题目
Figure 1 represents a network of roads. The number on each edge represents the length, in miles, of the corresponding road. Jan wishes to travel from A to J. She wishes to minimise the distance she travels.
[The total weight of the network is 193]
(a) Use Dijkstra’s algorithm to find the shortest path from A to J. Obtain the shortest path and state its length.
On Monday, Jan needs to travel from her gym at J to her home at H via her office at A.
(b) State the shortest path from J to H via A and its length.
On Tuesday, Jan needs to check each road. She must travel along each road at least once. Jan must start and finish at A.
(c) Use the route inspection algorithm to find the length of the shortest inspection route. State the roads that should be repeated. You should make your method and working clear.
On Wednesday, Jan decides to start her inspection route at G but can finish her route at a different node. The inspection route must still traverse each road at least once.
(d) Determine where the route should finish so that the length of the inspection route is minimised. You must give reasons for your answer and state the length of the route.
题目中文翻译
图 1 表示一个道路网络。每条边上的数字表示对应道路的长度（单位：英里）。Jan 希望从 A 到 J。她希望最小化旅行距离。
[网络总权重为 193]
(a) 使用 Dijkstra 算法找到从 A 到 J 的最短路径。获得最短路径并写出其长度。
周一，Jan 需要从健身房 J 经过办公室 A 回到家 H。
(b) 写出从 J 经过 A 到 H 的最短路径及其长度。
周二，Jan 需要检查每条道路。她必须每条道路至少经过一次。Jan 必须从 A 出发并回到 A。
(c) 使用路线检查算法找到最短检查路线的长度。写出应该重复的道路。必须清楚说明方法和计算过程。
周三，Jan 决定从 G 开始检查路线，但可以在不同的节点结束。检查路线仍然必须每条道路至少经过一次。
(d) 确定路线应该在哪里结束以使检查路线长度最短。必须给出理由并写出路线长度。