Lukua kutsutaan onnelliseksi, jos se johtaa 1:een vaihesarjan jälkeen, jossa jokainen askelnumero korvataan sen numeron neliöiden summalla, eli jos aloitamme onnellisilla numeroilla ja korvaamme sen numeroilla neliösumma, saavutamme 1:n. 

Esimerkkejä:  

 Input: n = 19   
 Output: True   
 19 is Happy Number   
 1^2 + 9^2 = 82   
 8^2 + 2^2 = 68   
 6^2 + 8^2 = 100   
 1^2 + 0^2 + 0^2 = 1   
 As we reached to 1 19 is a Happy Number.   
  
 Input: n = 20   
 Output: False  
 Numero ei ole onnellinen numero, kun se tekee sekvenssissään silmukan, eli se koskettaa numeroa järjestyksessä, jota on jo kosketettu. Joten tarkistaaksemme, onko numero onnellinen vai ei, voimme pitää joukon, jos sama numero toistuu, merkitsemme tuloksen ei-tyytyväiseksi. Yllä olevan lähestymistavan yksinkertainen funktio voidaan kirjoittaa seuraavasti -    
 C++   
   // method return true if n is Happy Number   int     numSquareSum  (  int     n  )     {      int     num     =     0  ;      while     (  n     !=     0  )     {      int     digit     =     n     %     10  ;      num     +=     digit     *     digit  ;      n     /=     10  ;      }      return     num  ;   }   int     isHappyNumber  (  int     n  )   {      set   <  int  >     st  ;      while     (  1  )      {      n     =     numSquareSum  (  n  );      if     (  n     ==     1  )      return     true  ;      if     (  st  .  find  (  n  )     !=     st  .  end  ())      return     false  ;      st  .  insert  (  n  );      }   }   
  Java   
   // method return true if n is Happy Number   public     static     int     numSquareSum  (  int     n  )   {      int     num     =     0  ;      while     (  n     !=     0  )     {      int     digit     =     n     %     10  ;      num     +=     digit     *     digit  ;      n     /=     10  ;      }      return     num  ;   }   static     boolean     isHappyNumber  (  int     n  )   {      HashSet   <  Integer  >     st     =     new     HashSet   <>  ();      while     (  true  )     {      n     =     numSquareSum  (  n  );      if     (  n     ==     1  )      return     true  ;      if     (  st  .  contains  (  n  ))      return     false  ;      st  .  add  (  n  );      }   }   // This code is contributed by Princi Singh   
  Python   
   # method return true if n is Happy Number   def   numSquareSum  (  n  ):   num   =   0   while  (  n  ):   digit   =   n   %   10   num   =   num   +   digit  *  digit   n   =   n   //   10   return   num   def   isHappyNumber  (  n  ):   st   =   set  ()   while   (  1  ):   n   =   numSquareSum  (  n  )   if   (  n   ==   1  ):   return   True   if   n   not   in   st  :   return   False   st  .  insert  (  n  )   
  C#   
   // Method return true if n is Happy Number   static     int     numSquareSum  (  int     n  )   {      int     num     =     0  ;      while     (  n     !=     0  )     {      int     digit     =     n     %     10  ;      num     +=     digit     *     digit  ;      n     /=     10  ;      }      return     num  ;   }   static     int     isHappyNumber  (  int     n  )   {      HashSet   <  int  >     st     =     new     HashSet   <>  ();      while     (  1  )     {      n     =     numSquareSum  (  n  );      if     (  n     ==     1  )      return     true  ;      if     (  st  .  Contains  (  n  ))      return     false  ;      st  .  Add  (  n  );      }   }   // This code is contributed by 29AjayKumar   
  JavaScript   
    <  script  >   // method return true if n is Happy Number      function     numSquareSum  (  n  )     {      let     num     =     0  ;      while     (  n     !==     0  )     {      let     digit     =     n     %     10  ;      num     +=     digit     *     digit  ;      n     =     Math  .  floor  (  n     /     10  );      }      return     num  ;      }      let     st     =     new     Set  ();      while     (  1  )      {      n     =     numSquareSum  (  n  );      if     (  n     ==     1  )      return     true  ;      if     (  st  .  has  (  n  ))      return     false  ;      st  .  add  (  n  );      }   }   //This code is contributed by Mayank Tyagi    <  /script>   
   
    Monimutkaisuusanalyysi:    
 
    Aika monimutkaisuus:    O(n*log(n)).    
    Aputila:    O(n), koska käytetään ylimääräistä sarjaa säilytykseen  
 
 Voimme ratkaista tämän ongelman ilman ylimääräistä tilaa ja tätä tekniikkaa voidaan käyttää myös joissakin muissa vastaavissa ongelmissa. Jos käsittelemme jokaista lukua solmuna ja korvaamista neliösummalla linkkinä, tämä ongelma on sama kuin    silmukan löytäminen linkkiluettelosta    :   
 
 Joten yllä olevan linkin ratkaisuehdotuksena pidämme kaksi numeroa hitaana ja nopeana sekä alustus annetusta numerosta hidas korvataan askel kerrallaan ja nopea kaksi askelta kerrallaan. Jos he kokoontuvat yhdeltä, annettu numero on onnellinen numero, muuten ei.    
 C++   
   // C++ program to check a number is a Happy number or not   #include          using     namespace     std  ;   // Utility method to return sum of square of digit of n   int     numSquareSum  (  int     n  )   {      int     squareSum     =     0  ;      while     (  n  )     {      squareSum     +=     (  n     %     10  )     *     (  n     %     10  );      n     /=     10  ;      }      return     squareSum  ;   }   // method return true if n is Happy number   bool     isHappynumber  (  int     n  )   {      int     slow       fast  ;      // initialize slow and fast by n      slow     =     fast     =     n  ;      do     {      // move slow number by one iteration      slow     =     numSquareSum  (  slow  );      // move fast number by two iteration      fast     =     numSquareSum  (  numSquareSum  (  fast  ));      }     while     (  slow     !=     fast  );      // if both number meet at 1 then return true      return     (  slow     ==     1  );   }   // Driver code to test above methods   int     main  ()   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      cout      < <     n      < <     ' is a Happy number  n  '  ;      else      cout      < <     n      < <     ' is not a Happy number  n  '  ;   }   // This code is contributed by divyeshrabadiya07   
  C   
   // C program to check a number is a Happy number or not   #include         #include         // Utility method to return sum of square of digit of n   int     numSquareSum  (  int     n  )   {      int     squareSum     =     0  ;      while     (  n  )     {      squareSum     +=     (  n     %     10  )     *     (  n     %     10  );      n     /=     10  ;      }      return     squareSum  ;   }   // method return true if n is Happy number   bool     isHappynumber  (  int     n  )   {      int     slow       fast  ;      // initialize slow and fast by n      slow     =     fast     =     n  ;      do     {      // move slow number by one iteration      slow     =     numSquareSum  (  slow  );      // move fast number by two iteration      fast     =     numSquareSum  (  numSquareSum  (  fast  ));      }     while     (  slow     !=     fast  );      // if both number meet at 1 then return true      return     (  slow     ==     1  );   }   // Driver code to test above methods   int     main  ()   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      printf  (  '%d is a Happy number  n  '       n  );      else      printf  (  '%d is not a Happy number  n  '       n  );   }   // This code is contributed by Sania Kumari Gupta   // (kriSania804)   
  Java   
   // Java program to check a number is a Happy   // number or not   class   GFG     {       // Utility method to return sum of square of   // digit of n   static     int     numSquareSum  (  int     n  )   {      int     squareSum     =     0  ;      while     (  n  !=     0  )      {      squareSum     +=     (  n     %     10  )     *     (  n     %     10  );      n     /=     10  ;      }      return     squareSum  ;   }       // method return true if n is Happy number   static     boolean     isHappynumber  (  int     n  )   {      int     slow       fast  ;          // initialize slow and fast by n      slow     =     fast     =     n  ;      do      {      // move slow number      // by one iteration      slow     =     numSquareSum  (  slow  );          // move fast number      // by two iteration      fast     =     numSquareSum  (  numSquareSum  (  fast  ));          }      while     (  slow     !=     fast  );          // if both number meet at 1      // then return true      return     (  slow     ==     1  );   }       // Driver code to test above methods   public     static     void     main  (  String  []     args  )   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      System  .  out  .  println  (  n     +         ' is a Happy number'  );      else      System  .  out  .  println  (  n     +         ' is not a Happy number'  );   }   }   
  Python   
   # Python3 program to check if a number is a Happy number or not   # Utility method to return the sum of squares of digits of n   def   num_square_sum  (  n  ):   square_sum   =   0   while   n  :   square_sum   +=   (  n   %   10  )   **   2   n   //=   10   return   square_sum   # Method returns True if n is a Happy number   def   is_happy_number  (  n  ):   # Initialize slow and fast pointers   slow   =   n   fast   =   n   while   True  :   # Move slow pointer by one iteration   slow   =   num_square_sum  (  slow  )   # Move fast pointer by two iterations   fast   =   num_square_sum  (  num_square_sum  (  fast  ))   if   slow   !=   fast  :   continue   else  :   break   # If both pointers meet at 1 then return True   return   slow   ==   1   # Driver Code   n   =   13   if   is_happy_number  (  n  ):   print  (  n     'is a Happy number'  )   else  :   print  (  n     'is not a Happy number'  )   
  C#   
   // C# program to check a number   // is a Happy number or not   using     System  ;   class     GFG     {   // Utility method to return    // sum of square of digit of n   static     int     numSquareSum  (  int     n  )   {      int     squareSum     =     0  ;      while     (  n  !=     0  )      {      squareSum     +=     (  n     %     10  )     *         (  n     %     10  );      n     /=     10  ;      }      return     squareSum  ;   }   // method return true if   // n is Happy number   static     bool     isHappynumber  (  int     n  )   {      int     slow       fast  ;      // initialize slow and      // fast by n      slow     =     fast     =     n  ;      do      {          // move slow number      // by one iteration      slow     =     numSquareSum  (  slow  );      // move fast number      // by two iteration      fast     =     numSquareSum  (  numSquareSum  (  fast  ));      }      while     (  slow     !=     fast  );      // if both number meet at 1      // then return true      return     (  slow     ==     1  );   }   // Driver code   public     static     void     Main  ()   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      Console  .  WriteLine  (  n     +         ' is a Happy number'  );      else      Console  .  WriteLine  (  n     +         ' is not a Happy number'  );   }   }   // This code is contributed by anuj_67.   
  JavaScript   
    <  script  >   // Javascript program to check a number is a Happy   // number or not   // Utility method to return sum of square of   // digit of n   function     numSquareSum  (  n  )   {      var     squareSum     =     0  ;      while     (  n  !=     0  )      {      squareSum     +=     (  n     %     10  )     *     (  n     %     10  );      n     =     parseInt  (  n  /  10  );      }      return     squareSum  ;   }       // method return true if n is Happy number   function     isHappynumber  (  n  )   {      var     slow       fast  ;          // initialize slow and fast by n      slow     =     fast     =     n  ;      do      {      // move slow number      // by one iteration      slow     =     numSquareSum  (  slow  );          // move fast number      // by two iteration      fast     =     numSquareSum  (  numSquareSum  (  fast  ));          }      while     (  slow     !=     fast  );          // if both number meet at 1      // then return true      return     (  slow     ==     1  );   }       // Driver code to test above methods   var     n     =     13  ;   if     (  isHappynumber  (  n  ))      document  .  write  (  n     +         ' is a Happy number'  );   else      document  .  write  (  n     +         ' is not a Happy number'  );       // This code contributed by Princi Singh     <  /script>   
  PHP   
      // PHP program to check a number   // is a Happy number or not   // Utility method to return    // sum of square of digit of n   function   numSquareSum  (   $n  )   {   $squareSum   =   0  ;   while   (  $n  )   {   $squareSum   +=   (  $n   %   10  )   *   (  $n   %   10  );   $n   /=   10  ;   }   return   $squareSum  ;   }   // method return true if   // n is Happy number   function   isHappynumber  (   $n  )   {   $slow  ;   $fast  ;   // initialize slow    // and fast by n   $slow   =   $n  ;   $fast   =   $n  ;   do   {   // move slow number   // by one iteration   $slow   =   numSquareSum  (  $slow  );   // move fast number   // by two iteration   $fast   =   numSquareSum  (  numSquareSum  (  $fast  ));   }   while   (  $slow   !=   $fast  );   // if both number meet at 1    // then return true   return   (  $slow   ==   1  );   }   // Driver Code   $n   =   13  ;   if   (  isHappynumber  (  $n  ))   echo   $n      ' is a Happy number  n  '  ;   else   echo   n      ' is not a Happy number  n  '  ;   // This code is contributed by anuj_67.   ?>   
   
    Lähtö:       
 
 13 is a Happy Number  
    Monimutkaisuusanalyysi:    
 
    Aika monimutkaisuus:    O(n*log(n)).   
    Aputila:    O(1).   
 
  
    Toinen tapa ratkaista tämä ongelma ilman ylimääräistä tilaa.     
 Numero ei voi olla onnellinen luku     jos jossakin vaiheessa saatujen numeroiden neliön summa on yksinumeroinen luku lukuun ottamatta 1 tai 7    . Tämä johtuu siitä, että 1 ja 7 ovat ainoat yksinumeroiset onnelliset luvut. Näiden tietojen avulla voimme kehittää lähestymistavan alla olevan koodin mukaisesti -   
 C++   
   // C++ program to check if a number is a Happy number or   // not.   #include          using     namespace     std  ;   // Method - returns true if the input is a happy number else   // returns false   bool     isHappynumber  (  int     n  )   {      int     sum     =     n       x     =     n  ;      // This loop executes till the sum of square of digits      // obtained is not a single digit number      while     (  sum     >     9  )     {      sum     =     0  ;      // This loop finds the sum of square of digits      while     (  x     >     0  )     {      int     d     =     x     %     10  ;      sum     +=     d     *     d  ;      x     /=     10  ;      }      x     =     sum  ;      }      if     (  sum     ==     7     ||     sum     ==     1  )      return     true  ;      return     false  ;   }   int     main  ()   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      cout      < <     n      < <     ' is a Happy number'  ;      else      cout      < <     n      < <     ' is not a Happy number'  ;      return     0  ;   }   // This code is contributed by Sania Kumari Gupta   
  C   
   // C program to check if a number is a Happy number or   // not.   #include         #include         // Method - returns true if the input is a happy number else   // returns false   bool     isHappynumber  (  int     n  )   {      int     sum     =     n       x     =     n  ;      // This loop executes till the sum of square of digits      // obtained is not a single digit number      while     (  sum     >     9  )     {      sum     =     0  ;      // This loop finds the sum of square of digits      while     (  x     >     0  )     {      int     d     =     x     %     10  ;      sum     +=     d     *     d  ;      x     /=     10  ;      }      x     =     sum  ;      }      if     (  sum     ==     7     ||     sum     ==     1  )      return     true  ;      return     false  ;   }   int     main  ()   {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      printf  (  '%d is a Happy number'       n  );      else      printf  (  '%d is not a Happy number'       n  );      return     0  ;   }   // This code is contributed by Sania Kumari Gupta   
  Java   
   // This code is contributed by Vansh Sodhi.   // Java program to check if a number is a Happy number or   // not.   class   GFG     {      // method - returns true if the input is a happy      // number else returns false      static     boolean     isHappynumber  (  int     n  )      {      int     sum     =     n       x     =     n  ;      // this loop executes till the sum of square of      // digits obtained is not a single digit number      while     (  sum     >     9  )     {      sum     =     0  ;      // this loop finds the sum of square of digits      while     (  x     >     0  )     {      int     d     =     x     %     10  ;      sum     +=     d     *     d  ;      x     /=     10  ;      }      x     =     sum  ;      }      if     (  sum     ==     1     ||     sum     ==     7  )      return     true  ;      return     false  ;      }      // Driver code      public     static     void     main  (  String  []     args  )      {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      System  .  out  .  println  (  n     +     ' is a Happy number'  );      else      System  .  out  .  println  (  n      +     ' is not a Happy number'  );      }   }   
  Python   
   # Python3 program to check if a number is a Happy number or not.   # Method - returns true if the input is   # a happy number else returns false   def   isHappynumber  (  n  ):   Sum     x   =   n     n   # This loop executes till the sum   # of square of digits obtained is   # not a single digit number   while   Sum   >   9  :   Sum   =   0   # This loop finds the sum of   # square of digits   while   x   >   0  :   d   =   x   %   10   Sum   +=   d   *   d   x   =   int  (  x   /   10  )   x   =   Sum   if   Sum   ==   1   or   Sum   ==   7  :   return   True   return   False   n   =   13   if   isHappynumber  (  n  ):   print  (  n     'is a Happy number'  )   else  :   print  (  n     'is not a Happy number'  )   # This code is contributed by mukesh07.   
  C#   
   // C# program to check if a number   // is a Happy number or not.   using     System  ;   class     GFG     {      // Method - returns true if the input is      // a happy number else returns false      static     bool     isHappynumber  (  int     n  )      {      int     sum     =     n       x     =     n  ;      // This loop executes till the sum      // of square of digits obtained is      // not a single digit number      while     (  sum     >     9  )     {      sum     =     0  ;      // This loop finds the sum of      // square of digits      while     (  x     >     0  )     {      int     d     =     x     %     10  ;      sum     +=     d     *     d  ;      x     /=     10  ;      }      x     =     sum  ;      }      if     (  sum     ==     1     ||     sum     ==     7  )      return     true  ;      return     false  ;      }      // Driver code      public     static     void     Main  (  String  []     args  )      {      int     n     =     13  ;      if     (  isHappynumber  (  n  ))      Console  .  WriteLine  (  n     +     ' is a Happy number'  );      else      Console  .  WriteLine  (  n     +     ' is not a Happy number'  );      }   }   // This code is contributed by 29AjayKumar   
  JavaScript   
    <  script  >   // This code is contributed by Vansh Sodhi.   // javascript program to check if a number is a Happy number or not.      // method - returns true if the input is a happy      // number else returns false      function     isHappynumber  (  n  )      {      var     sum     =     n       x     =     n  ;      // this loop executes till the sum of square of      // digits obtained is not a single digit number      while  (  sum     >     9  )         {      sum     =     0  ;      // this loop finds the sum of square of digits      while     (  x     >     0  )         {      var     d     =     x     %     10  ;      sum     +=     d     *     d  ;      x     /=     10  ;      }      x     =     sum  ;      }      if  (  sum     ==     1     ||     sum     ==     7  )      return     true  ;      return     false  ;   }   // Driver code      var     n     =     13  ;      if     (  isHappynumber  (  n  ))      document  .  write  (  n     +         ' is a Happy number'  );      else      document  .  write  (  n     +         ' is not a Happy number'  );       // This code is contributed by 29AjayKumar     <  /script>   
    
  Lähtö   
13 is a Happy number 
 
    Monimutkaisuusanalyysi:    
 
    Aika monimutkaisuus:    O(n*log(n)).   
    Aputila:    O(1).   
 
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