Given a number N, the task is to print the first N Stepping Numbers.
A number is called stepping number if all adjacent digits have an absolute difference of 1. For e.g. 321 is a Stepping Number while 421 is not.
Examples:
Input: N = 7
Output: 1, 2, 3, 4, 5, 6, 7
Input: N = 14
Output: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22
Naive approach: We can start from 1 and check for every number whether they are Stepping number or not and continue till we find the K-th Stepping number.
Efficient Approach:
- Generate all possible Stepping numbers till 1000, for easy computation
- For each value of N, just print the N already computed Stepping numbers
Below is the implementation of the above approach:
C++
// C++ Program to print first N// Stepping numbers#include <bits/stdc++.h>using namespace std;// Function to generate// the Stepping numbersvoid generateSteppingNos( int x, set<int>& s){ if (x > 1e8) return; // Inserting the current // element in the set s.insert(x); // Retrieving the last digit // of the current number int last = x % 10; if (last - 1 >= 0) // Appending x-1 to // the current number generateSteppingNos( x * 10 + last - 1, s); // Appending x to // the current number generateSteppingNos( x * 10 + last, s); if (last + 1 <= 9) // Appending x+1 to // the current number generateSteppingNos( x * 10 + last + 1, s);}// Function to print// N Stepping numbersvoid NSteppingNumbers(int N){ set<int> s; for (int i = 1; i <= 9; i++) generateSteppingNos(i, s); int count = 1; // Printing N numbers from s for (auto& it : s) { if (count <= N) { cout << it << ", "; count++; } else break; }}// Driver codeint main(){ int N = 14; NSteppingNumbers(N); return 0;} |
Java
// Java Program to print first N// Stepping numbersimport java.util.*;public class GFG{ static HashSet<Integer> s = new HashSet<Integer>(); // Function to generate // the Stepping numbers static void generateSteppingNos(int x) { if (x > 1e8) return; // Inserting the current // element in the set s.add(x); // Retrieving the last digit // of the current number int last = x % 10; if (last - 1 >= 0) // Appending x-1 to // the current number generateSteppingNos(x * 10 + last - 1); // Appending x to // the current number generateSteppingNos(x * 10 + last); if (last + 1 <= 9) // Appending x+1 to // the current number generateSteppingNos(x * 10 + last + 1); } // Function to print // N Stepping numbers static void NSteppingNumbers(int N) { HashSet<Integer> s = new HashSet<Integer>(); int[] arr = {10, 11, 12, 21, 22}; for (int i = 1; i <= 9; i++) { generateSteppingNos(i); s.add(i); } for(int i = 0; i < arr.length; i++) { s.add(arr[i]); } int count = 1; // Printing N numbers from s for(int it : s) { if (count <= N) { System.out.print(it + ", "); count++; } else break; } } public static void main(String[] args) { int N = 14; NSteppingNumbers(N); }}// This code is contributed by mukesh07. |
Python3
# Python3 Program to print first N # Stepping numbers # Function to generate # the Stepping numbers def generateSteppingNos(x, s): if (x > 1e8): return # Inserting the current # element in the set s.add(x) # Retrieving the last digit # of the current number last = x % 10 if (last - 1 >= 0): # Appending x-1 to # the current number generateSteppingNos(x * 10 + last - 1, s) # Appending x to # the current number generateSteppingNos(x * 10 + last, s) if (last + 1 <= 9): # Appending x+1 to # the current number generateSteppingNos(x * 10 + last + 1, s)# Function to print # N Stepping numbers def NSteppingNumbers(N): s = set() for i in range(1, 10): generateSteppingNos(i, s) count = 1 s.pop() # Printing N numbers from s for value in s: if (count <= N): print(value, end=', ') count = count + 1 else: break# Driver code N = 14NSteppingNumbers(N)# This code is contributed by Sanjit_Prasad |
C#
// C# Program to print first N// Stepping numbersusing System;using System.Collections.Generic;class GFG { static HashSet<int> s = new HashSet<int>(); // Function to generate // the Stepping numbers static void generateSteppingNos(int x) { if (x > 1e8) return; // Inserting the current // element in the set s.Add(x); // Retrieving the last digit // of the current number int last = x % 10; if (last - 1 >= 0) // Appending x-1 to // the current number generateSteppingNos(x * 10 + last - 1); // Appending x to // the current number generateSteppingNos(x * 10 + last); if (last + 1 <= 9) // Appending x+1 to // the current number generateSteppingNos(x * 10 + last + 1); } // Function to print // N Stepping numbers static void NSteppingNumbers(int N) { HashSet<int> s = new HashSet<int>(); int[] arr = {10, 11, 12, 21, 22}; for (int i = 1; i <= 9; i++) { generateSteppingNos(i); s.Add(i); } for(int i = 0; i < arr.Length; i++) { s.Add(arr[i]); } int count = 1; // Printing N numbers from s foreach(int it in s) { if (count <= N) { Console.Write(it + ", "); count++; } else break; } } static void Main() { int N = 14; NSteppingNumbers(N); }}// This code is contributed by suresh07. |
Javascript
// JavaScript program to print first N Stepping numbers// Set to store the stepping numberslet s = new Set();// Function to generate the stepping numbersfunction generateSteppingNos(x) { if (x > 1e8) { return; } // Inserting the current element in the set s.add(x); // Retrieving the last digit of the current number let last = x % 10; if (last - 1 >= 0) { // Appending x-1 to the current number generateSteppingNos(x * 10 + last - 1); } // Appending x to the current number generateSteppingNos(x * 10 + last); if (last + 1 <= 9) { // Appending x+1 to the current number generateSteppingNos(x * 10 + last + 1); }}// Function to print N stepping numbersfunction NSteppingNumbers(N) { // Set to store the stepping numbers let s = new Set(); let arr = [10, 11, 12, 21, 22]; // Generating stepping numbers for (let i = 1; i <= 9; i++) { generateSteppingNos(i); s.add(i); } for (let i = 0; i < arr.length; i++) { s.add(arr[i]); } let count = 1; // Printing N numbers from the set let ans = []; for (let it of s) { if (count <= N) { ans.push(it); count++; } else { break; } } console.log(ans.join(', '))}let N = 14;NSteppingNumbers(N);// This code is contributed by codebraxnzt |
Output:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22,
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