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EXM.1.AHL.TZ0.23

pestleMathematicsAIHLPaper 1EXM· ahl-3-16-tree-and-cycle-algorithms-chinese-postman-travelling-salesmansource ↗

Sameer is trying to design a road system to connect six towns, A, B, C, D, E and F.

The possible roads and the costs of building them are shown in the graph below. Each vertex represents a town, each edge represents a road and the weight of each edge is the cost of building that road. He needs to design the lowest cost road system that will connect the six towns.

Name an algorithm that will allow Sameer to find the lowest cost road system.

[1]
a.

Find the lowest cost road system and state the cost of building it. Show clearly the steps of the algorithm.

[7]
b.
Markscheme / solution

EITHER          

Prim’s algorithm      A1

OR

Kruskal’s algorithm       A1

[1 mark]

a.

EITHER          

using Prim’s algorithm, starting at A

       A1A1A1A1A1

lowest cost road system contains roads AC, CD, CF, FE and AB       A1

cost is 20       A1

OR

using Kruskal’s algorithm

       A1A1A1A1A1

lowest cost road system contains roads CD, CF, FE, AC and AB       A1

cost is 20       A1

Note: Accept alternative correct solutions.

[7 marks]

b.
Examiners’ report
[N/A]
a.
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b.