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

Given a number N, the task is to find the Nth 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.

## Recommended: Please solve it on {IDE} first, before moving on to the solution.

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 ` `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<

## 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 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 `

Output:

```45
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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Improved By : ipg2016107, amit143katiyar