Given two N-digit prime numbers A and B, the task is to find the minimum number of steps taken to convert A to B. Condition for the conversion is that only 1 digit of the current prime number can be modified such that the new number formed is also a prime number. If no such conversion is possible, print -1.
Note: The range of N is [1, 5].
Input: N = 4, A = 1033, B = 8179
Explanation: The steps of conversion are 1033 -> 1733 -> 3733 -> 3739 -> 3779 -> 8779 -> 8179. While changing numbers from 1033->1733, they differ by only one digit and the same happens for subsequent steps.
Input: N = 4, A = 1373, B = 8179
Input: N = 2, A = 11, B = 37
Explanation: The steps of conversion are 11 -> 17 -> 37
Approach: Using Breadth First Search Algorithm
- Find all N digit prime numbers and make a graph with these numbers.
- Consider each prime number as a node of a graph and create an edge from one node to another if they differ by a single digit.
- Apply BFS traversal and find out the number of edges between A and B.
- If no path exists, print -1.
- Else print the no. of edges, which is the required solution.
Below is the implementation of the above approach.
Time Complexity: O(102N)
Auxillary Space Complexity: O(105)
- Count of prime factors of N to be added at each step to convert N to M
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- Steps to reduce N to zero by subtracting its most significant digit at every step
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- Minimize steps to reach K from 0 by adding 1 or doubling at each step
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