Posted on by Kalkicode
Code Backtracking

Print all N digit jumping numbers

In this article, we will discuss the problem of printing all N-digit jumping numbers. Jumping numbers are numbers where the absolute difference between adjacent digits is always 1. For example, 121 and 3434 are jumping numbers, but 123 and 222 are not.

Problem Statement

Given an integer N, we need to find and print all N-digit jumping numbers. The output should be in ascending order.

Example

Let's understand the problem with an example. Suppose N = 2. The possible jumping numbers of 2 digits are: 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98. These numbers have the absolute difference between adjacent digits as 1.

Algorithm

To solve this problem, we can use a recursive approach. Here is the algorithm:

    1. Define a function called printSequence() that takes an array of integers and the number of elements to be printed.
    2. Inside the printSequence() function, iterate over the array and print each element.
    3. Define a recursive function called findCombination() that takes the result array, the current index, and the total number of digits as parameters.
    4. In the findCombination() function, check the base cases:
       - If the current index is equal to the total number of digits, call the printSequence() function to print the current combination and return.
       - If the current index is greater than the total number of digits, return.
    5. If the current index is greater than 0, check the previous digit:
       - If the previous digit is not 0, set the new digit by reducing the previous digit by one and recursively call findCombination() with the updated index.
       - If the previous digit is not 9, set the new digit by increasing the previous digit by one and recursively call findCombination() with the updated index.
    6. If the current index is 0, iterate from 1 to 9 and set each digit as the first element of the result array. Recursively call findCombination() with the updated index.
    7. Define a function called jumpingNumber() that takes an integer N as a parameter.
    8. Inside the jumpingNumber() function, check if N is less than or equal to 0. If so, return.
    9. Initialize the result array.
    10. If N is equal to 1, print 0 as the only jumping number.
    11. Call the findCombination() function with the result array, initial index 0, and N as parameters.

Pseudocode

    function printSequence(result[], k):
        for i from 0 to k:
            print result[i]
        print new line

    function findCombination(result[], index, n):
        if index = n:
            printSequence(result, index)
            return
        if index > n:
            return
        if index > 0:
            if result[index - 1] != 0:
                result[index] = result[index - 1] - 1
                findCombination(result, index + 1, n)
            if result[index - 1] != 9:
                result[index] = result[index - 1] + 1
                findCombination(result, index + 1, n)
        else:
            for i from 1 to 9:
                result[index] = i
                findCombination(result, index + 1, n)

    function jumpingNumber(n):
        if n ≤ 0:
            return
        print "Given n: ", n
        result = array of size n
        if n = 1:
            print 0
        findCombination(result, 0, n)

    jumpingNumber(4)

Code Example

/*
    C program for
    Print all N digit jumping numbers
*/
#include <stdio.h>

// Display result
void printSequence(int result[], int k)
{
	for (int i = 0; i < k; ++i)
	{
		printf("%d", result[i]);
	}
	printf("\n ");
}
void findCombination(int result[], int index, int n)
{
	if (index == n)
	{
		// Display calculated result
		printSequence(result, index);
		return;
	}
	if (index > n)
	{
		return;
	}
	if (index > 0)
	{
		if (result[index - 1] != 0)
		{
			// Set new digit by reduce previous digit by one
			result[index] = result[index - 1] - 1;
			findCombination(result, index + 1, n);
		}
		if (result[index - 1] != 9)
		{
			// Set new digit by increase previous digit by one
			result[index] = result[index - 1] + 1;
			// Find next digit
			findCombination(result, index + 1, n);
		}
	}
	else
	{
		// This is used to setup first element
		for (int i = 1; i <= 9; ++i)
		{
			result[index] = i;
			findCombination(result, index + 1, n);
		}
	}
}
// Handles the request of find combination of given n
void jumpingNumber(int n)
{
	if (n <= 0)
	{
		return;
	}
	printf("\n Given n : %d  \n ", n);
	// Collect result
	int result[n];
	if (n == 1)
	{
		printf("\n 0 \n ");
	}
	// Test
	findCombination(result, 0, n);
}
int main(int argc, char
	const *argv[])
{
	// Test
	jumpingNumber(4);
	return 0;
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
/*
    Java program
    Print all N digit jumping numbers
*/
public class JumpingNumber
{
	// Display result
	public void printSequence(int[] result, int k)
	{
		for (int i = 0; i < k; ++i)
		{
			System.out.print(result[i]);
		}
		System.out.print("\n ");
	}
	public void findCombination(int[] result, int index, int n)
	{
		if (index == n)
		{
			// Display calculated result
			printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				findCombination(result, index + 1, n);
			}
			if (result[index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				findCombination(result, index + 1, n);
			}
		}
		else
		{
			// This is used to setup first element
			for (int i = 1; i <= 9; ++i)
			{
				result[index] = i;
				findCombination(result, index + 1, n);
			}
		}
	}
	// Handles the request of find combination of given n
	public void jumpingNo(int n)
	{
		if (n <= 0)
		{
			return;
		}
		System.out.print("\n Given n : " + n + " \n ");
		// Collect result
		int[] result = new int[n];
		if (n == 1)
		{
			System.out.print("\n 0 \n ");
		}
		// Test
		findCombination(result, 0, n);
	}
	public static void main(String[] args)
	{
		JumpingNumber task = new JumpingNumber();
		// Test
		task.jumpingNo(4);
	}
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
// Include header file
#include <iostream>
using namespace std;
/*
    C++ program
    Print all N digit jumping numbers
*/
class JumpingNumber
{
	public:
		// Display result
		void printSequence(int result[], int k)
		{
			for (int i = 0; i < k; ++i)
			{
				cout << result[i];
			}
			cout << "\n ";
		}
	void findCombination(int result[], int index, int n)
	{
		if (index == n)
		{
			// Display calculated result
			this->printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				this->findCombination(result, index + 1, n);
			}
			if (result[index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				this->findCombination(result, index + 1, n);
			}
		}
		else
		{
			// This is used to setup first element
			for (int i = 1; i <= 9; ++i)
			{
				result[index] = i;
				this->findCombination(result, index + 1, n);
			}
		}
	}
	// Handles the request of find combination of given n
	void jumpingNo(int n)
	{
		if (n <= 0)
		{
			return;
		}
		cout << "\n Given n : " << n << " \n ";
		// Collect result
		int result[n];
		if (n == 1)
		{
			cout << "\n 0 \n ";
		}
		// Test
		this->findCombination(result, 0, n);
	}
};
int main()
{
	JumpingNumber *task = new JumpingNumber();
	// Test
	task->jumpingNo(4);
	return 0;
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
// Include namespace system
using System;
/*
    Csharp program
    Print all N digit jumping numbers
*/
public class JumpingNumber
{
	// Display result
	public void printSequence(int[] result, int k)
	{
		for (int i = 0; i < k; ++i)
		{
			Console.Write(result[i]);
		}
		Console.Write("\n ");
	}
	public void findCombination(int[] result, int index, int n)
	{
		if (index == n)
		{
			// Display calculated result
			this.printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				this.findCombination(result, index + 1, n);
			}
			if (result[index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				this.findCombination(result, index + 1, n);
			}
		}
		else
		{
			// This is used to setup first element
			for (int i = 1; i <= 9; ++i)
			{
				result[index] = i;
				this.findCombination(result, index + 1, n);
			}
		}
	}
	// Handles the request of find combination of given n
	public void jumpingNo(int n)
	{
		if (n <= 0)
		{
			return;
		}
		Console.Write("\n Given n : " + n + " \n ");
		// Collect result
		int[] result = new int[n];
		if (n == 1)
		{
			Console.Write("\n 0 \n ");
		}
		// Test
		this.findCombination(result, 0, n);
	}
	public static void Main(String[] args)
	{
		JumpingNumber task = new JumpingNumber();
		// Test
		task.jumpingNo(4);
	}
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
package main
import "fmt"
/*
    Go program
    Print all N digit jumping numbers
*/
type JumpingNumber struct {}
func getJumpingNumber() * JumpingNumber {
	var me *JumpingNumber = &JumpingNumber {}
	return me
}
// Display result
func(this JumpingNumber) printSequence(result[] int, k int) {
	for i := 0 ; i < k ; i++ {
		fmt.Print(result[i])
	}
	fmt.Print("\n ")
}
func(this JumpingNumber) findCombination(result[] int, index int, n int) {
	if index == n {
		// Display calculated result
		this.printSequence(result, index)
		return
	}
	if index > n {
		return
	}
	if index > 0 {
		if result[index - 1] != 0 {
			// Set new digit by reduce previous digit by one
			result[index] = result[index - 1] - 1
			this.findCombination(result, index + 1, n)
		}
		if result[index - 1] != 9 {
			// Set new digit by increase previous digit by one
			result[index] = result[index - 1] + 1
			// Find next digit
			this.findCombination(result, index + 1, n)
		}
	} else {
		// This is used to setup first element
		for i := 1 ; i <= 9 ; i++ {
			result[index] = i
			this.findCombination(result, index + 1, n)
		}
	}
}
// Handles the request of find combination of given n
func(this JumpingNumber) jumpingNo(n int) {
	if n <= 0 {
		return
	}
	fmt.Print("\n Given n : ", n, " \n ")
	// Collect result
	var result = make([] int, n)
	if n == 1 {
		fmt.Print("\n 0 \n ")
	}
	// Test
	this.findCombination(result, 0, n)
}
func main() {
	var task * JumpingNumber = getJumpingNumber()
	// Test
	task.jumpingNo(4)
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
<?php
/*
    Php program
    Print all N digit jumping numbers
*/
class JumpingNumber
{
	// Display result
	public	function printSequence($result, $k)
	{
		for ($i = 0; $i < $k; ++$i)
		{
			echo($result[$i]);
		}
		echo("\n ");
	}
	public	function findCombination($result, $index, $n)
	{
		if ($index == $n)
		{
			// Display calculated result
			$this->printSequence($result, $index);
			return;
		}
		if ($index > $n)
		{
			return;
		}
		if ($index > 0)
		{
			if ($result[$index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				$result[$index] = $result[$index - 1] - 1;
				$this->findCombination($result, $index + 1, $n);
			}
			if ($result[$index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				$result[$index] = $result[$index - 1] + 1;
				// Find next digit
				$this->findCombination($result, $index + 1, $n);
			}
		}
		else
		{
			// This is used to setup first element
			for ($i = 1; $i <= 9; ++$i)
			{
				$result[$index] = $i;
				$this->findCombination($result, $index + 1, $n);
			}
		}
	}
	// Handles the request of find combination of given n
	public	function jumpingNo($n)
	{
		if ($n <= 0)
		{
			return;
		}
		echo("\n Given n : ".$n.
			" \n ");
		// Collect result
		$result = array_fill(0, $n, 0);
		if ($n == 1)
		{
			echo("\n 0 \n ");
		}
		// Test
		$this->findCombination($result, 0, $n);
	}
}

function main()
{
	$task = new JumpingNumber();
	// Test
	$task->jumpingNo(4);
}
main();

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
/*
    Node JS program
    Print all N digit jumping numbers
*/
class JumpingNumber
{
	// Display result
	printSequence(result, k)
	{
		for (var i = 0; i < k; ++i)
		{
			process.stdout.write("" + result[i]);
		}
		process.stdout.write("\n ");
	}
	findCombination(result, index, n)
	{
		if (index == n)
		{
			// Display calculated result
			this.printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				this.findCombination(result, index + 1, n);
			}
			if (result[index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				this.findCombination(result, index + 1, n);
			}
		}
		else
		{
			// This is used to setup first element
			for (var i = 1; i <= 9; ++i)
			{
				result[index] = i;
				this.findCombination(result, index + 1, n);
			}
		}
	}
	// Handles the request of find combination of given n
	jumpingNo(n)
	{
		if (n <= 0)
		{
			return;
		}
		process.stdout.write("\n Given n : " + n + " \n ");
		// Collect result
		var result = Array(n).fill(0);
		if (n == 1)
		{
			process.stdout.write("\n 0 \n ");
		}
		// Test
		this.findCombination(result, 0, n);
	}
}

function main()
{
	var task = new JumpingNumber();
	// Test
	task.jumpingNo(4);
}
main();

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
#    Python 3 program
#    Print all N digit jumping numbers
class JumpingNumber :
	#  Display result
	def printSequence(self, result, k) :
		i = 0
		while (i < k) :
			print(result[i], end = "")
			i += 1
		
		print("\n ", end = "")
	
	def findCombination(self, result, index, n) :
		if (index == n) :
			#  Display calculated result
			self.printSequence(result, index)
			return
		
		if (index > n) :
			return
		
		if (index > 0) :
			if (result[index - 1] != 0) :
				#  Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1
				self.findCombination(result, index + 1, n)
			
			if (result[index - 1] != 9) :
				#  Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1
				#  Find next digit
				self.findCombination(result, index + 1, n)
			
		else :
			i = 1
			#  This is used to setup first element
			while (i <= 9) :
				result[index] = i
				self.findCombination(result, index + 1, n)
				i += 1
			
		
	
	#  Handles the request of find combination of given n
	def jumpingNo(self, n) :
		if (n <= 0) :
			return
		
		print("\n Given n : ", n ," \n ", end = "")
		#  Collect result
		result = [0] * (n)
		if (n == 1) :
			print("\n 0 \n ", end = "")
		
		#  Test
		self.findCombination(result, 0, n)
	

def main() :
	task = JumpingNumber()
	#  Test
	task.jumpingNo(4)

if __name__ == "__main__": main()

Output

 Given n :  4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
#    Ruby program
#    Print all N digit jumping numbers
class JumpingNumber 
	#  Display result
	def printSequence(result, k) 
		i = 0
		while (i < k) 
			print(result[i])
			i += 1
		end

		print("\n ")
	end

	def findCombination(result, index, n) 
		if (index == n) 
			#  Display calculated result
			self.printSequence(result, index)
			return
		end

		if (index > n) 
			return
		end

		if (index > 0) 
			if (result[index - 1] != 0) 
				#  Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1
				self.findCombination(result, index + 1, n)
			end

			if (result[index - 1] != 9) 
				#  Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1
				#  Find next digit
				self.findCombination(result, index + 1, n)
			end

		else
 
			i = 1
			#  This is used to setup first element
			while (i <= 9) 
				result[index] = i
				self.findCombination(result, index + 1, n)
				i += 1
			end

		end

	end

	#  Handles the request of find combination of given n
	def jumpingNo(n) 
		if (n <= 0) 
			return
		end

		print("\n Given n : ", n ," \n ")
		#  Collect result
		result = Array.new(n) {0}
		if (n == 1) 
			print("\n 0 \n ")
		end

		#  Test
		self.findCombination(result, 0, n)
	end

end

def main() 
	task = JumpingNumber.new()
	#  Test
	task.jumpingNo(4)
end

main()

Output

 Given n : 4 
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
 
/*
    Scala program
    Print all N digit jumping numbers
*/
class JumpingNumber()
{
	// Display result
	def printSequence(result: Array[Int], k: Int): Unit = {
		var i: Int = 0;
		while (i < k)
		{
			print(result(i));
			i += 1;
		}
		print("\n ");
	}
	def findCombination(result: Array[Int], index: Int, n: Int): Unit = {
		if (index == n)
		{
			// Display calculated result
			printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result(index - 1) != 0)
			{
				// Set new digit by reduce previous digit by one
				result(index) = result(index - 1) - 1;
				findCombination(result, index + 1, n);
			}
			if (result(index - 1) != 9)
			{
				// Set new digit by increase previous digit by one
				result(index) = result(index - 1) + 1;
				// Find next digit
				findCombination(result, index + 1, n);
			}
		}
		else
		{
			var i: Int = 1;
			// This is used to setup first element
			while (i <= 9)
			{
				result(index) = i;
				findCombination(result, index + 1, n);
				i += 1;
			}
		}
	}
	// Handles the request of find combination of given n
	def jumpingNo(n: Int): Unit = {
		if (n <= 0)
		{
			return;
		}
		print("\n Given n : " + n + " \n ");
		// Collect result
		var result: Array[Int] = Array.fill[Int](n)(0);
		if (n == 1)
		{
			print("\n 0 \n ");
		}
		// Test
		findCombination(result, 0, n);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: JumpingNumber = new JumpingNumber();
		// Test
		task.jumpingNo(4);
	}
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
/*
    Swift 4 program
    Print all N digit jumping numbers
*/
class JumpingNumber
{
	// Display result
	func printSequence(_ result: [Int], _ k: Int)
	{
		var i: Int = 0;
		while (i < k)
		{
			print(result[i], terminator: "");
			i += 1;
		}
		print("\n ", terminator: "");
	}
	func findCombination(_ result: inout[Int], _ index: Int, _ n: Int)
	{
		if (index == n)
		{
			// Display calculated result
			self.printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1]  != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				self.findCombination(&result, index + 1, n);
			}
			if (result[index - 1]  != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				self.findCombination(&result, index + 1, n);
			}
		}
		else
		{
			var i: Int = 1;
			// This is used to setup first element
			while (i <= 9)
			{
				result[index] = i;
				self.findCombination(&result, index + 1, n);
				i += 1;
			}
		}
	}
	// Handles the request of find combination of given n
	func jumpingNo(_ n: Int)
	{
		if (n <= 0)
		{
			return;
		}
		print("\n Given n : ", n ," \n ", terminator: "");
		// Collect result
		var result: [Int] = Array(repeating: 0, count: n);
		if (n == 1)
		{
			print("\n 0 \n ", terminator: "");
		}
		// Test
		self.findCombination(&result, 0, n);
	}
}
func main()
{
	let task: JumpingNumber = JumpingNumber();
	// Test
	task.jumpingNo(4);
}
main();

Output

 Given n :  4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898
/*
    Kotlin program
    Print all N digit jumping numbers
*/
class JumpingNumber
{
	// Display result
	fun printSequence(result: Array < Int > , k: Int): Unit
	{
		var i: Int = 0;
		while (i < k)
		{
			print(result[i]);
			i += 1;
		}
		print("\n ");
	}
	fun findCombination(result: Array < Int > , index: Int, n: Int): Unit
	{
		if (index == n)
		{
			// Display calculated result
			this.printSequence(result, index);
			return;
		}
		if (index > n)
		{
			return;
		}
		if (index > 0)
		{
			if (result[index - 1] != 0)
			{
				// Set new digit by reduce previous digit by one
				result[index] = result[index - 1] - 1;
				this.findCombination(result, index + 1, n);
			}
			if (result[index - 1] != 9)
			{
				// Set new digit by increase previous digit by one
				result[index] = result[index - 1] + 1;
				// Find next digit
				this.findCombination(result, index + 1, n);
			}
		}
		else
		{
			var i: Int = 1;
			// This is used to setup first element
			while (i <= 9)
			{
				result[index] = i;
				this.findCombination(result, index + 1, n);
				i += 1;
			}
		}
	}
	// Handles the request of find combination of given n
	fun jumpingNo(n: Int): Unit
	{
		if (n <= 0)
		{
			return;
		}
		print("\n Given n : " + n + " \n ");
		// Collect result
		val result: Array < Int > = Array(n)
		{
			0
		};
		if (n == 1)
		{
			print("\n 0 \n ");
		}
		// Test
		this.findCombination(result, 0, n);
	}
}
fun main(args: Array < String > ): Unit
{
	val task: JumpingNumber = JumpingNumber();
	// Test
	task.jumpingNo(4);
}

Output

 Given n : 4
 1010
 1012
 1210
 1212
 1232
 1234
 2101
 2121
 2123
 2321
 2323
 2343
 2345
 3210
 3212
 3232
 3234
 3432
 3434
 3454
 3456
 4321
 4323
 4343
 4345
 4543
 4545
 4565
 4567
 5432
 5434
 5454
 5456
 5654
 5656
 5676
 5678
 6543
 6545
 6565
 6567
 6765
 6767
 6787
 6789
 7654
 7656
 7676
 7678
 7876
 7878
 7898
 8765
 8767
 8787
 8789
 8987
 8989
 9876
 9878
 9898

Explanation

The above code uses a recursive approach to find and print all N-digit jumping numbers. It starts by checking the base cases: if the current index is equal to N, it calls the printSequence() function to print the result, and if the current index is greater than N, it returns.

If the current index is greater than 0, it checks the previous digit. If the previous digit is not 0, it sets the new digit by reducing the previous digit by one and recursively calls the findCombination() function with the updated index. Similarly, if the previous digit is not 9, it sets the new digit by increasing the previous digit by one and recursively calls the findCombination() function with the updated index.

If the current index is 0, it means we are setting up the first element. In this case, it iterates from 1 to 9 and sets each digit as the first element of the result array. It then recursively calls the findCombination() function with the updated index.

The jumpingNumber() function handles the request to find and print all N-digit jumping numbers. It first checks if N is less than or equal to 0, and if so, it returns. Then, it initializes the result array. If N is equal to 1, it prints 0 as the only jumping number. Finally, it calls the findCombination() function with the result array, initial index 0, and N as parameters.

In the provided example, the code is executed with N = 4. The output is a list of all 4-digit jumping numbers. Each number represents a sequence of digits, where the absolute difference between adjacent digits is always 1.

The time complexity of the code depends on the number of jumping numbers generated for a given value of N. As the number of jumping numbers increases exponentially with N, the time complexity can be approximated as O(2^N). However, it's important to note that the actual time complexity may vary based on implementation details and the specific environment in which the code is executed.

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