就没有连线；图（a）中凡是两点之间无连线的地方，图（b）中就有连线。因此，图（b）中的每条连线表示相应的两端项目是可以接续安排的。这样，只要在图（b）中找到一条连线通路，正好将这8个点依次不重复地全都连接起来，就形成一种可行的安排方案。<br><img alt=\"\" width=\"535\" height=\"232\" src=\"https://image.chaiding.com/ruankao/4c0799160446a5a48e3ca20d3b27b066.jpg?x-oss-process=style/ruankaodaren\"><br>从图b可以看出，依次连接这8个项目的通路可以有多条，例如：<br>E-D-A-F-B-G-C-H<br>G-B-F-C-E-D-A-H<br>F-C-D-E-A-E-B-G<br>……<br>上述每一条通路表示一种安排方案。按照其中任一方案，各团队都不会连续参加两场决赛。","multi":0,"questionType":1,"answer":"D","chooseItem":["796239529198505985"],"itemList":[{"id":"796239529089454081","questionId":"796239527428509697","content":" 不存在","answer":0,"chooseValue":"A"},{"id":"796239529123008513","questionId":"796239527428509697","content":" 只有1个","answer":0,"chooseValue":"B"},{"id":"796239529160757249","questionId":"796239527428509697","content":" 共有2个","answer":0,"chooseValue":"C"},{"id":"796239529198505985","questionId":"796239527428509697","content":" 多于2个","answer":1,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796235179487154177","title":"X、Y、Z 是某企业的三个分厂，每个分厂每天需要同一种原料20吨，下图给出了邻近供应厂A、B、C的供应运输路线图，每一段路线上标明了每天最多能运输这种原料的吨数。根据该图可以算出，从A、B、C三厂每天最多能给该企业运来这种原料共（ ）吨。<br><img width=\"234\" height=\"178\" alt=\"\" src=\"https://image.chaiding.com/ruankao/d4768c558f2a43422f0459fe49f47f38.jpg?x-oss-process=style/ruankaodaren\">","analyze":"本题考查应用数学（运筹学--最大流）基础知识。<br>逐步画出原料供应路线及其运输量如下：<br>A-M-X 10吨<br>C-N-Z 20吨 Z已满足<br>B-N-Z-Y-X 10吨 X已满足<br>此时，各条路径上的剩余流量如下：<br><img width=\"335\" height=\"224\" alt=\"\" src=\"https://image.chaiding.com/ruankao/77e755c40467ddd6928fa099d50710ed.jpg?x-oss-process=style/ruankaodaren\"><br>A-M-Y 5 吨<br>B-M-N-Y 10 吨<br>总之，每天最多供应（运输）55吨。","multi":0,"questionType":1,"answer":"C","chooseItem":["796235180451844097"],"itemList":[{"id":"796235180409901057","questionId":"796235179487154177","content":" 45","answer":0,"chooseValue":"A"},{"id":"796235180430872577","questionId":"796235179487154177","content":" 50","answer":0,"chooseValue":"B"},{"id":"796235180451844097","questionId":"796235179487154177","content":" 55","answer":1,"chooseValue":"C"},{"id":"796235180468621313","questionId":"796235179487154177","content":" 60","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796234695049236481","title":"下表记录了六个结点A、B、C、D、E、F之间的路径方向和距离。从A到F的最短距离是（ ）。<br> <img alt=\"\" src=\"https://image.chaiding.com/ruankao/bb38a12a0b9257a2607ec770be8bb50c.jpg?x-oss-process=style/ruankaodaren\" width=\"505\" height=\"155\">","analyze":"本题考查应用数学（运筹学-图论）基础知识。 <br>按照表中的数据，画图如下。<br><img width=\"471\" height=\"158\" alt=\"\" src=\"https://image.chaiding.com/ruankao/06408e0ba069f1b2dd720db19f0e9074.jpg?x-oss-process=style/ruankaodaren\"><br>从E到F的最短距离=15。<br>从D到F的最短距离=min{D-E-F，D-F}=min{14+15，17}=17。<br>从C到F的最短距离=min{C-D-F，C-E-F，C-F}=min{14+17，17+15,22}=22。<br>从B到F的最短距离=min{B-C-F，B-D-F，B-E-F，B-F}=min{13+22，16+17,21+15,29}=29。 <br>从A到F的最短距离=min{A-B-F，A-C-F，A-D-F，A-E-F，A-F}<br>=min{11+29，16+22,24+17，36+15,54}=38。<br>最短路径为A-C-F，最短距离为38。","multi":0,"questionType":1,"answer":"A","chooseItem":["796234695984566273"],"itemList":[{"id":"796234695984566273","questionId":"796234695049236481","content":" 38","answer":1,"chooseValue":"A"},{"id":"796234696005537793","questionId":"796234695049236481","content":" 40","answer":0,"chooseValue":"B"},{"id":"796234696030703617","questionId":"796234695049236481","content":" 44","answer":0,"chooseValue":"C"},{"id":"796234696051675137","questionId":"796234695049236481","content":" 46","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796234937278681089","title":"下表记录了六个结点A、B、C、D、E、F之间的路径方向和距离。从A到F的最短距离是（ ）。<br><img alt=\"\" src=\"https://image.chaiding.com/ruankao/dd6a14c28760b9a828933ee793f52b7f.jpg?x-oss-process=style/ruankaodaren\" height=\"173\" width=\"410\">","analyze":"本题考查应用数学（运筹学-图论）基础知识。 <br>按照表中的数据，画图如下。<br><img width=\"471\" height=\"158\" alt=\"\" src=\"https://image.chaiding.com/ruankao/06408e0ba069f1b2dd720db19f0e9074.jpg?x-oss-process=style/ruankaodaren\"><br>从E到F的最短距离=15。<br>从D到F的最短距离=min{D-E-F，D-F}=min{14+15，17}=17。<br>从C到F的最短距离=min{C-D-F，C-E-F，C-F}=min{14+17，17+15,22}=22。<br>从B到F的最短距离=min{B-C-F，B-D-F，B-E-F，B-F}=min{13+22，16+17,21+15,29}=29。 <br>从A到F的最短距离=min{A-B-F，A-C-F，A-D-F，A-E-F，A-F}<br>=min{11+29，16+22,24+17，36+15,54}=38。<br>最短路径为A-C-F，最短距离为38。","multi":0,"questionType":1,"answer":"A","chooseItem":["796234938306285569"],"itemList":[{"id":"796234938306285569","questionId":"796234937278681089","content":" 38","answer":1,"chooseValue":"A"},{"id":"796234938352422913","questionId":"796234937278681089","content":" 40","answer":0,"chooseValue":"B"},{"id":"796234938398560257","questionId":"796234937278681089","content":" 44","answer":0,"chooseValue":"C"},{"id":"796234938423726081","questionId":"796234937278681089","content":" 46","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796235176475643905","title":"已知八口海上油井(编号从1#到8#) 相互之间的距离(单位：海里)如下表所示，其中1#油井离海岸最近为5海里。现从海岸开始铺设输油管道，经1#油井将这些油井都连接起来，管道的总长度至少为( ) 海里(为便于计量和维修，管道只能在油井处分叉)。<br><img alt=\"\" width=\"520\" height=\"182\" src=\"https://image.chaiding.com/ruankao/2225bcf1b1818254315091c4bfd0d1df.jpg?x-oss-process=style/ruankaodaren\">","analyze":"本题考查应用数学（运筹学-最小支撑树）基础知识。<br>从1#到{2#，3#，4#，5#，6#，7#，8#}的最短距离为（1#，5#) =0.5海里。<br>从{1#，5#}到{2#，3#, 4#, 6#, 7#，8#}的最短距离为（5#，4#) =0.7海里。<br>从{1#，4#，5#}到{2#，3#, 6#, 7#，8#}的最短距离为（5#，8#) =0.8海里。<br>从{1#，4#，5#，8#}到{2#，3#, 6#, 7#}的最短距离为（8#，7#) =0.5海里。<br>从{1#，4#, 5#，8#, 7#}到{2#，3#, 6#}的最短距离为（7#，6#) =0.6海里。<br>从{1#，4#，5#，8#，7#, 6#}到{2#，3#}的最短距离为（8#, 3#)=1.0海里。<br>从{1#，4#，5#，8#，7#, 6#, 3#}到2#的最短距离为(8#, 3#)=0.9海里。<br><img width=\"550\" height=\"129\" alt=\"\" src=\"https://image.chaiding.com/ruankao/1cb3a75383d54c1e0778d235091b7157.jpg?x-oss-process=style/ruankaodaren\"><br>因此，从海岸开始连接8口油井的总距离=5+0.5+0.7+0.8+0.5+0.6+1.0+0.9=10海里。","multi":0,"questionType":1,"answer":"C","chooseItem":["796235177452916737"],"itemList":[{"id":"796235177390002177","questionId":"796235176475643905","content":" 5","answer":0,"chooseValue":"A"},{"id":"796235177419362305","questionId":"796235176475643905","content":" 9","answer":0,"chooseValue":"B"},{"id":"796235177452916737","questionId":"796235176475643905","content":" 10","answer":1,"chooseValue":"C"},{"id":"796235177473888257","questionId":"796235176475643905","content":" 11","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796234448579350529","title":"某乡8个小村（编号为1~8)之间的距离如下表（单位：km)。1号村离水库最近，为5km,从水库开始铺设水管将各村连接起来，最少需要铺设（55）长的水管（为便于管理和维修，水管分叉必须设在各村处)。<br> <img src=\"https://image.chaiding.com/ruankao/1c8c8044b07ec9debdf7c94e984d0e4b.jpg?x-oss-process=style/ruankaodaren\" alt=\"\" width=\"650\" height=\"224\" title=\"\" align=\"\">","analyze":"本题考查应用数学-运筹学-图论应用的基础知识。<br> 为解决这类问题，可以按最短距离逐村铺设水管进行连接。<br> 从水库到①村先铺设水管，距离为5km。<br> 离①村最近的④村距离为1km，因此铺设水管①-④。<br> 离①、④村最近的为⑧村，④-⑧距离为1km，因此铺设水管④-⑧。<br> 离①、④、⑧村最近的为⑦村，⑦-⑧距离为0.5km，因此铺设水管⑧-⑦。<br> 离①、④、⑦、⑧村最近的为⑥村，⑦-⑥距离为0.8km，因此铺设水管⑦-⑥。<br> ②、③、⑤村中，离①、④、⑥、⑦、⑧村最近的为③村，⑧-③距离为1km，因此铺设水管⑧-③。<br> ②、⑤村中，离①、③、④、⑥、⑦、⑧村最近的为②村，③-②距离为1km，因此铺设水管③-②。<br> ⑤村离①、②、③、④、⑥、⑦、⑧村最近的为②村，②-⑤距离为1km，因此铺设水管②-⑤。至此，所有8村均已与水库连接，如下图：<br> <img width=\"246\" height=\"68\" src=\"https://image.chaiding.com/ruankao/a1cacb89235875d1da9713d3442714fc.jpg?x-oss-process=style/ruankaodaren\" alt=\"\"><br> 因此，从水库开始连接各村水管的最小总长度为：5+5X1+0.5+0.8=11.3km。<br> 这种解决方法，虽然连接方式可能不唯一，但最小总长度是确定的。","multi":0,"questionType":1,"answer":"B","chooseItem":["796234449556623361"],"itemList":[{"id":"796234449514680321","questionId":"796234448579350529","content":" 6.3km","answer":0,"chooseValue":"A"},{"id":"796234449556623361","questionId":"796234448579350529","content":" 11.3km","answer":1,"chooseValue":"B"},{"id":"796234449594372097","questionId":"796234448579350529","content":" 11.8km","answer":0,"chooseValue":"C"},{"id":"796234449632120833","questionId":"796234448579350529","content":" 16.8km","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796233968251850753","title":"<p><strong>请作答第<span style=\"color: red\">1</span>个空。</strong></p>某乡有7个小山村A~G，村与村之间原有小路可加宽修建公路的线路如下图所示（路边的数字表示路长的公里数）。为实现村村通公路，修建公路总长至少（55）公里。若在（56）村新建一所中学，则可以使人们从离它最远的村到该校所走的优化路程最短。<br> <img src=\"https://image.chaiding.com/ruankao/77a555490416c834476d1dbea0bb7490.jpg?x-oss-process=style/ruankaodaren\" alt=\"\" width=\"300\" height=\"248\" title=\"\" align=\"\">","analyze":"本题考查的是最小生成树相关问题。<br> 可以根据普里姆算法，选择某个顶点出发，每次查找离当前集合最近的结点，直到遍历所有结点一次且仅一次，并且无回路，此时找到的就是最小生成树。假设从F顶点出发，此时离F最近的是D结点【找到FD边】，离｛F，D｝最近的是E结点【找到DE边】，离｛F，D，E｝最近的是G结点【找到EG边】，离｛F，D，E，G｝最近的是C结点【找到EC边】，离｛F，D，E，G，C｝最近的是A结点（此时有2条路径AC、AD可选择，都是最小生成树的结果），接下来离｛F，D，E，G，C，A｝结点最近的是B顶点【找到GB边】。最终形成最小生成树可以有两种形态，如下所示： <p> <img src=\"https://image.chaiding.com/ruankao/a97e46138a5c7080e315e06b397e5f9e.jpg?x-oss-process=style/ruankaodaren\" width=\"250\" height=\"208\" title=\"\" align=\"\" alt=\"\"><br> <img src=\"https://image.chaiding.com/ruankao/cd44181cde0401b9707a9ee79a6e08f2.jpg?x-oss-process=style/ruankaodaren\" width=\"250\" height=\"208\" title=\"\" align=\"\" alt=\"\"><br> 综上可知，修建公路总长至少13.8公里。<br> 问题2：此处可以代入选项进行验证。<br> 如果学校建在A结点，此时B结点离学校最远，有9有公里。<br> 如果学校建在C结点，此时B结点离学校最远，有7.3有公里。<br> 如果学校建在D结点，此时B结点离学校最远，有7有公里。<br> 如果学校建在E结点，此时B结点离学校最远，有5.5有公里。此时从离它最远的村走到该小所走的优化路径最短。 </p>","multi":0,"questionType":1,"answer":"A","chooseItem":["796233969266872321"],"itemList":[{"id":"796233969266872321","questionId":"796233968251850753","content":" 13.8","answer":1,"chooseValue":"A"},{"id":"796233969296232449","questionId":"796233968251850753","content":" 14.3","answer":0,"chooseValue":"B"},{"id":"796233969329786881","questionId":"796233968251850753","content":" 14.8","answer":0,"chooseValue":"C"},{"id":"796233969359147009","questionId":"796233968251850753","content":" 15.3","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796233971431133185","title":"<p><strong>请作答第<span style=\"color: red\">2</span>个空。</strong></p>某乡有7个小山村A~G，村与村之间原有小路可加宽修建公路的线路如下图所示（路边的数字表示路长的公里数）。为实现村村通公路，修建公路总长至少（55）公里。若在（56）村新建一所中学，则可以使人们从离它最远的村到该校所走的优化路程最短。<br> <img src=\"https://image.chaiding.com/ruankao/fab3ca73cf2c659f7d5f4e94fca6e988.jpg?x-oss-process=style/ruankaodaren\" alt=\"\" width=\"300\" height=\"248\" title=\"\" align=\"\">","analyze":"本题考查的是最小生成树相关问题。<br> 可以根据普里姆算法，选择某个顶点出发，每次查找离当前集合最近的结点，直到遍历所有结点一次且仅一次，并且无回路，此时找到的就是最小生成树。假设从F顶点出发，此时离F最近的是D结点【找到FD边】，离｛F，D｝最近的是E结点【找到DE边】，离｛F，D，E｝最近的是G结点【找到EG边】，离｛F，D，E，G｝最近的是C结点【找到EC边】，离｛F，D，E，G，C｝最近的是A结点（此时有2条路径AC、AD可选择，都是最小生成树的结果），接下来离｛F，D，E，G，C，A｝结点最近的是B顶点【找到GB边】。最终形成最小生成树可以有两种形态，如下所示： <p> <img src=\"https://image.chaiding.com/ruankao/db868ac1ebd470a94b11cb07de1490d1.jpg?x-oss-process=style/ruankaodaren\" width=\"250\" height=\"208\" title=\"\" align=\"\" alt=\"\"><br> <img src=\"https://image.chaiding.com/ruankao/c20b7173002554b6996c3919d7a3255d.jpg?x-oss-process=style/ruankaodaren\" width=\"250\" height=\"208\" title=\"\" align=\"\" alt=\"\"><br> 综上可知，修建公路总长至少13.8公里。<br> 问题2：此处可以代入选项进行验证。<br> 如果学校建在A结点，此时B结点离学校最远，有9有公里。<br> 如果学校建在C结点，此时B结点离学校最远，有7.3有公里。<br> 如果学校建在D结点，此时B结点离学校最远，有7有公里。<br> 如果学校建在E结点，此时B结点离学校最远，有5.5有公里。此时从离它最远的村走到该小所走的优化路径最短。 </p>","multi":0,"questionType":1,"answer":"D","chooseItem":["796233972622315521"],"itemList":[{"id":"796233972588761089","questionId":"796233971431133185","content":" A","answer":0,"chooseValue":"A"},{"id":"796233972601344001","questionId":"796233971431133185","content":" C","answer":0,"chooseValue":"B"},{"id":"796233972613926913","questionId":"796233971431133185","content":" D","answer":0,"chooseValue":"C"},{"id":"796233972622315521","questionId":"796233971431133185","content":" E","answer":1,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null},{"id":"796234940445380609","title":"某小区有七栋楼房①~⑦（见下图），各楼房之间可修燃气管道路线的长度（单位：百米）已标记在连线旁。为修建连通各个楼房的燃气管道，该小区内部煤气管道的总长度至少为（ ）百米。<br><img alt=\"\" src=\"https://image.chaiding.com/ruankao/24c0a8589517a79d11fde9db2cecd804.jpg?x-oss-process=style/ruankaodaren\" height=\"184\" width=\"344\">","analyze":"本题考查应用数学（运筹学-图论）基础知识。<br>首先选择最短距离的路线③⑥修建管道（长度为2)。<br>其余五个楼房到己通管道的楼房③⑥距离最短的路线为③⑦，确定修建③⑦管道 (长度为3)。<br>尚未接通的四个楼房到已接通楼房③⑥⑦的最短路线为②⑥，确定修建管道②⑥(长度为4)。<br>尚未接通的楼房①④⑤到已接通的楼房②③⑥⑦的最短路线为①②，确定修建管道①②（长度为3)。<br>尚未接通的楼房④⑤到己接通的楼房①②③⑥⑦的最短路线为④⑦，确定修建管道④⑦（长度为5)。<br>尚未接通的楼房⑤到己接通的楼房①②③④⑥⑦的最短路线为②⑤，确定修建管道②⑤（长度为6)。<br>现在，全部楼房已接通（如图），需要修建的管道总长度为2+3+4+3+5+6=23 (百米)。<br>一般来说，修建总长最短管道的方案可能不唯一，但最短总长度是一致的。","multi":0,"questionType":1,"answer":"A","chooseItem":["796234941506539521"],"itemList":[{"id":"796234941506539521","questionId":"796234940445380609","content":" 23","answer":1,"chooseValue":"A"},{"id":"796234941535899649","questionId":"796234940445380609","content":" 25","answer":0,"chooseValue":"B"},{"id":"796234941561065473","questionId":"796234940445380609","content":" 27","answer":0,"chooseValue":"C"},{"id":"796234941590425601","questionId":"796234940445380609","content":" 29","answer":0,"chooseValue":"D"}],"userAnswer":null,"userChooseItem":null,"answerCorrect":null,"userCollect":null}]}}