Problem Description
Given the root node of a binary tree, your task is to create a string representation of the tree following a specific set of formatting rules. The representation should be based on a preorder traversal of the binary tree and must adhere to the following guidelines:
- Each node in the tree should be represented by its integer value.
- If a node has at least one child, its children should be represented inside parentheses. If a node has a left child, the value of the left child should be enclosed in parentheses immediately following the node's value. If a node has a right child, the value of the right child should also be enclosed in parentheses.
- Any empty parentheses pairs should be omitted from the final string representation of the tree, except when a node has a right child but no left child. In such cases, an empty pair of parentheses must be included to indicate the absence of the left child.
Key Insights
- Preorder traversal is necessary to construct the string representation in the correct order.
- Special care must be taken with how to handle empty parentheses, particularly when a right child exists without a left child.
- A recursive approach is well-suited for traversing the tree and building the string representation.
Space and Time Complexity
Time Complexity: O(N), where N is the number of nodes in the binary tree, as we visit each node exactly once. Space Complexity: O(H), where H is the height of the binary tree, due to the recursion stack.
Solution
To solve the problem, we can use a recursive function that performs a preorder traversal of the binary tree. The function will:
- Append the current node's value to the result string.
- If the node has a left child, recursively call the function for the left child and append its result.
- If the node has a right child, check if the left child exists. If not, append an empty pair of parentheses to indicate the absence of a left child, then recursively call the function for the right child.
This approach ensures that we construct the string representation in the required format while respecting the rules about parentheses.