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 numberint 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 Codeint main(){ // initialise K int N = 16; cout << NthSmallest(N) << "\n"; return 0;} |
Java
// Java implementation to find// N'th stepping natural Numberimport java.util.*;class GFG{ // Function to find the// Nth stepping natural numberstatic 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 Codepublic 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 numberdef 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 Codeif __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 Numberusing System;using System.Collections.Generic;class GFG{ // Function to find the// Nth stepping natural numberstatic 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 Codepublic 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 numberfunction 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 Kvar N = 16;document.write( NthSmallest(N));// This code is contributed by famously.</script> |
Output:
32
Time Complexity: O(N)
Auxiliary Space: O(N)
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