Koračni brojevi

Koračni brojevi
Isprobajte na GfG Practice #practiceLinkDiv { display: none !important; }

Zadana su dva cijela broja 'n' i 'm', pronađite sve brojeve koraka u rasponu [n m]. Poziva se broj broj koraka ako sve susjedne znamenke imaju apsolutnu razliku od 1. 321 je koračni broj dok 421 nije.

Primjeri: 

  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 
Recommended Practice Brojevi s jednom apsolutnom razlikom Probajte!

Metoda 1: Pristup grubom silom
U ovoj se metodi pristup grubom silom koristi za ponavljanje kroz sve cijele brojeve od n do m i provjeru je li to broj u koraku. 

C++
   // A C++ program to find all the Stepping Number in [n m]   #include       using     namespace     std  ;   // This function checks if an integer n is a Stepping Number   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  )      {      // 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 [NM]      // 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 function   int     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 [NM]      // 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 [nm]      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 Number   def   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 [NM]   # and check if it’s a stepping number.   for   i   in   range  (  n     m   +   1  ):   if   (  isStepNum  (  i  )):   print  (  i     end   =   ' '  )   # Driver code   if   __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 [NM] 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 [nm]      displaySteppingNumbers  (  n       m  );      }   }   // This code is contributed by nitin mittal.   
JavaScript
    <  script  >      // A Javascript program to find all the Stepping Number in [n m]          // This function checks if an integer n is a Stepping Number      function     isStepNum  (  n  )      {      // Initialize prevDigit with -1      let     prevDigit     =     -  1  ;      // Iterate through all digits of n and compare difference      // between value of previous and current digits      while     (  n     >     0  )      {      // Get Current digit      let     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     (  Math  .  abs  (  prevDigit     -     curDigit  )     !=     1  )      return     false  ;      }      prevDigit     =     curDigit  ;      n     =     parseInt  (  n     /     10       10  );      }      return     true  ;      }      // A brute force approach based function to find all      // stepping numbers.      function     displaySteppingNumbers  (  n       m  )      {      // Iterate through all the numbers from [NM]      // and check if it’s a stepping number.      for     (  let     i     =     n  ;     i      <=     m  ;     i  ++  )      if     (  isStepNum  (  i  ))      document  .  write  (  i     +     ' '  );      }      let     n     =     0       m     =     21  ;          // Display Stepping Numbers in      // the range [n m]      displaySteppingNumbers  (  n       m  );          // This code is contributed by mukesh07.    <  /script>   

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

Metoda 2: Korištenje BFS/DFS

Ideja je koristiti a Traži prvo u širinu / Prvo pretraživanje dubine obilazak.

Kako izgraditi grafikon?  
Svaki čvor na grafikonu predstavlja broj koraka; bit će usmjeren brid od čvora U do V ako se V može transformirati iz U. (U i V su brojevi koraka) Broj koraka V može se transformirati iz U na sljedeći način.
lastDigit odnosi se na posljednju znamenku U (tj. U % 10) 
Susjedni broj V može biti:  

  • U*10 + zadnja znamenka + 1 (susjed A)
  • U*10 + zadnja znamenka – 1 (susjed B)


Primjenom gornjih operacija U se dodaje nova znamenka, ona je ili lastDigit-1 ili lastDigit+1 tako da je novi broj V formiran od U također Koračni broj. 
Stoga će svaki čvor imati najviše 2 susjedna čvora.
Rubna kućišta: Kada je zadnja znamenka U ili 9

    1. slučaj: lastDigit je 0 : U ovom slučaju može se dodati samo znamenka '1'. Slučaj 2: lastDigit je 9 : U ovom slučaju može se dodati samo znamenka '8'.

Što će biti izvorni/početni čvor?   

  • Svaki broj s jednom znamenkom smatra se brojem koraka tako da će bfs traversal za svaku znamenku dati sve brojeve koraka počevši od te znamenke.
  • Napravite bfs/dfs traversal za sve brojeve iz [09].

Bilješka: Za čvor 0 nema potrebe za istraživanjem susjeda tijekom BFS obilaska jer će to dovesti do 01 012 010 i oni će biti pokriveni BFS obilaskom počevši od čvora 1. 
Primjer za pronalaženje svih brojeva od 0 do 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. 

Rješenje temeljeno na BFS-u:

C++
   // A C++ program to find all the Stepping Number from N=n   // to m using BFS Approach   #include       using     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   <  int  >     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 function   int     main  ()   {      int     n     =     0       m     =     21  ;      // Display Stepping Numbers in the      // range [nm]      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   <  Integer  >     q     =     new     LinkedList   <  Integer  >     ();      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 [nm] 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 [nm]      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 code   n     m   =   0     21   # Display Stepping Numbers in the   # range [nm]   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   <  int  >     q     =     new     Queue   <  int  >  ();      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 [nm] 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 [nm]      displaySteppingNumbers  (  n    m  );      }   }   // This code is contributed by avanitrachhadiya2155   
JavaScript
    <  script  >   // A Javascript program to find all   // the Stepping Number in   // range [n m]          // Prints all stepping numbers       // reachable from num      // and in range [n m]      function     bfs  (  n    m    num  )      {      // Queue will contain all the       // stepping Numbers      let     q     =     [];          q  .  push  (  num  );          while     (  q  .  length  !=  0  )      {      // Get the front element and pop from      // the queue      let     stepNum     =     q  .  shift  ();          // If the Stepping Number is in      // the range [nm] then display      if     (  stepNum      <=     m     &&     stepNum     >=     n  )      {      document  .  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      let     lastDigit     =     stepNum     %     10  ;          // There can be 2 cases either digit      // to be appended is lastDigit + 1 or      // lastDigit - 1      let     stepNumA     =     stepNum     *     10     +     (  lastDigit  -     1  );      let     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.      function     displaySteppingNumbers  (  n    m  )      {      // For every single digit Number 'i'      // find all the Stepping Numbers      // starting with i      for     (  let     i     =     0     ;     i      <=     9     ;     i  ++  )      bfs  (  n       m       i  );      }              // Driver code      let     n     =     0       m     =     21  ;          // Display Stepping Numbers in      // the range [nm]      displaySteppingNumbers  (  n    m  );              // This code is contributed by unknown2108        <  /script>   

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

Rješenje temeljeno na DFS-u:

C++
   // A C++ program to find all the Stepping Numbers   // in range [n m] using DFS Approach   #include       using     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 [nm] 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 function   int     main  ()   {      int     n     =     0       m     =     21  ;      // Display Stepping Numbers in      // the range [nm]      displaySteppingNumbers  (  n    m  );      return     0  ;   }   
Java
   // A Java program to find all the Stepping Numbers   // in range [n m] using DFS Approach   import     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 [nm] 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 [nm]      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 [nm] 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 [nm]   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 Approach   using     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 [nm] 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 [nm]      displaySteppingNumbers  (  n    m  );      }   }   // This code is contributed by rag2127.   
JavaScript
    <  script  >   // A Javascript program to find all the Stepping Numbers   // in range [n m] using DFS Approach   // Method display's all the stepping numbers      // in range [n m]   function     dfs  (  n       m       stepNum  )   {      // If Stepping Number is in the      // range [nm] then display      if     (  stepNum      <=     m     &&     stepNum     >=     n  )      document  .  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      let     lastDigit     =     stepNum     %     10  ;          // There can be 2 cases either digit      // to be appended is lastDigit + 1 or      // lastDigit - 1      let     stepNumA     =     stepNum  *  10     +     (  lastDigit  -  1  );      let     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.   function     displaySteppingNumbers  (  n       m  )   {      // For every single digit Number 'i'      // find all the Stepping Numbers      // starting with i      for     (  let     i     =     0     ;     i      <=     9     ;     i  ++  )      dfs  (  n       m       i  );   }   // Driver code   let     n     =     0       m     =     21  ;       // Display Stepping Numbers in   // the range [nm]   displaySteppingNumbers  (  n    m  );   // This code is contributed by ab2127    <  /script>   

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

Vremenska složenost: O(N log N)

Prostorna složenost: O(N) ovdje je N broj koraka unutar raspona.