أطول تسلسل متتالي في الشجرة الثنائية

أطول تسلسل متتالي في الشجرة الثنائية
جربه على ممارسة GfG أطول تسلسل متتالي في الشجرة الثنائية #practiceLinkDiv { العرض: لا شيء! مهم؛ }

بالنظر إلى شجرة ثنائية، ابحث عن طول المسار الأطول الذي يتكون من عقد ذات قيم متتالية بترتيب متزايد. تعتبر كل عقدة بمثابة مسار بطول 1.
أمثلة:  
 

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

الممارسة الموصى بها أطول تسلسل متتالي في الشجرة الثنائية جربه!

يمكننا حل المشكلة المذكورة أعلاه بشكل متكرر. في كل عقدة نحتاج إلى معلومات عن العقدة الأصلية الخاصة بها، إذا كانت العقدة الحالية لها قيمة واحدة أكثر من العقدة الأصلية، فإنها تقوم بإنشاء مسار متتالي في كل عقدة، وسنقارن قيمة العقدة بقيمتها الأصلية ونقوم بتحديث أطول مسار متتالي وفقًا لذلك. 

للحصول على قيمة العقدة الأصلية، سنمرر (node_value + 1) كوسيطة للطريقة العودية ونقارن قيمة العقدة بقيمة الوسيطة هذه إذا استوفت تحديث الطول الحالي للمسار المتتالي وإلا قم بإعادة تهيئة طول المسار الحالي بمقدار 1. 

يرجى الاطلاع على الكود أدناه لفهم أفضل: 

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>   

الإخراج
3 

التعقيد الزمني: O(N) حيث N هو عدد العقد في شجرة ثنائية معينة.
المساحة المساعدة: O(log(N))
تمت مناقشته أيضًا على الرابط أدناه: 
الحد الأقصى لطول المسار المتزايد المتتالي في الشجرة الثنائية

 

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