OCR D1 2013 June — Question 5

Exam BoardOCR
ModuleD1 (Decision Mathematics 1)
Year2013
SessionJune
TopicNumber Theory

5 This question uses the same network as question 4. The total weight of the arcs in the network is 224.
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  1. Apply Dijkstra's algorithm to the network, starting at \(A\), to find the shortest route from \(A\) to \(G\).
  2. Dijkstra's algorithm has quadratic order (order \(n ^ { 2 }\) ). It takes 2.25 seconds for a certain computer to apply Dijkstra's algorithm to a network with 7 vertices. Calculate approximately how many hours it will take to apply Dijkstra's algorithm to a network with 1400 vertices.
  3. How much shorter would the path \(C E\) need to be for it to become part of a shortest path from \(A\) to \(G\) ? Following a landslip, the paths \(A C\) and \(C E\) become blocked and cannot be used. A warden needs to travel along all the remaining paths to check that there are no more landslips.
  4. Find the shortest distance that the warden must travel, assuming that she starts and ends at vertex \(C\). Show your working.