# Print Nth Stepping or Autobiographical number

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, ….

Examples:

```Input: N = 16
Output: 32
Explanation:
16th Stepping number is 32.

Input: N = 14
Output: 22
Explanation:
14th Stepping number is 22.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

## C++

 `// C++ implementation to find ` `// N’th stepping natural Number ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the ` `// Nth stepping natural number ` `int` `NthSmallest(``int` `K) ` `{ ` ` `  `    ``// Declare the queue ` `    ``queue<``int``> Q; ` ` `  `    ``int` `x; ` ` `  `    ``// Enqueue 1, 2, ..., 9 in this order ` `    ``for` `(``int` `i = 1; i < 10; i++) ` `        ``Q.push(i); ` ` `  `    ``// Perform K operation on queue ` `    ``for` `(``int` `i = 1; i <= K; i++) { ` ` `  `        ``// Get the ith Stepping number ` `        ``x = Q.front(); ` ` `  `        ``// Perform Dequeue from the Queue ` `        ``Q.pop(); ` ` `  `        ``// If x mod 10 is not equal to 0 ` `        ``if` `(x % 10 != 0) { ` ` `  `            ``// then Enqueue 10x + (x mod 10) - 1 ` `            ``Q.push(x * 10 + x % 10 - 1); ` `        ``} ` ` `  `        ``// Enqueue 10x + (x mod 10) ` `        ``Q.push(x * 10 + x % 10); ` ` `  `        ``// If x mod 10 is not equal to 9 ` `        ``if` `(x % 10 != 9) { ` ` `  `            ``// then Enqueue 10x + (x mod 10) + 1 ` `            ``Q.push(x * 10 + x % 10 + 1); ` `        ``} ` `    ``} ` ` `  `    ``// Return the dequeued number of the K-th ` `    ``// operation as the Nth stepping number ` `    ``return` `x; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``// initialise K ` `    ``int` `N = 16; ` ` `  `    ``cout << NthSmallest(N) << ``"\n"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to find ` `// N'th stepping natural Number ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `  `  `// Function to find the ` `// Nth stepping natural number ` `static` `int` `NthSmallest(``int` `K) ` `{ ` `  `  `    ``// Declare the queue ` `    ``Queue Q = ``new` `LinkedList<>(); ` `  `  `    ``int` `x = ``0``; ` `  `  `    ``// Enqueue 1, 2, ..., 9 in this order ` `    ``for` `(``int` `i = ``1``; i < ``10``; i++) ` `        ``Q.add(i); ` `  `  `    ``// Perform K operation on queue ` `    ``for` `(``int` `i = ``1``; i <= K; i++) { ` `  `  `        ``// Get the ith Stepping number ` `        ``x = Q.peek(); ` `  `  `        ``// Perform Dequeue from the Queue ` `        ``Q.remove(); ` `  `  `        ``// If x mod 10 is not equal to 0 ` `        ``if` `(x % ``10` `!= ``0``) { ` `  `  `            ``// then Enqueue 10x + (x mod 10) - 1 ` `            ``Q.add(x * ``10` `+ x % ``10` `- ``1``); ` `        ``} ` `  `  `        ``// Enqueue 10x + (x mod 10) ` `        ``Q.add(x * ``10` `+ x % ``10``); ` `  `  `        ``// If x mod 10 is not equal to 9 ` `        ``if` `(x % ``10` `!= ``9``) { ` `  `  `            ``// then Enqueue 10x + (x mod 10) + 1 ` `            ``Q.add(x * ``10` `+ x % ``10` `+ ``1``); ` `        ``} ` `    ``} ` `  `  `    ``// Return the dequeued number of the K-th ` `    ``// operation as the Nth stepping number ` `    ``return` `x; ` `} ` `  `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `  `  `    ``// initialise K ` `    ``int` `N = ``16``; ` `  `  `    ``System.out.print(NthSmallest(N)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 implementation to find ` `# N’th stepping natural Number ` ` `  `# Function to find the ` `# Nth stepping natural number ` `def` `NthSmallest(K): ` `    ``# Declare the queue ` `    ``Q ``=` `[] ` ` `  `    ``# Enqueue 1, 2, ..., 9 in this order ` `    ``for` `i ``in` `range``(``1``,``10``): ` `        ``Q.append(i) ` ` `  `    ``# Perform K operation on queue ` `    ``for` `i ``in` `range``(``1``,K``+``1``): ` `        ``# Get the ith Stepping number ` `        ``x ``=` `Q[``0``] ` ` `  `        ``# Perform Dequeue from the Queue ` `        ``Q.remove(Q[``0``]) ` ` `  `        ``# If x mod 10 is not equal to 0 ` `        ``if` `(x ``%` `10` `!``=` `0``): ` `            ``# then Enqueue 10x + (x mod 10) - 1 ` `            ``Q.append(x ``*` `10` `+` `x ``%` `10` `-` `1``) ` ` `  `        ``# Enqueue 10x + (x mod 10) ` `        ``Q.append(x ``*` `10` `+` `x ``%` `10``) ` ` `  `        ``# If x mod 10 is not equal to 9 ` `        ``if` `(x ``%` `10` `!``=` `9``): ` `            ``# then Enqueue 10x + (x mod 10) + 1 ` `            ``Q.append(x ``*` `10` `+` `x ``%` `10` `+` `1``) ` ` `  `    ``# Return the dequeued number of the K-th ` `    ``# operation as the Nth stepping number ` `    ``return` `x ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``# initialise K ` `    ``N ``=` `16` ` `  `    ``print``(NthSmallest(N)) ` ` `  `# This code is contributed by Surendra_Gangwar `

## C#

 `// C# implementation to find ` `// N'th stepping natural Number ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` `   `  `// Function to find the ` `// Nth stepping natural number ` `static` `int` `NthSmallest(``int` `K) ` `{ ` `   `  `    ``// Declare the queue ` `    ``List<``int``> Q = ``new` `List<``int``>(); ` `   `  `    ``int` `x = 0; ` `   `  `    ``// Enqueue 1, 2, ..., 9 in this order ` `    ``for` `(``int` `i = 1; i < 10; i++) ` `        ``Q.Add(i); ` `   `  `    ``// Perform K operation on queue ` `    ``for` `(``int` `i = 1; i <= K; i++) { ` `   `  `        ``// Get the ith Stepping number ` `        ``x = Q; ` `   `  `        ``// Perform Dequeue from the Queue ` `        ``Q.RemoveAt(0); ` `   `  `        ``// If x mod 10 is not equal to 0 ` `        ``if` `(x % 10 != 0) { ` `   `  `            ``// then Enqueue 10x + (x mod 10) - 1 ` `            ``Q.Add(x * 10 + x % 10 - 1); ` `        ``} ` `   `  `        ``// Enqueue 10x + (x mod 10) ` `        ``Q.Add(x * 10 + x % 10); ` `   `  `        ``// If x mod 10 is not equal to 9 ` `        ``if` `(x % 10 != 9) { ` `   `  `            ``// then Enqueue 10x + (x mod 10) + 1 ` `            ``Q.Add(x * 10 + x % 10 + 1); ` `        ``} ` `    ``} ` `   `  `    ``// Return the dequeued number of the K-th ` `    ``// operation as the Nth stepping number ` `    ``return` `x; ` `} ` `   `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `   `  `    ``// initialise K ` `    ``int` `N = 16; ` `   `  `    ``Console.Write(NthSmallest(N)); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

Output:

```32
```

Time Complexity: O(N)

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