Trintal

Trintal
Prøv det på GfG Practice #practiceLinkDiv { display: ingen !important; }

Givet to heltal 'n' og 'm' find alle trintallene i området [n m]. Der ringes op til et nummer skridtnummer hvis alle tilstødende cifre har en absolut forskel på 1. 321 er et skridttal, mens 421 ikke er det.

Eksempler: 

  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 Tal med én absolut forskel Prøv det!

Metode 1: Brute force Approach
I denne metode bruges en brute force-tilgang til at iterere gennem alle heltal fra n til m og kontrollere, om det er et trintal. 

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>   

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

Metode 2: Brug af BFS/DFS

Tanken er at bruge en Breadth First Search / Dybde første søgning krydsning.

Hvordan bygger man grafen?  
Hver knude på grafen repræsenterer et skridtnummer; der vil være en rettet kant fra en node U til V, hvis V kan transformeres fra U. (U og V er Stepping Numbers) Et Stepping Number V kan transformeres fra U på følgende måde.
sidste cifre refererer til det sidste ciffer i U (dvs. U % 10) 
Et tilstødende nummer V kan være:  

  • U*10 + sidste cifret + 1 (nabo A)
  • U*10 + sidste cifret – 1 (nabo B)


Ved at anvende ovenstående operationer tilføjes et nyt ciffer til U, det er enten lastCifer-1 eller lastCifer+1, således at det nye tal V dannet af U også er et Stepping Number. 
Derfor vil hver node højst have 2 naboknuder.
Edge Cases: Når det sidste ciffer i U er eller 9

    Case 1: lastDigit er 0 : I dette tilfælde kan kun ciffer '1' tilføjes. Tilfælde 2: lastDigit er 9 : I dette tilfælde kan kun ciffer '8' tilføjes.

Hvad bliver kilden/startknuden?   

  • Hvert enkelt cifret tal betragtes som et trinnummer, så bfs gennemløb for hvert ciffer vil give alle trinnumre startende fra det ciffer.
  • Lav en bfs/dfs-gennemgang for alle tallene fra [09].

Note: For node 0 er det ikke nødvendigt at udforske naboer under BFS-gennemløbet, da det vil føre til 01 012 010, og disse vil være dækket af BFS-gennemgangen fra knudepunkt 1. 
Eksempel for at finde alle trintal fra 0 til 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 baseret løsning:

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>   

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

DFS baseret løsning:

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>   

Produktion
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Tidskompleksitet:O(N log N)

Rumkompleksitet:O(N) her er N antallet af skridttal inden for området.