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Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is 

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UGC NET Computer Science (Paper 2) 2020 Official Paper
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  1. 23
  2. 99
  3. 4
  4. 7

Answer (Detailed Solution Below)

Option 4 : 7
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UGC NET Paper 1: Held on 21st August 2024 Shift 1
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Detailed Solution

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The correct answer is option 4.

Key Points

Edge set consists of edges from i to j, using either two conditions are j = i + 1 or j = 3i
Second choice helps us to move from 1 to 100. The trick to slot this is to think the other way around. Try to find a 100 to 1 trail, instead of having a 1 trail to 100.
So, the edge sequence with the minimum number of edges is
1 → 3 → 9 → 10 → 11 → 33 → 99 → 100
which consists of 7 edges.

Hence the correct answer is 7.

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