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# Stepping Numbers

• Difficulty Level : Hard
• Last Updated : 23 Jun, 2021

Given two integers ‘n’ and ‘m’, find all the stepping numbers in range [n, m]. A number is called stepping number if all adjacent digits have an absolute difference of 1. 321 is a Stepping Number while 421 is not.

Examples :

Input : n = 0, m = 21
Output : 0 1 2 3 4 5 6 7 8 9 10 12 21

Input : n = 10, m = 15
Output : 10, 12

Method 1: Brute force Approach
In this method, a brute force approach is used to iterate through all the integers from n to m and check if it’s a stepping number.

## C++

 // A C++ program to find all the Stepping Number in [n, m]#includeusing namespace std; // This function checks if an integer n is a Stepping Numberbool isStepNum(int n){    // Initialize prevDigit with -1    int prevDigit = -1;     // Iterate through all digits of n and compare difference    // between value of previous and current digits    while (n)    {        // Get Current digit        int curDigit = n % 10;         // Single digit is consider as a        // Stepping Number        if (prevDigit == -1)            prevDigit = curDigit;        else        {            // Check if absolute difference between            // prev digit and current digit is 1            if (abs(prevDigit - curDigit) != 1)                 return false;        }        prevDigit = curDigit;        n /= 10;    }     return true;} // A brute force approach based function to find all// stepping numbers.void displaySteppingNumbers(int n, int m){    // Iterate through all the numbers from [N,M]    // and check if it’s a stepping number.    for (int i=n; i<=m; i++)        if (isStepNum(i))            cout << i << " ";} // Driver program to test above functionint main(){    int n = 0, m = 21;     // Display Stepping Numbers in    // the range [n, m]    displaySteppingNumbers(n, m);     return 0;}

## Java

 // A Java program to find all the Stepping Number in [n, m]class Main{    // This Method checks if an integer n    // is a Stepping Number    public static boolean isStepNum(int n)    {        // Initialize prevDigit with -1        int prevDigit = -1;         // Iterate through all digits of n and compare        // difference between value of previous and        // current digits        while (n > 0)        {            // Get Current digit            int curDigit = n % 10;             // Single digit is consider as a            // Stepping Number            if (prevDigit != -1)            {                // Check if absolute difference between                // prev digit and current digit is 1                if (Math.abs(curDigit-prevDigit) != 1)                    return false;            }            n /= 10;            prevDigit = curDigit;        }        return true;    }     // A brute force approach based function to find all    // stepping numbers.    public static void displaySteppingNumbers(int n,int m)    {        // Iterate through all the numbers from [N,M]        // and check if it is a stepping number.        for (int i = n; i <= m; i++)            if (isStepNum(i))                System.out.print(i+ " ");    }     // Driver code    public static void main(String args[])    {        int n = 0, m = 21;         // Display Stepping Numbers in the range [n,m]        displaySteppingNumbers(n,m);    }}

## Python3

 # A Python3 program to find all the Stepping Number in [n, m] # This function checks if an integer n is a Stepping Numberdef isStepNum(n):       # Initialize prevDigit with -1    prevDigit = -1     # Iterate through all digits of n and compare difference    # between value of previous and current digits    while (n):               # Get Current digit        curDigit = n % 10         # Single digit is consider as a        # Stepping Number        if (prevDigit == -1):            prevDigit = curDigit        else:                       # Check if absolute difference between            # prev digit and current digit is 1            if (abs(prevDigit - curDigit) != 1):                return False        prevDigit = curDigit        n //= 10    return True # A brute force approach based function to find all# stepping numbers.def displaySteppingNumbers(n, m):       # Iterate through all the numbers from [N,M]    # and check if it’s a stepping number.    for i in range(n, m + 1):        if (isStepNum(i)):            print(i, end = " ") # Driver codeif __name__ == '__main__':    n, m = 0, 21     # Display Stepping Numbers in    # the range [n, m]    displaySteppingNumbers(n, m) # This code is contributed by mohit kumar 29

## C#

 // A C# program to find all// the Stepping Number in [n, m]using System; class GFG{    // This Method checks if an    // integer n is a Stepping Number    public static bool isStepNum(int n)    {        // Initialize prevDigit with -1        int prevDigit = -1;         // Iterate through all digits        // of n and compare difference        // between value of previous        // and current digits        while (n > 0)        {            // Get Current digit            int curDigit = n % 10;             // Single digit is considered            // as a Stepping Number            if (prevDigit != -1)            {                // Check if absolute difference                // between prev digit and current                // digit is 1                if (Math.Abs(curDigit -                             prevDigit) != 1)                    return false;            }            n /= 10;            prevDigit = curDigit;        }        return true;    }     // A brute force approach based    // function to find all stepping numbers.    public static void displaySteppingNumbers(int n,                                              int m)    {        // Iterate through all the numbers        // from [N,M] and check if it is        // a stepping number.        for (int i = n; i <= m; i++)            if (isStepNum(i))                Console.Write(i+ " ");    }     // Driver code    public static void Main()    {        int n = 0, m = 21;         // Display Stepping Numbers        // in the range [n,m]        displaySteppingNumbers(n, m);    }} // This code is contributed by nitin mittal.

## Javascript



Output :

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

Method 2: Using BFS/DFS

The idea is to use a Breadth First Search/Depth First Search traversal.

How to build the graph?
Every node in the graph represents a stepping number; there will be a directed edge from a node U to V if V can be transformed from U. (U and V are Stepping Numbers) A Stepping Number V can be transformed from U in following manner.
lastDigit refers to the last digit of U (i.e. U % 10)
An adjacent number V can be:

• U*10 + lastDigit + 1 (Neighbor A)
• U*10 + lastDigit – 1 (Neighbor B)

By applying above operations a new digit is appended to U, it is either lastDigit-1 or lastDigit+1, so that the new number V formed from U is also a Stepping Number.
Therefore, every Node will have at most 2 neighboring Nodes.
Edge Cases: When the last digit of U is 0 or 9

• Case 1: lastDigit is 0 : In this case only digit ‘1’ can be appended.
• Case 2: lastDigit is 9 : In this case only digit ‘8’ can be appended.

What will be the source/starting Node?

• Every single digit number is considered as a stepping Number, so bfs traversal for every digit will give all the stepping numbers starting from that digit.
• Do a bfs/dfs traversal for all the numbers from [0,9].

Note: For node 0, no need to explore neighbors during BFS traversal since it will lead to 01, 012, 010 and these will be covered by the BFS traversal starting from node 1.
Example to find all the stepping numbers from 0 to 21

-> 0 is a stepping Number and it is in the range
so display it.
-> 1 is a Stepping Number, find neighbors of 1 i.e.,
10 and 12 and push them into the queue

How to get 10 and 12?
Here U is 1 and last Digit is also 1
V = 10 + 0 = 10 ( Adding lastDigit - 1 )
V = 10 + 2 = 12 ( Adding lastDigit + 1 )

Then do the same for 10 and 12 this will result into
101, 123, 121 but these Numbers are out of range.
Now any number transformed from 10 and 12 will result
into a number greater than 21 so no need to explore
their neighbors.

-> 2 is a Stepping Number, find neighbors of 2 i.e.
21, 23.
-> 23 is out of range so it is not considered as a
Stepping Number (Or a neighbor of 2)

The other stepping numbers will be 3, 4, 5, 6, 7, 8, 9.

BFS based Solution:

## C++

 // A C++ program to find all the Stepping Number from N=n// to m using BFS Approach#includeusing namespace std; // Prints all stepping numbers reachable from num// and in range [n, m]void bfs(int n, int m, int num){    // Queue will contain all the stepping Numbers    queue q;     q.push(num);     while (!q.empty())    {        // Get the front element and pop from the queue        int stepNum = q.front();        q.pop();         // If the Stepping Number is in the range        // [n, m] then display        if (stepNum <= m && stepNum >= n)            cout << stepNum << " ";         // If Stepping Number is 0 or greater than m,        // no need to explore the neighbors        if (num == 0 || stepNum > m)            continue;         // Get the last digit of the currently visited        // Stepping Number        int lastDigit = stepNum % 10;         // There can be 2 cases either digit to be        // appended is lastDigit + 1 or lastDigit - 1        int stepNumA = stepNum * 10 + (lastDigit- 1);        int stepNumB = stepNum * 10 + (lastDigit + 1);         // If lastDigit is 0 then only possible digit        // after 0 can be 1 for a Stepping Number        if (lastDigit == 0)            q.push(stepNumB);         //If lastDigit is 9 then only possible        //digit after 9 can be 8 for a Stepping        //Number        else if (lastDigit == 9)            q.push(stepNumA);         else        {            q.push(stepNumA);            q.push(stepNumB);        }    }} // Prints all stepping numbers in range [n, m]// using BFS.void displaySteppingNumbers(int n, int m){    // For every single digit Number 'i'    // find all the Stepping Numbers    // starting with i    for (int i = 0 ; i <= 9 ; i++)        bfs(n, m, i);} //Driver program to test above functionint main(){    int n = 0, m = 21;     // Display Stepping Numbers in the    // range [n,m]    displaySteppingNumbers(n,m);     return 0;}

## Java

 // A Java program to find all the Stepping Number in// range [n, m]import java.util.*; class Main{    // Prints all stepping numbers reachable from num    // and in range [n, m]    public static void bfs(int n,int m,int num)    {        // Queue will contain all the stepping Numbers        Queue q = new LinkedList ();         q.add(num);         while (!q.isEmpty())        {            // Get the front element and pop from            // the queue            int stepNum = q.poll();             // If the Stepping Number is in            // the range [n,m] then display            if (stepNum <= m && stepNum >= n)            {                System.out.print(stepNum + " ");            }             // If Stepping Number is 0 or greater            // then m, no need to explore the neighbors            if (stepNum == 0 || stepNum > m)                continue;             // Get the last digit of the currently            // visited Stepping Number            int lastDigit = stepNum % 10;             // There can be 2 cases either digit            // to be appended is lastDigit + 1 or            // lastDigit - 1            int stepNumA = stepNum * 10 + (lastDigit- 1);            int stepNumB = stepNum * 10 + (lastDigit + 1);             // If lastDigit is 0 then only possible            // digit after 0 can be 1 for a Stepping            // Number            if (lastDigit == 0)                q.add(stepNumB);             // If lastDigit is 9 then only possible            // digit after 9 can be 8 for a Stepping            // Number            else if (lastDigit == 9)                q.add(stepNumA);             else            {                q.add(stepNumA);                q.add(stepNumB);            }        }    }     // Prints all stepping numbers in range [n, m]    // using BFS.    public static void displaySteppingNumbers(int n,int m)    {        // For every single digit Number 'i'        // find all the Stepping Numbers        // starting with i        for (int i = 0 ; i <= 9 ; i++)            bfs(n, m, i);    }     //Driver code    public static void main(String args[])    {        int n = 0, m = 21;         // Display Stepping Numbers in        // the range [n,m]        displaySteppingNumbers(n,m);    }}

## Python3

 # A Python3 program to find all the Stepping Number from N=n# to m using BFS Approach # Prints all stepping numbers reachable from num# and in range [n, m]def bfs(n, m, num) :     # Queue will contain all the stepping Numbers    q = []    q.append(num)    while len(q) > 0 :             # Get the front element and pop from the queue        stepNum = q[0]        q.pop(0);         # If the Stepping Number is in the range        # [n, m] then display        if (stepNum <= m and stepNum >= n) :            print(stepNum, end = " ")         # If Stepping Number is 0 or greater than m,        # no need to explore the neighbors        if (num == 0 or stepNum > m) :            continue         # Get the last digit of the currently visited        # Stepping Number        lastDigit = stepNum % 10         # There can be 2 cases either digit to be        # appended is lastDigit + 1 or lastDigit - 1        stepNumA = stepNum * 10 + (lastDigit- 1)        stepNumB = stepNum * 10 + (lastDigit + 1)         # If lastDigit is 0 then only possible digit        # after 0 can be 1 for a Stepping Number        if (lastDigit == 0) :            q.append(stepNumB)         #If lastDigit is 9 then only possible        #digit after 9 can be 8 for a Stepping        #Number        elif (lastDigit == 9) :            q.append(stepNumA)         else :            q.append(stepNumA)            q.append(stepNumB) # Prints all stepping numbers in range [n, m]# using BFS.def displaySteppingNumbers(n, m) :     # For every single digit Number 'i'    # find all the Stepping Numbers    # starting with i    for i in range(10) :        bfs(n, m, i)         # Driver coden, m = 0, 21 # Display Stepping Numbers in the# range [n,m]displaySteppingNumbers(n, m) # This code is contributed by divyeshrabadiya07.

## C#

 // A C# program to find all the Stepping Number in// range [n, m]using System;using System.Collections.Generic;public class GFG{         // Prints all stepping numbers reachable from num    // and in range [n, m]    static void bfs(int n, int m, int num)    {               // Queue will contain all the stepping Numbers        Queue q = new Queue();        q.Enqueue(num);        while(q.Count != 0)        {                       // Get the front element and pop from            // the queue            int stepNum = q.Dequeue();                         // If the Stepping Number is in            // the range [n,m] then display            if (stepNum <= m && stepNum >= n)            {                Console.Write(stepNum + " ");            }                         // If Stepping Number is 0 or greater            // then m, no need to explore the neighbors            if (stepNum == 0 || stepNum > m)                continue;                         // Get the last digit of the currently            // visited Stepping Number            int lastDigit = stepNum % 10;              // There can be 2 cases either digit            // to be appended is lastDigit + 1 or            // lastDigit - 1            int stepNumA = stepNum * 10 + (lastDigit- 1);            int stepNumB = stepNum * 10 + (lastDigit + 1);                         // If lastDigit is 0 then only possible            // digit after 0 can be 1 for a Stepping            // Number            if (lastDigit == 0)                q.Enqueue(stepNumB);                         // If lastDigit is 9 then only possible            // digit after 9 can be 8 for a Stepping            // Number            else if (lastDigit == 9)                q.Enqueue(stepNumA);            else            {                q.Enqueue(stepNumA);                q.Enqueue(stepNumB);            }        }    }         // Prints all stepping numbers in range [n, m]    // using BFS.    static void displaySteppingNumbers(int n,int m)    {        // For every single digit Number 'i'        // find all the Stepping Numbers        // starting with i        for (int i = 0 ; i <= 9 ; i++)            bfs(n, m, i);    }         // Driver code    static public void Main ()    {        int n = 0, m = 21;          // Display Stepping Numbers in        // the range [n,m]        displaySteppingNumbers(n,m);    }} // This code is contributed by avanitrachhadiya2155

## Javascript



Output:

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

DFS based Solution

## C++

 // A C++ program to find all the Stepping Numbers// in range [n, m] using DFS Approach#includeusing namespace std; // Prints all stepping numbers reachable from num// and in range [n, m]void dfs(int n, int m, int stepNum){    // If Stepping Number is in the    // range [n,m] then display    if (stepNum <= m && stepNum >= n)        cout << stepNum << " ";     // If Stepping Number is 0 or greater    // than m, then return    if (stepNum == 0 || stepNum > m)        return ;     // Get the last digit of the currently    // visited Stepping Number    int lastDigit = stepNum % 10;     // There can be 2 cases either digit    // to be appended is lastDigit + 1 or    // lastDigit - 1    int stepNumA = stepNum*10 + (lastDigit-1);    int stepNumB = stepNum*10 + (lastDigit+1);     // If lastDigit is 0 then only possible    // digit after 0 can be 1 for a Stepping    // Number    if (lastDigit == 0)        dfs(n, m, stepNumB);     // If lastDigit is 9 then only possible    // digit after 9 can be 8 for a Stepping    // Number    else if(lastDigit == 9)        dfs(n, m, stepNumA);    else    {        dfs(n, m, stepNumA);        dfs(n, m, stepNumB);    }} // Method displays all the stepping// numbers in range [n, m]void displaySteppingNumbers(int n, int m){    // For every single digit Number 'i'    // find all the Stepping Numbers    // starting with i    for (int i = 0 ; i <= 9 ; i++)        dfs(n, m, i);} //Driver program to test above functionint main(){    int n = 0, m = 21;     // Display Stepping Numbers in    // the range [n,m]    displaySteppingNumbers(n,m);    return 0;}

## Java

 // A Java program to find all the Stepping Numbers// in range [n, m] using DFS Approachimport java.util.*; class Main{    // Method display's all the stepping numbers    // in range [n, m]    public static void dfs(int n,int m,int stepNum)    {        // If Stepping Number is in the        // range [n,m] then display        if (stepNum <= m && stepNum >= n)            System.out.print(stepNum + " ");         // If Stepping Number is 0 or greater        // than m then return        if (stepNum == 0 || stepNum > m)            return ;         // Get the last digit of the currently        // visited Stepping Number        int lastDigit = stepNum % 10;         // There can be 2 cases either digit        // to be appended is lastDigit + 1 or        // lastDigit - 1        int stepNumA = stepNum*10 + (lastDigit-1);        int stepNumB = stepNum*10 + (lastDigit+1);         // If lastDigit is 0 then only possible        // digit after 0 can be 1 for a Stepping        // Number        if (lastDigit == 0)            dfs(n, m, stepNumB);         // If lastDigit is 9 then only possible        // digit after 9 can be 8 for a Stepping        // Number        else if(lastDigit == 9)            dfs(n, m, stepNumA);        else        {            dfs(n, m, stepNumA);            dfs(n, m, stepNumB);        }    }     // Prints all stepping numbers in range [n, m]    // using DFS.    public static void displaySteppingNumbers(int n, int m)    {        // For every single digit Number 'i'        // find all the Stepping Numbers        // starting with i        for (int i = 0 ; i <= 9 ; i++)            dfs(n, m, i);    }     // Driver code    public static void main(String args[])    {        int n = 0, m = 21;         // Display Stepping Numbers in        // the range [n,m]        displaySteppingNumbers(n,m);    }}

## Python3

 # A Python3 program to find all the Stepping Numbers# in range [n, m] using DFS Approach # Prints all stepping numbers reachable from num# and in range [n, m]def dfs(n, m, stepNum) :     # If Stepping Number is in the    # range [n,m] then display    if (stepNum <= m and stepNum >= n) :        print(stepNum, end = " ")      # If Stepping Number is 0 or greater    # than m, then return    if (stepNum == 0 or stepNum > m) :        return      # Get the last digit of the currently    # visited Stepping Number    lastDigit = stepNum % 10      # There can be 2 cases either digit    # to be appended is lastDigit + 1 or    # lastDigit - 1    stepNumA = stepNum * 10 + (lastDigit - 1)    stepNumB = stepNum * 10 + (lastDigit + 1)      # If lastDigit is 0 then only possible    # digit after 0 can be 1 for a Stepping    # Number    if (lastDigit == 0) :        dfs(n, m, stepNumB)      # If lastDigit is 9 then only possible    # digit after 9 can be 8 for a Stepping    # Number    elif(lastDigit == 9) :        dfs(n, m, stepNumA)    else :             dfs(n, m, stepNumA)        dfs(n, m, stepNumB)         # Method displays all the stepping# numbers in range [n, m]def displaySteppingNumbers(n, m) :     # For every single digit Number 'i'    # find all the Stepping Numbers    # starting with i    for i in range(10) :        dfs(n, m, i)         n, m = 0, 21  # Display Stepping Numbers in# the range [n,m]displaySteppingNumbers(n, m) # This code is contributed by divyesh072019.

## C#

 // A C# program to find all the Stepping Numbers// in range [n, m] using DFS Approachusing System;public class GFG{   // Method display's all the stepping numbers  // in range [n, m]  static void dfs(int n, int m, int stepNum)  {     // If Stepping Number is in the    // range [n,m] then display    if (stepNum <= m && stepNum >= n)      Console.Write(stepNum + " ");     // If Stepping Number is 0 or greater    // than m then return    if (stepNum == 0 || stepNum > m)      return ;     // Get the last digit of the currently    // visited Stepping Number    int lastDigit = stepNum % 10;     // There can be 2 cases either digit    // to be appended is lastDigit + 1 or    // lastDigit - 1    int stepNumA = stepNum*10 + (lastDigit - 1);    int stepNumB = stepNum*10 + (lastDigit + 1);     // If lastDigit is 0 then only possible    // digit after 0 can be 1 for a Stepping    // Number    if (lastDigit == 0)      dfs(n, m, stepNumB);     // If lastDigit is 9 then only possible    // digit after 9 can be 8 for a Stepping    // Number    else if(lastDigit == 9)      dfs(n, m, stepNumA);    else    {      dfs(n, m, stepNumA);      dfs(n, m, stepNumB);    }  }   // Prints all stepping numbers in range [n, m]  // using DFS.  public static void displaySteppingNumbers(int n, int m)  {     // For every single digit Number 'i'    // find all the Stepping Numbers    // starting with i    for (int i = 0 ; i <= 9 ; i++)      dfs(n, m, i);  }   // Driver code  static public void Main ()  {    int n = 0, m = 21;     // Display Stepping Numbers in    // the range [n,m]    displaySteppingNumbers(n,m);  }} // This code is contributed by rag2127.

## Javascript



Output:

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

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