تقييم شجرة التعبير

تقييم شجرة التعبير

نظرا بسيطة شجرة التعبير تتكون من عوامل تشغيل ثنائية أساسية، مثل + - * و/ وبعض الأعداد الصحيحة تقوم بتقييم شجرة التعبير.

أمثلة:

مدخل: العقدة الجذرية للشجرة أدناه

pic2

الإخراج: 100

مدخل: العقدة الجذرية للشجرة أدناه

الموافقة المسبقة عن علم1

الإخراج: 110

الممارسة الموصى بها شجرة التعبير جربه!

يقترب: يعتمد أسلوب حل هذه المشكلة على الملاحظة التالية:

نظرًا لأن جميع العوامل في الشجرة ثنائية، فإن كل عقدة سيكون لها إما 0 أو 2 طفل. كما يمكن الاستدلال عليه من الأمثلة المذكورة أعلاه، ستظهر جميع قيم الأعداد الصحيحة في العقد الطرفية بينما تمثل العقد الداخلية العوامل.

ولذلك يمكننا أن نفعل الاجتياز الداخلي للشجرة الثنائية وتقييم التعبير ونحن نمضي قدما.

لتقييم شجرة بناء الجملة يمكن اتباع نهج عودي.

الخوارزمية:

  • دع t تكون شجرة بناء الجملة
  • إذا لم تكن فارغة      
    • إذا كان t.info هو المعامل إذن  
      • ارجع t.info
    • آخر
      • أ = حل (t.left)
      • ب = حل(t.right)
      • إرجاع عامل التشغيل B حيث يكون عامل التشغيل هو المعلومات الموجودة في t

وفيما يلي تنفيذ النهج المذكور أعلاه:

C++
   // C++ program to evaluate an expression tree    #include             using     namespace     std  ;      // Class to represent the nodes of syntax tree    class     node      {      public  :         string     info  ;         node     *  left     =     NULL       *  right     =     NULL  ;         node  (  string     x  )         {         info     =     x  ;         }      };      // Utility function to return the integer value    // of a given string    int     toInt  (  string     s  )      {         int     num     =     0  ;             // Check if the integral value is       // negative or not       // If it is not negative generate the number       // normally       if  (  s  [  0  ]  !=  '-'  )         for     (  int     i  =  0  ;     i   <  s  .  length  ();     i  ++  )         num     =     num  *  10     +     (  int  (  s  [  i  ])  -48  );         // If it is negative calculate the +ve number       // first ignoring the sign and invert the       // sign at the end       else      {         for     (  int     i  =  1  ;     i   <  s  .  length  ();     i  ++  )         num     =     num  *  10     +     (  int  (  s  [  i  ])  -48  );         num     =     num  *  -1  ;         }             return     num  ;      }      // This function receives a node of the syntax tree    // and recursively evaluates it    int     eval  (  node  *     root  )      {         // empty tree       if     (  !  root  )         return     0  ;         // leaf node i.e an integer       if     (  !  root  ->  left     &&     !  root  ->  right  )         return     toInt  (  root  ->  info  );         // Evaluate left subtree       int     l_val     =     eval  (  root  ->  left  );         // Evaluate right subtree       int     r_val     =     eval  (  root  ->  right  );         // Check which operator to apply       if     (  root  ->  info  ==  '+'  )         return     l_val  +  r_val  ;         if     (  root  ->  info  ==  '-'  )         return     l_val  -  r_val  ;         if     (  root  ->  info  ==  '*'  )         return     l_val  *  r_val  ;         return     l_val  /  r_val  ;      }      //driver function to check the above program    int     main  ()      {         // create a syntax tree       node     *  root     =     new     node  (  '+'  );         root  ->  left     =     new     node  (  '*'  );         root  ->  left  ->  left     =     new     node  (  '5'  );         root  ->  left  ->  right     =     new     node  (  '-4'  );         root  ->  right     =     new     node  (  '-'  );         root  ->  right  ->  left     =     new     node  (  '100'  );         root  ->  right  ->  right     =     new     node  (  '20'  );         cout      < <     eval  (  root  )      < <     endl  ;         delete  (  root  );         root     =     new     node  (  '+'  );         root  ->  left     =     new     node  (  '*'  );         root  ->  left  ->  left     =     new     node  (  '5'  );         root  ->  left  ->  right     =     new     node  (  '4'  );         root  ->  right     =     new     node  (  '-'  );         root  ->  right  ->  left     =     new     node  (  '100'  );         root  ->  right  ->  right     =     new     node  (  '/'  );         root  ->  right  ->  right  ->  left     =     new     node  (  '20'  );         root  ->  right  ->  right  ->  right     =     new     node  (  '2'  );         cout      < <     eval  (  root  );         return     0  ;      }      
Java
   // Java program to evaluate expression tree   import     java.lang.*  ;   class   GFG  {       Node     root  ;   // Class to represent the nodes of syntax tree   public     static     class   Node      {      String     data  ;      Node     left       right  ;      Node  (  String     d  )      {      data     =     d  ;      left     =     null  ;      right     =     null  ;      }   }   private     static     int     toInt  (  String     s  )   {      int     num     =     0  ;      // Check if the integral value is      // negative or not      // If it is not negative generate       // the number normally      if     (  s  .  charAt  (  0  )     !=     '-'  )      for  (  int     i     =     0  ;     i      <     s  .  length  ();     i  ++  )      num     =     num     *     10     +     ((  int  )  s  .  charAt  (  i  )     -     48  );          // If it is negative calculate the +ve number      // first ignoring the sign and invert the      // sign at the end      else      {      for  (  int     i     =     1  ;     i      <     s  .  length  ();     i  ++  )         num     =     num     *     10     +     ((  int  )(  s  .  charAt  (  i  ))     -     48  );      num     =     num     *     -  1  ;      }      return     num  ;   }   // This function receives a node of the syntax   // tree and recursively evaluate it   public     static     int     evalTree  (  Node     root  )   {          // Empty tree      if     (  root     ==     null  )      return     0  ;      // Leaf node i.e an integer      if     (  root  .  left     ==     null     &&     root  .  right     ==     null  )      return     toInt  (  root  .  data  );      // Evaluate left subtree      int     leftEval     =     evalTree  (  root  .  left  );      // Evaluate right subtree      int     rightEval     =     evalTree  (  root  .  right  );      // Check which operator to apply      if     (  root  .  data  .  equals  (  '+'  ))      return     leftEval     +     rightEval  ;      if     (  root  .  data  .  equals  (  '-'  ))      return     leftEval     -     rightEval  ;      if     (  root  .  data  .  equals  (  '*'  ))      return     leftEval     *     rightEval  ;      return     leftEval     /     rightEval  ;   }   // Driver code   public     static     void     main  (  String  []     args  )   {          // Creating a sample tree      Node     root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '-4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '20'  );      System  .  out  .  println  (  evalTree  (  root  ));      root     =     null  ;      // Creating a sample tree      root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '/'  );      root  .  right  .  right  .  left     =     new     Node  (  '20'  );      root  .  right  .  right  .  right     =     new     Node  (  '2'  );      System  .  out  .  println  (  evalTree  (  root  ));   }   }   // This code is contributed by Ankit Gupta   
Python3
   # Python program to evaluate expression tree   # Class to represent the nodes of syntax tree   class   node  :   def   __init__  (  self     value  ):   self  .  left   =   None   self  .  data   =   value   self  .  right   =   None   # This function receives a node of the syntax tree   # and recursively evaluate it   def   evaluateExpressionTree  (  root  ):   # empty tree   if   root   is   None  :   return   0   # leaf node   if   root  .  left   is   None   and   root  .  right   is   None  :   return   int  (  root  .  data  )   # evaluate left tree   left_sum   =   evaluateExpressionTree  (  root  .  left  )   # evaluate right tree   right_sum   =   evaluateExpressionTree  (  root  .  right  )   # check which operation to apply   if   root  .  data   ==   '+'  :   return   left_sum   +   right_sum   elif   root  .  data   ==   '-'  :   return   left_sum   -   right_sum   elif   root  .  data   ==   '*'  :   return   left_sum   *   right_sum   else  :   return   left_sum   //   right_sum   # Driver function to test above problem   if   __name__   ==   '__main__'  :   # creating a sample tree   root   =   node  (  '+'  )   root  .  left   =   node  (  '*'  )   root  .  left  .  left   =   node  (  '5'  )   root  .  left  .  right   =   node  (  '-4'  )   root  .  right   =   node  (  '-'  )   root  .  right  .  left   =   node  (  '100'  )   root  .  right  .  right   =   node  (  '20'  )   print   (  evaluateExpressionTree  (  root  ))   root   =   None   # creating a sample tree   root   =   node  (  '+'  )   root  .  left   =   node  (  '*'  )   root  .  left  .  left   =   node  (  '5'  )   root  .  left  .  right   =   node  (  '4'  )   root  .  right   =   node  (  '-'  )   root  .  right  .  left   =   node  (  '100'  )   root  .  right  .  right   =   node  (  '/'  )   root  .  right  .  right  .  left   =   node  (  '20'  )   root  .  right  .  right  .  right   =   node  (  '2'  )   print   (  evaluateExpressionTree  (  root  ))   # This code is contributed by Harshit Sidhwa   
C#
   // C# program to evaluate expression tree   using     System  ;   public     class     GFG      {      // Class to represent the nodes of syntax tree      public     class     Node     {      public      String     data  ;      public      Node     left       right  ;      public     Node  (  String     d  )     {      data     =     d  ;      left     =     null  ;      right     =     null  ;      }      }      private     static     int     toInt  (  String     s  )     {      int     num     =     0  ;      // Check if the integral value is      // negative or not      // If it is not negative generate      // the number normally      if     (  s  [  0  ]     !=     '-'  )      for     (  int     i     =     0  ;     i      <     s  .  Length  ;     i  ++  )      num     =     num     *     10     +     ((  int  )     s  [  i  ]     -     48  );      // If it is negative calculate the +ve number      // first ignoring the sign and invert the      // sign at the end      else     {      for     (  int     i     =     1  ;     i      <     s  .  Length  ;     i  ++  )      num     =     num     *     10     +     ((  int  )     (  s  [  i  ])     -     48  );      num     =     num     *     -  1  ;      }      return     num  ;      }      // This function receives a node of the syntax      // tree and recursively evaluate it      public     static     int     evalTree  (  Node     root  )     {      // Empty tree      if     (  root     ==     null  )      return     0  ;      // Leaf node i.e an integer      if     (  root  .  left     ==     null     &&     root  .  right     ==     null  )      return     toInt  (  root  .  data  );      // Evaluate left subtree      int     leftEval     =     evalTree  (  root  .  left  );      // Evaluate right subtree      int     rightEval     =     evalTree  (  root  .  right  );      // Check which operator to apply      if     (  root  .  data  .  Equals  (  '+'  ))      return     leftEval     +     rightEval  ;      if     (  root  .  data  .  Equals  (  '-'  ))      return     leftEval     -     rightEval  ;      if     (  root  .  data  .  Equals  (  '*'  ))      return     leftEval     *     rightEval  ;      return     leftEval     /     rightEval  ;      }      // Driver code      public     static     void     Main  (  String  []     args  )     {      // Creating a sample tree      Node     root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '-4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '20'  );      Console  .  WriteLine  (  evalTree  (  root  ));      root     =     null  ;      // Creating a sample tree      root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '/'  );      root  .  right  .  right  .  left     =     new     Node  (  '20'  );      root  .  right  .  right  .  right     =     new     Node  (  '2'  );      Console  .  WriteLine  (  evalTree  (  root  ));      }   }   // This code is contributed by umadevi9616    
JavaScript
    <  script  >   // javascript program to evaluate expression tree      var     root  ;      // Class to represent the nodes of syntax tree      class     Node     {      constructor  (  val  )     {      this  .  data     =     val  ;      this  .  left     =     null  ;      this  .  right     =     null  ;      }      }      function     toInt  (     s  )     {      var     num     =     0  ;          // Check if the integral value is      // negative or not      // If it is not negative generate      // the number normally      if     (  s  .  charAt  (  0  )     !=     '-'  )      for     (  i     =     0  ;     i      <     s  .  length  ;     i  ++  )      num     =     num     *     10     +     (     s  .  charCodeAt  (  i  )     -     48  );      // If it is negative calculate the +ve number      // first ignoring the sign and invert the      // sign at the end      else     {      for     (  i     =     1  ;     i      <     s  .  length  ;     i  ++  )      num     =     num     *     10     +     (  s  .  charCodeAt  (  i  )     -     48  );      num     =     num     *     -  1  ;      }      return     num  ;      }      // This function receives a node of the syntax      // tree and recursively evaluate it      function     evalTree  (  root  )     {      // Empty tree      if     (  root     ==     null  )      return     0  ;      // Leaf node i.e an integer      if     (  root  .  left     ==     null     &&     root  .  right     ==     null  )      return     toInt  (  root  .  data  );      // Evaluate left subtree      var     leftEval     =     evalTree  (  root  .  left  );      // Evaluate right subtree      var     rightEval     =     evalTree  (  root  .  right  );      // Check which operator to apply      if     (  root  .  data     ===     (  '+'  ))      return     leftEval     +     rightEval  ;      if     (  root  .  data     ===     (  '-'  ))      return     leftEval     -     rightEval  ;      if     (  root  .  data     ===     (  '*'  ))      return     leftEval     *     rightEval  ;      return     leftEval     /     rightEval  ;      }      // Driver code          // Creating a sample tree      var     root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '-4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '20'  );      document  .  write  (  evalTree  (  root  ));      root     =     null  ;      // Creating a sample tree      root     =     new     Node  (  '+'  );      root  .  left     =     new     Node  (  '*'  );      root  .  left  .  left     =     new     Node  (  '5'  );      root  .  left  .  right     =     new     Node  (  '4'  );      root  .  right     =     new     Node  (  '-'  );      root  .  right  .  left     =     new     Node  (  '100'  );      root  .  right  .  right     =     new     Node  (  '/'  );      root  .  right  .  right  .  left     =     new     Node  (  '20'  );      root  .  right  .  right  .  right     =     new     Node  (  '2'  );      document  .  write  (  '  
'
+ evalTree ( root )); // This code is contributed by gauravrajput1 < /script>

الإخراج
60 110 

تعقيد الوقت: O(n) حيث تتم زيارة كل عقدة مرة واحدة.
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