Convert ternary expression to Binary Tree using Stack

Given a string str that contains a ternary expression which may be nested. The task is to convert the given ternary expression to a binary tree and return the root.


Input: str = "a?b:c"
Output: a b c
 / \
b   c
The preorder traversal of the above tree is a b c.

Input: str = "a?b?c:d:e"
Output: a b c d e
   / \
  b   e
 / \
c   d

Approach: This is a stack-based approach to the given problem. Since the ternary operator has associativity from right-to-left, the string can be traversed from right to left. Take the letters one by one skipping the letters ‘?’ and ‘:’ as these letters are used to decide whether the current letter (alphabet [a to z]) will go into the stack or be used to pop the top 2 elements from the top of the stack to make them the children of the current letter which is then itself pushed into the stack. This forms the tree in a bottom-up manner and the last remaining element in the stack after the entire string is processed is the root of the tree.

Below is the implementation of the above approach:





// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Node structure
struct Node {
    char data;
    Node *left, *right;
// Function to create a new node
Node* createNewNode(int data)
    Node* node = new Node;
    node->data = data;
    node->left = NULL, node->right = NULL;
    return node;
// Function to print the preorder
// traversal of the tree
void preorder(Node* root)
    if (root == NULL)
    cout << root->data << " ";
// Function to convert the expression to a binary tree
Node* convertExpression(string str)
    stack<Node*> s;
    // If the letter is the last letter of
    // the string or is of the type :letter: or ?letter:
    // we push the node pointer containing
    // the letter to the stack
    for (int i = str.length() - 1; i >= 0;) {
        if ((i == str.length() - 1)
            || (i != 0 && ((str[i - 1] == ':'
                            && str[i + 1] == ':')
                           || (str[i - 1] == '?'
                               && str[i + 1] == ':')))) {
        // If we do not push the current letter node to stack,
        // it means the top 2 nodes in the stack currently are the
        // left and the right children of the current node
        // So pop these elements and assign them as the
        // children of the current letter node and then
        // push this node into the stack
        else {
            Node* lnode =;
            Node* rnode =;
            Node* node = createNewNode(str[i]);
            node->left = lnode;
            node->right = rnode;
        i -= 2;
    // Finally, there will be only 1 element
    // in the stack which will be the
    // root of the binary tree
// Driver code
int main()
    string str = "a?b?c:d:e";
    // Convert expression
    Node* root = convertExpression(str);
    // Print the preorder traversal
    return 0;



a b c d e

Time Complexity: O(n)

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