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Print all Jumping Numbers smaller than or equal to a given value

  • Difficulty Level : Hard
  • Last Updated : 26 Aug, 2021

A number is called as a Jumping Number if all adjacent digits in it differ by 1. The difference between ‘9’ and ‘0’ is not considered as 1. 
All single digit numbers are considered as Jumping Numbers. For example 7, 8987 and 4343456 are Jumping numbers but 796 and 89098 are not. 
Given a positive number x, print all Jumping Numbers smaller than or equal to x. The numbers can be printed in any order.

Example: 

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Input: x = 20
Output:  0 1 2 3 4 5 6 7 8 9 10 12

Input: x = 105
Output:  0 1 2 3 4 5 6 7 8 9 10 12
         21 23 32 34 43 45 54 56 65
         67 76 78 87 89 98 101

Note: Order of output doesn't matter, 
i.e. numbers can be printed in any order

We strongly recommend that you click here and practice it, before moving on to the solution.

One Simple Solution is to traverse all numbers from 0 to x. For every traversed number, check if it is a Jumping number. If yes, then print it. Otherwise ignore it. Time Complexity of this solution is O(x).

An Efficient Solution can solve this problem in O(k) time where k is number of Jumping Numbers smaller than or equal to x. The idea is use BFS or DFS
Assume that we have a graph where the starting node is 0 and we need to traverse it from the start node to all the reachable nodes.



With the restrictions given in the graph about the jumping numbers, what do you think should be the restrictions defining the next transitions in the graph.

Lets take a example for input x = 90

Start node = 0
From 0, we can move to 1 2 3 4 5 6 7 8 9 
[these are not in our range so we don't add it]

Now from 1, we can move to 12 and 10 
From 2, 23 and 21
From 3, 34 and 32
.
.
.
.
.
.
and so on.

Below is BFS based implementation of above idea. 

C++




// Finds and prints all jumping numbers smaller than or
// equal to x.
#include <bits/stdc++.h>
using namespace std;
  
// Prints all jumping numbers smaller than or equal to x starting
// with 'num'. It mainly does BFS starting from 'num'.
void bfs(int x, int num)
{
    // Create a queue and enqueue 'i' to it
    queue<int> q;
    q.push(num);
  
    // Do BFS starting from i
    while (!q.empty()) {
        num = q.front();
        q.pop();
  
        if (num <= x) {
            cout << num << " ";
            int last_dig = num % 10;
  
            // If last digit is 0, append next digit only
            if (last_dig == 0)
                q.push((num * 10) + (last_dig + 1));
  
            // If last digit is 9, append previous digit only
            else if (last_dig == 9)
                q.push((num * 10) + (last_dig - 1));
  
            // If last digit is neighter 0 nor 9, append both
            // previous and next digits
            else {
                q.push((num * 10) + (last_dig - 1));
                q.push((num * 10) + (last_dig + 1));
            }
        }
    }
}
  
// Prints all jumping numbers smaller than or equal to
// a positive number x
void printJumping(int x)
{
    cout << 0 << " ";
    for (int i = 1; i <= 9 && i <= x; i++)
        bfs(x, i);
}
  
// Driver program
int main()
{
    int x = 40;
    printJumping(x);
    return 0;
}

Java




// Finds and prints all jumping numbers smaller than or
// equal to x.
import java.util.*;
import java.lang.*;
import java.io.*;
  
class GFG {
  
    // Prints all jumping numbers smaller than or equal to x starting
    // with 'num'. It mainly does BFS starting from 'num'.
    public void bfs(int x, int num)
    {
        // Create a queue and enqueue 'i' to it
        Queue<Integer> q = new LinkedList<Integer>();
        q.add(num);
  
        // Do BFS starting from i
        while (!q.isEmpty()) {
            num = q.peek();
            q.poll();
            if (num <= x) {
                System.out.print(num + " ");
                int last_digit = num % 10;
  
                // If last digit is 0, append next digit only
                if (last_digit == 0) {
                    q.add((num * 10) + (last_digit + 1));
                }
  
                // If last digit is 9, append previous digit only
                else if (last_digit == 9) {
                    q.add((num * 10) + (last_digit - 1));
                }
  
                // If last digit is neighter 0 nor 9, append both
                // previous and next digits
                else {
                    q.add((num * 10) + (last_digit - 1));
                    q.add((num * 10) + (last_digit + 1));
                }
            }
        }
    }
  
    // Prints all jumping numbers smaller than or equal to
    // a positive number x
    public void printJumping(int x)
    {
        System.out.print("0 ");
  
        for (int i = 1; i <= 9 && i <= x; i++) {
            this.bfs(x, i);
        }
    }
  
    // Driver program
    public static void main(String[] args) throws IOException
    {
        int x = 40;
        GFG obj = new GFG();
        obj.printJumping(x);
    }
}

Python3




# Class queue for use later
class Queue:
    def __init__(self):
        self.lst = []
  
    def is_empty(self):
        return self.lst == []
  
    def enqueue(self, elem):
        self.lst.append(elem)
  
    def dequeue(self):
        return self.lst.pop(0)
  
# Prints all jumping numbers smaller than or equal to
# x starting with 'num'. It mainly does BFS starting
# from 'num'.
def bfs(x, num):
  
    # Create a queue and enqueue i to it
    q = Queue()
    q.enqueue(num)
  
    # Do BFS starting from 1
    while (not q.is_empty()):
        num = q.dequeue()
  
        if num<= x:
            print(str(num), end =' ')
            last_dig = num % 10
  
            # If last digit is 0, append next digit only
            if last_dig == 0:
                q.enqueue((num * 10) + (last_dig + 1))
  
            # If last digit is 9, append previous digit
            # only
            elif last_dig == 9:
                q.enqueue((num * 10) + (last_dig - 1))
  
            # If last digit is neighter 0 nor 9, append
            # both previous digit and next digit
            else:
                q.enqueue((num * 10) + (last_dig - 1))
                q.enqueue((num * 10) + (last_dig + 1))
  
# Prints all jumping numbers smaller than or equal to
# a positive number x
def printJumping(x):
    print (str(0), end =' ')
    for i in range(1, 10):
        bfs(x, i)
  
# Driver Program ( Change value of x as desired )
x = 40
printJumping(x)
  
# This code is contributed by Saket Modi

C#




// C# program to finds and prints all jumping 
// numbers smaller than or equal to x.
using System;
using System.Collections.Generic;
  
class GFG 
{
  
    // Prints all jumping numbers smaller than or 
    // equal to x starting with 'num'. It mainly
    // does BFS starting from 'num'.
    public void bfs(int x, int num)
    {
        // Create a queue and enqueue 'i' to it
        Queue<int> q = new Queue<int>();
        q.Enqueue(num);
  
        // Do BFS starting from i
        while (q.Count!=0) 
        {
            num = q.Peek();
            q.Dequeue();
            if (num <= x) 
            {
                Console.Write(num + " ");
                int last_digit = num % 10;
  
                // If last digit is 0, append next digit only
                if (last_digit == 0) 
                {
                    q.Enqueue((num * 10) + (last_digit + 1));
                }
  
                // If last digit is 9, append previous digit only
                else if (last_digit == 9) 
                {
                    q.Enqueue((num * 10) + (last_digit - 1));
                }
  
                // If last digit is neighter 0 nor 9, append both
                // previous and next digits
                else 
                {
                    q.Enqueue((num * 10) + (last_digit - 1));
                    q.Enqueue((num * 10) + (last_digit + 1));
                }
            }
        }
    }
  
    // Prints all jumping numbers smaller than or equal to
    // a positive number x
    public void printJumping(int x)
    {
        Console.Write("0 ");
  
        for (int i = 1; i <= 9 && i <= x; i++) 
        {
            this.bfs(x, i);
        }
    }
  
    // Driver code
    public static void Main(String[] args) 
    {
        int x = 40;
        GFG obj = new GFG();
        obj.printJumping(x);
    }
}
  
// This code has been contributed by 29AjayKumar

Javascript




<script>
  
// Finds and prints all jumping numbers 
// smaller than or equal to x.
  
// Prints all jumping numbers smaller than
// or equal to x starting with 'num'. It 
// mainly does BFS starting from 'num'.
function bfs(x, num)
{
      
    // Create a queue and enqueue 'i' to it
    let q = [];
    q.push(num);
  
    // Do BFS starting from i
    while (q.length != 0) 
    {
        num = q.shift();
          
        if (num <= x) 
        {
            document.write(num + " ");
            let last_digit = num % 10;
  
            // If last digit is 0, append next digit only
            if (last_digit == 0) 
            {
                q.push((num * 10) + (last_digit + 1));
            }
  
            // If last digit is 9, append previous 
            // digit only
            else if (last_digit == 9)
            {
                q.push((num * 10) + (last_digit - 1));
            }
  
            // If last digit is neighter 0 nor 9, 
            // append both previous and next digits
            else 
            {
                q.push((num * 10) + (last_digit - 1));
                q.push((num * 10) + (last_digit + 1));
            }
        }
    }
}
  
// Prints all jumping numbers smaller 
// than or equal to a positive number x
function printJumping(x)
{
    document.write("0 ");
    
    for(let i = 1; i <= 9 && i <= x; i++)
    {
        bfs(x, i);
    }
}
  
// Driver code
let x = 40;
printJumping(x);
  
// This code is contributed by rag2127
  
</script>

Output: 

0 1 10 12 2 21 23 3 32 34 4 5 6 7 8 9 

Thanks to Gaurav Ahirwar for above solution.
 

Exercise: 

  1. Change the above solution to use DFS instead of BFS.
  2. Extend your solution to print all numbers in sorted order instead of any order.
  3. Further extend the solution to print all numbers in a given range.

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