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Évaluation de l'arbre d'expression

Étant donné un simple arbre d'expression composé d'opérateurs binaires de base, c'est-à-dire + - * et / et de quelques entiers évaluent l'arbre d'expression.

Exemples :



Saisir: Nœud racine de l'arborescence ci-dessous

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Sortir: 100



Saisir: Nœud racine de l'arborescence ci-dessous

la chaîne est vide

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Sortir: 110



Pratique recommandée Arbre d'expression Essayez-le !

Approche: L’approche pour résoudre ce problème est basée sur l’observation suivante :

Comme tous les opérateurs de l'arborescence sont binaires, chaque nœud aura 0 ou 2 enfants. Comme on peut le déduire des exemples ci-dessus, toutes les valeurs entières apparaîtraient au niveau des nœuds feuilles tandis que les nœuds intérieurs représenteraient les opérateurs.

On peut donc faire parcours dans l'ordre de l'arbre binaire et évaluez l'expression à mesure que nous avançons.

Pour évaluer l'arbre syntaxique, une approche récursive peut être suivie.

Algorithme:

  • Soit t l'arbre syntaxique
  • Si t n'est pas nul, alors      
    • Si t.info est l'opérande alors  
      • Retourner t.info
    • Autre
      • A = résoudre (t.gauche)
      • B = résoudre (t.right)
      • retourner un opérateur B où l'opérateur est l'information contenue dans t

Vous trouverez ci-dessous la mise en œuvre de l’approche ci-dessus :

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>

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Complexité temporelle : O(n) car chaque nœud est visité une fois.
Espace auxiliaire : Sur)