Evaluation of Expression Tree in C++

In this problem, we are given an expression tree that consist of binary operations like +, - , /, *. We need to do the evaluation of the expression tree and then return the result.

Expression Tree is a special type of binary tree in which each node either consist of an operator or operand which are distributed as−

  • Leaf nodes of the tree are values on which the operation is to be performed. 
  • Non-leaf nodes consist of the binary operator denoting the operation to be performed. 

Let’s take an example to understand the problem,


Output: 1


Decoding the expression tree,

Exp             = ( (5+9) / (2*7) )
                   = ( 14 / 14 )

= 1

Solution Approach:

A simple solution to the problem is by performing one operation each from root, for operends we will solve the subtree. As all operations are binary the nodes of a tree either have two childrens or none.

We will use recursion to solve each node's binary operation.

Program to illustrate the working of our solution,


Live Demo

#include <bits/stdc++.h>
using namespace std;

class node {
      string value;
      node *left = NULL, *right = NULL;
      node(string x)
         value = x;

int solveExpressionTree(node* root) {
   if (!root)
      return 0;

   if (!root->left &amp;&amp; !root->right)
      return stoi(root->value);

   int leftSubTreeSol = solveExpressionTree(root->left);
   int rightSubTreeSol = solveExpressionTree(root->right);

   if (root->value == "+")
      return leftSubTreeSol + rightSubTreeSol;

   if (root->value == "-")
      return leftSubTreeSol - rightSubTreeSol;

   if (root->value == "*")
      return leftSubTreeSol * rightSubTreeSol;
   if (root -> value == "/")
      return leftSubTreeSol / rightSubTreeSol;
   return -1;

int main()
   node *root = new node("/");
   root->left = new node("+");
   root->left->left = new node("9");
   root->left->right = new node("5");
   root->right = new node("*");
   root->right->left = new node("2");
   root->right->right = new node("7");
   cout<<"The evaluation of expression tree is "<<solveExpressionTree(root);
   return 0;

Output −

The evaluation of expression tree is 1

Updated on: 22-Jan-2021


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