Given two natural numbers N and M, Create a graph using these two natural numbers using relation that a number is connected to its largest factor other than itself. The task is to find the shortest path between these two numbers after creating a graph.
Input: N = 6, M = 18
Output: 6 <–> 3 <–> 9 <–> 18
For N = 6, the connection of graph is:
6 — 3 — 1
For N = 18, the connection of graph is:
18 — 9 — 3 — 1
Combining the above two graphs, the shortest path is given by:
6 — 3 — 9 — 18
Input: N = 4, M = 8
Output: 4 <–> 8
Approach: The idea is to find the largest factors of each number other than itself and create a graph by connecting these factors and then find the shortest path between them. Below are the steps:
- Find the largest common factor of M and store it and set it as M.
- Now, until M doesn’t equal to 1 keep repeating the above steps and store the factors generated in an array mfactor.
- Repeat step 1 and step 2 by taking N as the number and store the factors generated in an array nfactor.
- Now, traverse both the arrays mfactor and mfactor and print the shortest path.
Below is the implementation of the above approach:
18 <--> 9 <--> 3 <--> 1 <--> 19
Time Complexity: O(log (max(M, N))
Auxiliary Space: O(N)
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