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.

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 <bits/stdc++.h>
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<Integer> 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[0];

        // 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

Javascript

<script>

// Javascript implementation to find
// N’th stepping natural Number

// Function to find the
// Nth stepping natural number
function NthSmallest(K)
{

    // Declare the queue
    var Q = [];

    var x;

    // Enqueue 1, 2, ..., 9 in this order
    for (var i = 1; i < 10; i++)
        Q.push(i);

    // Perform K operation on queue
    for (var i = 1; i <= K; i++) {

        // Get the ith Stepping number
        x = Q[0];

        // Perform Dequeue from the Queue
        Q.shift();

        // 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
// initialise K
var N = 16;
document.write( NthSmallest(N));

// This code is contributed by famously.
</script>

Output:

32

Time Complexity: O(N)

Auxiliary Space: O(N)