Nth positive number whose absolute difference of adjacent digits is at most 1

Last Updated : 16 Nov, 2021

Given a number N, the task is to find the N^th number which has an absolute difference of 1 between every pair of its adjacent digits.
Examples:

Input : N = 5
Output : 5
Explanation:
The first 5 such numbers are 1,2,3,4 and 5.
Input : N = 15
Output : 23
Explanation:
The first 15 such numbers are 1,2,3,4,5,6,7,8,9,10,11,12,21,22 and 23.

Approach: In order to solve this problem we are using the Queue data structure.

Prepare an empty Queue, and Enqueue all integers 1 to 9 in increasing order.
Now perform the following operation N times.
- Dequeue and store in array arr which stores ith number of required type in arr[i].
- If (arr[i] % 10 != 0), then enqueue 10 * arr[i] + (arr[i] % 10) - 1.
- Enqueue 10 * arr[i] + (arr[i] % 10).
- If (arr[i] % 10 != 9), then enqueue 10 * arr[i] + (arr[i] % 10) + 1.
Return arr[N] as the answer.

Below is the implementation of the given approach:

C++

// C++ Program to find Nth number with
// absolute difference between all 
// adjacent digits at most 1.

#include <bits/stdc++.h>
using namespace std;


// Return Nth number with
// absolute difference between all 
// adjacent digits at most 1.
void findNthNumber(int N)
{
    // To store all such numbers
    long long arr[N + 1];
    
    queue<long long> q;

    // Enqueue all integers from 1 to 9 
    // in increasing order.
    for (int i = 1; i <= 9; i++)
        q.push(i);

    // Perform the operation N times so that
    // we can get all such N numbers.
    for (int i = 1; i <= N; i++) {

        // Store the front element of queue,
        // in array and pop it from queue.
        arr[i] = q.front();
        q.pop();

        // If the last digit of dequeued integer is
        // not 0, then enqueue the next such number.
        if (arr[i] % 10 != 0)
            q.push(arr[i] * 10 + arr[i] % 10 - 1);

        // Enqueue the next such number
        q.push(arr[i] * 10 + arr[i] % 10);

        // If the last digit of dequeued integer is
        // not 9, then enqueue the next such number.
        if (arr[i] % 10 != 9)
            q.push(arr[i] * 10 + arr[i] % 10 + 1);
    }
    
    cout<<arr[N]<<endl;
}

// Driver Code
int main()
{
    int N = 21;
    findNthNumber(N);
    return 0;
}

Java

// Java program to find Nth number with
// absolute difference between all 
// adjacent digits at most 1.
import java.util.*;

class GFG{

// Return Nth number with
// absolute difference between all 
// adjacent digits at most 1.
static void findNthNumber(int N)
{
    
    // To store all such numbers
    int []arr = new int[N + 1];
    
    Queue<Integer> q = new LinkedList<>();

    // Enqueue all integers from 1 to 9 
    // in increasing order.
    for(int i = 1; i <= 9; i++)
       q.add(i);

    // Perform the operation N times so 
    // that we can get all such N numbers.
    for(int i = 1; i <= N; i++)
    {
       
       // Store the front element of queue,
       // in array and pop it from queue.
       arr[i] = q.peek();
       q.remove();
       
       // If the last digit of dequeued 
       // integer is not 0, then enqueue
       // the next such number.
       if (arr[i] % 10 != 0)
           q.add(arr[i] * 10 + arr[i] % 10 - 1);
       
       // Enqueue the next such number
       q.add(arr[i] * 10 + arr[i] % 10);
       
       // If the last digit of dequeued 
       // integer is not 9, then enqueue 
       // the next such number.
       if (arr[i] % 10 != 9)
           q.add(arr[i] * 10 + arr[i] % 10 + 1);
    }
    System.out.println(arr[N]);
}

// Driver Code
public static void main(String[] args)
{
    int N = 21;
    
    findNthNumber(N);
}
}

// This code is contributed by Amit Katiyar

Python3

# Python 3 Program to find Nth number with
# absolute difference between all 
# adjacent digits at most 1.

# Return Nth number with
# absolute difference between all 
# adjacent digits at most 1.
def findNthNumber(N):
    
    # To store all such numbers
    arr = [0 for i in range(N + 1)]
    
    q = []

    # Enqueue all integers from 1 to 9 
    # in increasing order.
    for i in range(1, 10, 1):
        q.append(i)

    # Perform the operation N times so that
    # we can get all such N numbers.
    for i in range(1, N+1, 1):
        
        # Store the front element of queue,
        # in array and pop it from queue.
        arr[i] = q[0]
        q.remove(q[0])

        # If the last digit of dequeued integer is
        # not 0, then enqueue the next such number.
        if (arr[i] % 10 != 0):
            q.append(arr[i] * 10 + arr[i] % 10 - 1)

        # Enqueue the next such number
        q.append(arr[i] * 10 + arr[i] % 10)

        # If the last digit of dequeued integer is
        # not 9, then enqueue the next such number.
        if (arr[i] % 10 != 9):
            q.append(arr[i] * 10 + arr[i] % 10 + 1)
    
    print(arr[N])

# Driver Code
if __name__ == '__main__':
    
    N = 21
    findNthNumber(N)

# This code is contributed by Samarth

// C# program to find Nth number with
// absolute difference between all 
// adjacent digits at most 1.
using System;
using System.Collections.Generic;

class GFG{

// Return Nth number with
// absolute difference between all 
// adjacent digits at most 1.
static void findNthNumber(int N)
{
    
    // To store all such numbers
    int []arr = new int[N + 1];
    
    Queue<int> q = new Queue<int>();

    // Enqueue all integers from 1 to 9 
    // in increasing order.
    for(int i = 1; i <= 9; i++)
       q.Enqueue(i);

    // Perform the operation N times so 
    // that we can get all such N numbers.
    for(int i = 1; i <= N; i++)
    {
       
       // Store the front element of queue,
       // in array and pop it from queue.
       arr[i] = q.Peek();
       q.Dequeue();
       
       // If the last digit of dequeued 
       // integer is not 0, then enqueue
       // the next such number.
       if (arr[i] % 10 != 0)
           q.Enqueue(arr[i] * 10 +
                     arr[i] % 10 - 1);
       
       // Enqueue the next such number
       q.Enqueue(arr[i] * 10 + arr[i] % 10);
       
       // If the last digit of dequeued 
       // integer is not 9, then enqueue 
       // the next such number.
       if (arr[i] % 10 != 9)
           q.Enqueue(arr[i] * 10 + 
                     arr[i] % 10 + 1);
    }
    Console.WriteLine(arr[N]);
}

// Driver Code
public static void Main(String[] args)
{
    int N = 21;
    
    findNthNumber(N);
}
}

// This code is contributed by Rohit_ranjan

JavaScript

<script>

    // JavaScript program to find Nth number with
    // absolute difference between all
    // adjacent digits at most 1.
    
    // Return Nth number with
    // absolute difference between all
    // adjacent digits at most 1.
    function findNthNumber(N)
    {

        // To store all such numbers
        let arr = new Array(N + 1);

        let q = [];

        // Enqueue all integers from 1 to 9
        // in increasing order.
        for(let i = 1; i <= 9; i++)
           q.push(i);

        // Perform the operation N times so
        // that we can get all such N numbers.
        for(let i = 1; i <= N; i++)
        {

           // Store the front element of queue,
           // in array and pop it from queue.
           arr[i] = q[0];
           q.shift();

           // If the last digit of dequeued
           // integer is not 0, then enqueue
           // the next such number.
           if (arr[i] % 10 != 0)
               q.push(arr[i] * 10 + arr[i] % 10 - 1);

           // Enqueue the next such number
           q.push(arr[i] * 10 + arr[i] % 10);

           // If the last digit of dequeued
           // integer is not 9, then enqueue
           // the next such number.
           if (arr[i] % 10 != 9)
               q.push(arr[i] * 10 + arr[i] % 10 + 1);
        }
        document.write(arr[N] + "</br>");
    }
    
    let N = 21;
     
    findNthNumber(N);

</script>

Output:

Time Complexity: O(N)

Auxiliary Space: O(N)

Program to delete Nth digit of a Number

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Nth positive number whose absolute difference of adjacent digits is at most 1

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