Construct a Binary Tree from String with bracket representation | Set 2

Given a string s consisting of parentheses {'(' and ')'} and integers, the task is to construct a Binary Tree from it and print its Preorder traversal.

Examples:

Input: S = "1(2)(3)"
Output: 1 2 3
Explanation: The corresponding binary tree is as follows:
            1
          /   \                      
        2     3                       

Input: "4(2(3)(1))(6(5))"
Output: 4 2 3 1 6 5
Explanation:
The corresponding binary tree is as follows:

              4
           /     \                  
         2       6          
      /  \     /                        
   3    1   5                       

Recursive Approach: Refer to the previous article to solve the problem recursively. 
Time Complexity: O(N²) 
Auxiliary Space: O(N)

Approach: This problem can be solved using stack data structure. Follow the steps below to solve the problem:

• Update the character at position 0 as root of the binary tree and initialize a stack stk.
• Iterate in the range [1, N-1] using the variable i: 
  • If '(' is encountered, push the root to the stack stk.
  • Otherwise, if ')' is encountered update root as the topmost element of the stack and pop the topmost element.
  • Otherwise, if the character is a number, then, branch into the part that is null (left or right).
• At the end of the above steps, return the root node of the binary tree.

Below is the implementation of the above approach:

4 2 3 1 6 5

Time Complexity: O(N)
Auxiliary Space: O(N)