הרצף הארוך ביותר ברציפות בעץ בינארי

הרצף הארוך ביותר ברציפות בעץ בינארי
נסה את זה ב-GfG Practice הרצף הארוך ביותר ברציפות בעץ בינארי #practiceLinkDiv { display: none !חשוב; }

בהינתן עץ בינארי מצא את אורך הנתיב הארוך ביותר הכולל צמתים עם ערכים עוקבים בסדר הולך וגדל. כל צומת נחשב כנתיב באורך 1.
דוגמאות:  
 

In below diagram binary tree with longest consecutive path(LCP) are shown : 

תרגול מומלץ הרצף הארוך ביותר ברציפות בעץ בינארי נסה את זה!

אנחנו יכולים לפתור את הבעיה שלעיל באופן רקורסיבי. בכל צומת אנו זקוקים למידע על הצומת האב שלו אם לצומת הנוכחי יש ערך אחד יותר מהצומת האב שלו אז הוא עושה נתיב רצוף בכל צומת נשווה את הערך של הצומת עם ערך האב שלו ונעדכן את הנתיב הרצוף הארוך ביותר בהתאם. 

לקבלת הערך של צומת האב, נעביר את (node_value + 1) כארגומנט לשיטה הרקורסיבית ונשווה את ערך הצומת עם ערך הארגומנט הזה אם עונה על עדכון האורך הנוכחי של נתיב עוקב, אחרת אתחול מחדש את אורך הנתיב הנוכחי ב-1. 

אנא עיין בקוד למטה להבנה טובה יותר: 

C++
   // C/C++ program to find longest consecutive   // sequence in binary tree   #include          using     namespace     std  ;   /* A binary tree node has data pointer to left    child and a pointer to right child */   struct     Node   {      int     data  ;      Node     *  left       *  right  ;   };   // A utility function to create a node   Node  *     newNode  (  int     data  )   {      Node  *     temp     =     new     Node  ;      temp  ->  data     =     data  ;      temp  ->  left     =     temp  ->  right     =     NULL  ;      return     temp  ;   }   // Utility method to return length of longest   // consecutive sequence of tree   void     longestConsecutiveUtil  (  Node  *     root       int     curLength        int     expected       int  &     res  )   {      if     (  root     ==     NULL  )      return  ;      // if root data has one more than its parent      // then increase current length      if     (  root  ->  data     ==     expected  )      curLength  ++  ;      else      curLength     =     1  ;      // update the maximum by current length      res     =     max  (  res       curLength  );      // recursively call left and right subtree with      // expected value 1 more than root data      longestConsecutiveUtil  (  root  ->  left       curLength        root  ->  data     +     1       res  );      longestConsecutiveUtil  (  root  ->  right       curLength        root  ->  data     +     1       res  );   }   // method returns length of longest consecutive   // sequence rooted at node root   int     longestConsecutive  (  Node  *     root  )   {      if     (  root     ==     NULL  )      return     0  ;      int     res     =     0  ;      // call utility method with current length 0      longestConsecutiveUtil  (  root       0       root  ->  data       res  );      return     res  ;   }   // Driver code to test above methods   int     main  ()   {      Node  *     root     =     newNode  (  6  );      root  ->  right     =     newNode  (  9  );      root  ->  right  ->  left     =     newNode  (  7  );      root  ->  right  ->  right     =     newNode  (  10  );      root  ->  right  ->  right  ->  right     =     newNode  (  11  );      printf  (  '%d  n  '       longestConsecutive  (  root  ));      return     0  ;   }   
Java
   // Java program to find longest consecutive    // sequence in binary tree   class   Node   {      int     data  ;      Node     left       right  ;      Node  (  int     item  )      {      data     =     item  ;      left     =     right     =     null  ;      }   }   class   Result      {      int     res     =     0  ;   }   class   BinaryTree   {      Node     root  ;      // method returns length of longest consecutive       // sequence rooted at node root       int     longestConsecutive  (  Node     root  )      {      if     (  root     ==     null  )      return     0  ;      Result     res     =     new     Result  ();          // call utility method with current length 0       longestConsecutiveUtil  (  root       0       root  .  data       res  );          return     res  .  res  ;      }      // Utility method to return length of longest       // consecutive sequence of tree       private     void     longestConsecutiveUtil  (  Node     root       int     curlength           int     expected       Result     res  )      {      if     (  root     ==     null  )      return  ;      // if root data has one more than its parent       // then increase current length       if     (  root  .  data     ==     expected  )      curlength  ++  ;      else      curlength     =     1  ;      // update the maximum by current length       res  .  res     =     Math  .  max  (  res  .  res       curlength  );      // recursively call left and right subtree with       // expected value 1 more than root data       longestConsecutiveUtil  (  root  .  left       curlength       root  .  data     +     1       res  );      longestConsecutiveUtil  (  root  .  right       curlength       root  .  data     +     1       res  );      }      // Driver code      public     static     void     main  (  String     args  []  )         {      BinaryTree     tree     =     new     BinaryTree  ();      tree  .  root     =     new     Node  (  6  );      tree  .  root  .  right     =     new     Node  (  9  );      tree  .  root  .  right  .  left     =     new     Node  (  7  );      tree  .  root  .  right  .  right     =     new     Node  (  10  );      tree  .  root  .  right  .  right  .  right     =     new     Node  (  11  );      System  .  out  .  println  (  tree  .  longestConsecutive  (  tree  .  root  ));      }   }   // This code is contributed by shubham96301   
Python3
   # Python3 program to find longest consecutive    # sequence in binary tree    # A utility class to create a node    class   newNode  :   def   __init__  (  self     data  ):   self  .  data   =   data   self  .  left   =   self  .  right   =   None   # Utility method to return length of    # longest consecutive sequence of tree    def   longestConsecutiveUtil  (  root     curLength     expected     res  ):   if   (  root   ==   None  ):   return   # if root data has one more than its    # parent then increase current length    if   (  root  .  data   ==   expected  ):   curLength   +=   1   else  :   curLength   =   1   # update the maximum by current length    res  [  0  ]   =   max  (  res  [  0  ]   curLength  )   # recursively call left and right subtree    # with expected value 1 more than root data    longestConsecutiveUtil  (  root  .  left     curLength     root  .  data   +   1     res  )   longestConsecutiveUtil  (  root  .  right     curLength     root  .  data   +   1     res  )   # method returns length of longest consecutive    # sequence rooted at node root    def   longestConsecutive  (  root  ):   if   (  root   ==   None  ):   return   0   res   =   [  0  ]   # call utility method with current length 0    longestConsecutiveUtil  (  root     0     root  .  data     res  )   return   res  [  0  ]   # Driver Code   if   __name__   ==   '__main__'  :   root   =   newNode  (  6  )   root  .  right   =   newNode  (  9  )   root  .  right  .  left   =   newNode  (  7  )   root  .  right  .  right   =   newNode  (  10  )   root  .  right  .  right  .  right   =   newNode  (  11  )   print  (  longestConsecutive  (  root  ))   # This code is contributed by PranchalK   
C#
   // C# program to find longest consecutive    // sequence in binary tree    using     System  ;      class     Node      {         public     int     data  ;         public     Node     left       right  ;         public     Node  (  int     item  )         {         data     =     item  ;         left     =     right     =     null  ;         }      }      class     Result      {         public     int     res     =     0  ;      }      class     GFG      {         Node     root  ;         // method returns length of longest consecutive       // sequence rooted at node root       int     longestConsecutive  (  Node     root  )         {         if     (  root     ==     null  )         return     0  ;         Result     res     =     new     Result  ();             // call utility method with current length 0       longestConsecutiveUtil  (  root       0       root  .  data       res  );             return     res  .  res  ;         }         // Utility method to return length of longest       // consecutive sequence of tree       private     void     longestConsecutiveUtil  (  Node     root       int     curlength           int     expected       Result     res  )         {         if     (  root     ==     null  )         return  ;         // if root data has one more than its parent       // then increase current length       if     (  root  .  data     ==     expected  )         curlength  ++  ;         else      curlength     =     1  ;         // update the maximum by current length       res  .  res     =     Math  .  Max  (  res  .  res       curlength  );         // recursively call left and right subtree with       // expected value 1 more than root data       longestConsecutiveUtil  (  root  .  left       curlength           root  .  data     +     1       res  );         longestConsecutiveUtil  (  root  .  right       curlength           root  .  data     +     1       res  );         }         // Driver code       public     static     void     Main  (  String     []  args  )         {         GFG     tree     =     new     GFG  ();         tree  .  root     =     new     Node  (  6  );         tree  .  root  .  right     =     new     Node  (  9  );         tree  .  root  .  right  .  left     =     new     Node  (  7  );         tree  .  root  .  right  .  right     =     new     Node  (  10  );         tree  .  root  .  right  .  right  .  right     =     new     Node  (  11  );         Console  .  WriteLine  (  tree  .  longestConsecutive  (  tree  .  root  ));         }      }      // This code is contributed by 29AjayKumar   
JavaScript
    <  script  >   // JavaScript program to find longest consecutive    // sequence in binary tree   class     Node   {      constructor  (  item  )      {      this  .  data  =  item  ;      this  .  left     =     this  .  right     =     null  ;      }   }   let     res     =     0  ;   let     root  ;   function     longestConsecutive  (  root  )   {      if     (  root     ==     null  )      return     0  ;          res  =  [  0  ];             // call utility method with current length 0       longestConsecutiveUtil  (  root       0       root  .  data       res  );          return     res  [  0  ];   }      // Utility method to return length of longest       // consecutive sequence of tree    function     longestConsecutiveUtil  (  root    curlength       expected    res  )   {      if     (  root     ==     null  )      return  ;          // if root data has one more than its parent       // then increase current length       if     (  root  .  data     ==     expected  )      curlength  ++  ;      else      curlength     =     1  ;          // update the maximum by current length       res  [  0  ]     =     Math  .  max  (  res  [  0  ]     curlength  );          // recursively call left and right subtree with       // expected value 1 more than root data       longestConsecutiveUtil  (  root  .  left       curlength           root  .  data     +     1       res  );      longestConsecutiveUtil  (  root  .  right       curlength           root  .  data     +     1       res  );   }   // Driver code   root     =     new     Node  (  6  );   root  .  right     =     new     Node  (  9  );   root  .  right  .  left     =     new     Node  (  7  );   root  .  right  .  right     =     new     Node  (  10  );   root  .  right  .  right  .  right     =     new     Node  (  11  );   document  .  write  (  longestConsecutive  (  root  ));   // This code is contributed by rag2127    <  /script>   

תְפוּקָה
3 

מורכבות זמן: O(N) כאשר N הוא מספר הצמתים בעץ בינארי נתון.
רווח עזר: O(log(N))
נדון גם בקישור הבא: 
אורך נתיב מרבי רצוף הולך וגדל בעץ בינארי

 

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