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Expression Trees Using Classes in C++ with Implementation

  • Last Updated : 23 Nov, 2021

Prerequisite: Expression Tree

The expression tree is a binary tree in which each internal node corresponds to the operator and each leaf node corresponds to the operand so for example expression tree for 3 + ((5+9)*2) would be:

Expression Tree

In expression trees, leaf nodes are operands and non-leaf nodes are operators. That means an expression tree is a binary tree where internal nodes are operators and leaves are operands. An expression tree consists of binary expressions. But for a unary operator, one subtree will be empty. 

Construction of Expression Tree:

  • The user will provide a postfix expression for which the program will construct the expression tree. 
  • Inorder traversal of binary tree/expression tree will provide Infix expression of the given input.


Input:  A B C*+ D/
Output: A + B * C / D

Step 1: The first three symbols are operands, so create tree nodes and push pointers to them onto a stack as shown below.

Create tree nodes

Step 2: In the Next step, an operator ‘*’ will going read, so two pointers to trees are popped, a new tree is formed and a pointer to it is pushed onto the stack

New tree is formed

Step 3: In the Next step,  an operator ‘+’ will read, so two pointers to trees are popped, a new tree is formed and a pointer to it is pushed onto the stack.

push on stack

Step 4: Similarly, as above cases first we push ‘D’ into the stack and then in the last step first, will read ‘/’ and then as previous step topmost element will pop out and then will be right subtree of root  ‘/’ and other node will be right subtree.

Final Constructed Expression Tree is:

Final Constructed expression tree

Below is the C++ program to implement the above approach:


// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
class node {
    char value;
    node* left;
    node* right;
    node* next = NULL;
    node(char c)
        this->value = c;
        left = NULL;
        right = NULL;
        left = NULL;
        right = NULL;
    friend class Stack;
    friend class expression_tree;
// Class stack to hold
// tree nodes
class Stack {
    node* head = NULL;
    void push(node*);
    node* pop();
    friend class expression_tree;
// Class to implement
// inorder traversal
class expression_tree {
    // Function to implement
    // inorder traversal
    void inorder(node* x)
        if (x == NULL)
        else {
            cout << x->value << "  ";
// Function to push values
// onto the stack
void Stack::push(node* x)
    if (head == NULL) {
        head = x;
    // We are inserting nodes at
    // the top of the stack [
    // following LIFO principle]
    else {
        x->next = head;
        head = x;
// Function to implement pop
// operation in the stack
node* Stack::pop()
    // Poping out the top most[
    // pointed with head] element
    node* p = head;
    head = head->next;
    return p;
// Driver code
int main()
    // Postfix expression
    string s = "ABC*+D/";
    Stack e;
    expression_tree a;
    node *x, *y, *z;
    int l = s.length();
    for (int i = 0; i < l; i++) {
        // if read character is operator
        // then poping two other elements
        // from stack and making a binary
        // tree
        if (s[i] == '+' || s[i] == '-'
            || s[i] == '*' || s[i] == '/'
            || s[i] == '^') {
            z = new node(s[i]);
            x = e.pop();
            y = e.pop();
            z->left = y;
            z->right = x;
        else {
            z = new node(s[i]);
    // Print the inorder traversal
    cout << " The Inorder Traversal of Expression Tree: ";
    return 0;

The Inorder Traversal of Expression Tree: A + B * C / D

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