# Convert Ternary Expression to a Binary Tree

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2021

Given a string that contains ternary expressions. The expressions may be nested, task is convert the given ternary expression to a binary Tree.

Examples:

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```Input :  string expression =   a?b:c
Output :        a
/  \
b    c

Input : expression =  a?b?c:d:e
Output :     a
/  \
b    e
/  \
c    d```

Idea is that we traverse a string make first character as root and do following step recursively .
1. If we see Symbol ‘?’
…….. then we add next character as the left child of root.
2. If we see Symbol ‘:’
…….. then we add it as the right child of current root.
do this process until we traverse all element of “String”.

Below is the implementation of above idea

## C++

 `// C++ program to convert a ternary expression to``// a tree.``#include``using` `namespace` `std;` `// tree structure``struct` `Node``{``    ``char` `data;``    ``Node *left, *right;``};` `// function create a new node``Node *newNode(``char` `Data)``{``    ``Node *new_node = ``new` `Node;``    ``new_node->data = Data;``    ``new_node->left = new_node->right = NULL;``    ``return` `new_node;``}` `// Function to convert Ternary Expression to a Binary``// Tree. It return the root of tree``//Notice that we pass index i by reference because we want to skip the characters in the subtree``Node *convertExpression(string str, ``int` `& i)``{``    ``// store current character of expression_string``    ``// [ 'a' to 'z']``    ``Node * root =newNode(str[i]);` `    ``//If it was last character return``    ``//Base Case``    ``if``(i==str.length()-1) ``return` `root;` `    ``// Move ahead in str``    ``i++;``    ``//If the next character is '?'.Then there will be subtree for the current node``    ``if``(str[i]==``'?'``)``    ``{``        ``//skip the '?'``        ``i++;` `        ``//construct the left subtree``        ``//Notice after the below recursive call i will point to ':' just before the right child of current node since we pass i by reference``        ``root->left = convertExpression(str,i);``        ` `        ``//skip the ':' character``        ``i++;` `        ``//construct the right subtree``        ``root->right = convertExpression(str,i);``        ``return` `root;``    ``}``    ``//If the next character is not '?' no subtree just return it``    ``else` `return` `root;``}` `// function print tree``void` `printTree( Node *root)``{``    ``if` `(!root)``        ``return` `;``    ``cout << root->data <<``" "``;``    ``printTree(root->left);``    ``printTree(root->right);``}` `// Driver program to test above function``int` `main()``{``    ``string expression = ``"a?b?c:d:e"``;``    ``int` `i=0;``    ``Node *root = convertExpression(expression, i);``    ``printTree(root) ;``    ``return` `0;``}`

## Java

 `// Java program to convert a ternary``// expreesion to a tree.``import` `java.util.Queue;``import` `java.util.LinkedList;`` ` `// Class to represent Tree node``class` `Node``{``    ``char` `data;``    ``Node left, right;`` ` `    ``public` `Node(``char` `item)``    ``{``        ``data = item;``        ``left = ``null``;``        ``right = ``null``;``    ``}``}`` ` `// Class to convert a ternary expression to a Tree``class` `BinaryTree``{``    ``// Function to convert Ternary Expression to a Binary``    ``// Tree. It return the root of tree``    ``Node convertExpression(``char``[] expression, ``int` `i)``    ``{``        ``// Base case``        ``if` `(i >= expression.length)``            ``return` `null``;``     ` `        ``// store current character of expression_string``        ``// [ 'a' to 'z']``        ``Node root = ``new` `Node(expression[i]);``     ` `        ``// Move ahead in str``        ``++i;``     ` `        ``// if current character of ternary expression is '?'``        ``// then we add next character as a left child of``        ``// current node``        ``if` `(i < expression.length && expression[i]==``'?'``)``            ``root.left = convertExpression(expression, i+``1``);``     ` `        ``// else we have to add it as a right child of``        ``// current node expression.at(0) == ':'``        ``else` `if` `(i < expression.length)``            ``root.right = convertExpression(expression, i+``1``);``     ` `        ``return` `root;``    ``}``    ` `    ``// function print tree``    ``public` `void` `printTree( Node root)``    ``{``        ``if` `(root == ``null``)``            ``return``;``                ` `        ``System.out.print(root.data +``" "``);``        ``printTree(root.left);``        ``printTree(root.right);``    ``}``    ` `// Driver program to test above function``    ``public` `static` `void` `main(String args[])``    ``{``        ``String exp = ``"a?b?c:d:e"``;``        ``BinaryTree tree = ``new` `BinaryTree();``        ``char``[] expression=exp.toCharArray();``        ``Node root = tree.convertExpression(expression, ``0``);``        ``tree.printTree(root) ;``    ``}``}` `/* This code is contributed by Mr. Somesh Awasthi */`

## Python3

 `# Class to define a node``# structure of the tree``class` `Node:``    ``def` `__init__(``self``, key):``        ``self``.data ``=` `key``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Function to convert ternary``# expression to a Binary tree``# It returns the root node``# of the tree``def` `convert_expression(expression, i):``    ``if` `i >``=` `len``(expression):``        ``return` `None` `    ``# Create a new node object``    ``# for the expression at``    ``# ith index``    ``root ``=` `Node(expression[i])` `    ``i ``+``=` `1` `    ``# if current character of``    ``# ternary expression is '?'``    ``# then we add next character``    ``# as a left child of``    ``# current node``    ``if` `(i < ``len``(expression) ``and``                ``expression[i] ``is` `"?"``):``        ``root.left ``=` `convert_expression(expression, i ``+` `1``)``        ` `    ``# else we have to add it``    ``# as a right child of``    ``# current node expression == ':'``    ``elif` `i < ``len``(expression):``        ``root.right ``=` `convert_expression(expression, i ``+` `1``)``    ``return` `root` `# Function to print the tree``# in a pre-order traversal pattern``def` `print_tree(root):``    ``if` `not` `root:``        ``return``    ``print``(root.data, end``=``' '``)``    ``print_tree(root.left)``    ``print_tree(root.right)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``string_expression ``=` `"a?b?c:d:e"``    ``root_node ``=` `convert_expression(string_expression, ``0``)``    ``print_tree(root_node)` `# This code is contributed``# by Kanav Malhotra`

## C#

 `// C# program to convert a ternary``// expreesion to a tree.``using` `System;` `// Class to represent Tree node``public` `class` `Node``{``    ``public` `char` `data;``    ``public` `Node left, right;` `    ``public` `Node(``char` `item)``    ``{``        ``data = item;``        ``left = ``null``;``        ``right = ``null``;``    ``}``}` `// Class to convert a ternary``// expression to a Tree``public` `class` `BinaryTree``{``    ``// Function to convert Ternary Expression``    ``// to a Binary Tree. It return the root of tree``    ``public` `virtual` `Node convertExpression(``char``[] expression,``                                          ``int` `i)``    ``{``        ``// Base case``        ``if` `(i >= expression.Length)``        ``{``            ``return` `null``;``        ``}` `        ``// store current character of``        ``// expression_string [ 'a' to 'z']``        ``Node root = ``new` `Node(expression[i]);` `        ``// Move ahead in str``        ``++i;` `        ``// if current character of ternary expression``        ``// is '?' then we add next character as a``        ``// left child of current node``        ``if` `(i < expression.Length && expression[i] == ``'?'``)``        ``{``            ``root.left = convertExpression(expression, i + 1);``        ``}` `        ``// else we have to add it as a right child``        ``// of current node expression.at(0) == ':'``        ``else` `if` `(i < expression.Length)``        ``{``            ``root.right = convertExpression(expression, i + 1);``        ``}` `        ``return` `root;``    ``}` `    ``// function print tree``    ``public` `virtual` `void` `printTree(Node root)``    ``{``        ``if` `(root == ``null``)``        ``{``            ``return``;``        ``}` `        ``Console.Write(root.data + ``" "``);``        ``printTree(root.left);``        ``printTree(root.right);``    ``}` `// Driver Code``public` `static` `void` `Main(``string``[] args)``{``    ``string` `exp = ``"a?b?c:d:e"``;``    ``BinaryTree tree = ``new` `BinaryTree();``    ``char``[] expression = exp.ToCharArray();``    ``Node root = tree.convertExpression(expression, 0);``    ``tree.printTree(root);``}``}` `// This code is contributed by Shrikant13`

## Javascript

 ``

Output :

`a b c d e `

Time Complexity : O(n) [ here n is length of String ]
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