Given a natural number N, the task is to print the Nth Stepping or Autobiographical number.
A number is called stepping number if all adjacent digits have an absolute difference of 1. The following series is a list of Stepping natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, ….
Input: N = 16 Output: 32 Explanation: 16th Stepping number is 32. Input: N = 14 Output: 22 Explanation: 14th Stepping number is 22.
Approach: This problem can be solved using Queue data structure. First, prepare an empty queue, and Enqueue 1, 2, …, 9 in this order.
Then inorder the generate the Nth Stepping number, the following operations has to be performed N times:
- Perform Dequeue from the Queue. Let x be the dequeued element.
- If x mod 10 is not equal to 0, then Enqueue 10x + (x mod 10) – 1
- Enqueue 10x + (x mod 10).
- If x mod 10 is not equal to 9, then Enqueue 10x + (x mod 10) + 1.
The dequeued number in the N-th operation is the N-th Stepping Number.
Below is the implementation of the above approach:
Time Complexity: O(N)
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