Aspire Faculty ID #18936 · Topic: UGC NET Computer Science Nov 2020 (Paper II) · Just now
UGC NET Computer Science Nov 2020 (Paper II)

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 _____

Solution

We need shortest path from 1 to 100 using operations:

$i \to i+1$ or $i \to 3i$

A shortest path is:

$1 \to 3 \to 9 \to 10 \to 11 \to 33 \to 99 \to 100$

Number of edges $=7$

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