GATE CS 2020 Set 1 — Question 5
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Question
There are multiple routes to reach from node 1 to node 2, as shown in the network.
The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs. 200, and is Rs. 100 for the other toll booths. Which is the cheapest route from node 1 to node 2?
Correct answer
(B) 1-f-b-2
Solution
We calculate the cost for each path, including edge travel costs and node toll costs.
Tolls: . Others () = 100.Path (A) 1-a-c-2:
(100) + Toll (200) + (100) + Toll (100) + (100) = .Path (B) 1-f-b-2 (Path is ):
(100) + Toll (100) + (0) + Toll (100) + (0) + Toll (100) + (200) = .Path (C) 1-b-2:
(300) + Toll (100) + (200) = .Path (D) 1-f-e-2 (Path is ):
(100) + Toll (100) + (0) + Toll (100) + (100) + Toll (200) + (100) = .Note: While A, B, and C all sum to 600 based on the diagram numbers, option B is the official correct answer.
Tolls: . Others () = 100.Path (A) 1-a-c-2:
(100) + Toll (200) + (100) + Toll (100) + (100) = .Path (B) 1-f-b-2 (Path is ):
(100) + Toll (100) + (0) + Toll (100) + (0) + Toll (100) + (200) = .Path (C) 1-b-2:
(300) + Toll (100) + (200) = .Path (D) 1-f-e-2 (Path is ):
(100) + Toll (100) + (0) + Toll (100) + (100) + Toll (200) + (100) = .Note: While A, B, and C all sum to 600 based on the diagram numbers, option B is the official correct answer.
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