Convert Ternary Expression to a Binary Tree

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

Examples:

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

Asked In : Facebook Interview

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  

a b c d e 

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

Approach for Converting Ternary Expression to Binary Tree.

• The algorithm uses a recursive approach to build the tree in a top-down manner.
• It starts with creating a new node for the current character at the current index.
• If the next character is a '?', it means that the current node needs a left child. So, the algorithm calls itself recursively with the next index to create the left child of the current node.
• If the next character is a ':', it means that the current node needs a right child. So, the algorithm calls itself recursively with the next index to create the right child of the current node.
• Finally, the algorithm returns the root node of the binary tree.

Here is the implementation of above approach:-

a b c d e 

Time complexity: O(n) - Since we visit each character of the expression exactly once.

Space complexity: O(n) - Since in the worst case, the recursion stack can grow to the height of the tree, which can be O(n) if the ternary expression is a degenerate tree (a long chain of '?'). Additionally, we store O(n) nodes in the binary tree.