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 either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is
(A)
4
(B)
7
(C)
23
(D)
99
Answer: (B)
Explanation:
The task is to find minimum number of edges in a path in G from vertex 1 to vertex 100 such that we can move to either i+1 or 3i from a vertex i.
Since the task is to minimize number of edges, we would prefer to follow 3*i. Let us follow multiple of 3. 1 => 3 => 9 => 27 => 81, now we can\'t follow multiple of 3. So we will have to follow i+1. This solution gives a long path. What if we begin from end, and we reduce by 1 if the value is not multiple of 3, else we divide by 3. 100 => 99 => 33 => 11 => 10 => 9 => 3 => 1 So we need total 7 edges.
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