题目
The network shown in Figure 1 represents the paths between nine attractions in a theme park. The number on each edge is the length, in metres, of the corresponding path.
[The total weight of the network is 1960 m]
(a) (i) Use Dijkstra’s algorithm to find the shortest path from A to J.
(ii) State the length of the shortest path from A to J in metres.
Sarita needs to inspect the paths between the attractions. She must travel along each path at least once.
Sarita decides to start and finish her inspection route at A. She wishes to minimise the length of her route.
(b) By considering the pairings of all relevant nodes, find the length of Sarita’s route.
Sarita now decides to start her inspection route at A, but finish at a different attraction. She must still minimise the length of her route and travel along each path at least once.
(c) (i) Determine where Sarita should finish her route. You must justify your answer.
(ii) Calculate the difference between the lengths of the two inspection routes.
题目中文翻译
图 1 表示主题公园中九个景点之间的路径网络。每条边上的数字是对应路径的长度（单位：米）。
[网络总长度为 1960 m]
(a) (i) 使用 Dijkstra 算法求从 A 到 J 的最短路径。
(ii) 说明从 A 到 J 的最短路径长度（米）。
Sarita 需要检查景点之间的路径。她必须每条路径至少经过一次。
Sarita 决定从 A 出发并回到 A。她希望最小化路线长度。
(b) 通过考虑所有相关节点的配对，求 Sarita 路线的长度。
Sarita 现在决定从 A 出发，但在不同景点结束。她仍然必须最小化路线长度且每条路径至少经过一次。
(c) (i) 确定 Sarita 应在哪里结束路线。必须说明理由。
(ii) 计算两条检查路线长度之差。