Understanding the Problem
We are given a string that represents a binary tree using a bracketed structure. Each node is a number, and its children are enclosed in parentheses. For example, the string 4(2(3)(1))(6(5))
represents a binary tree where 4 is the root, 2 is the left child, and 6 is the right child. The left child 2 further has children 3 and 1. The task is to construct this binary tree from the string.
This problem is recursive in nature — every subtree is itself a valid string that can be parsed into a smaller binary tree. We need to handle parsing the string carefully, tracking open and closed parentheses to determine the subtree boundaries.
Step-by-Step Solution with Example
step 1: Identify the root value
We begin by extracting the integer value at the start of the string. This is the root node of our binary tree. For example, in 4(2(3)(1))(6(5))
, we extract 4 as the root.
step 2: Locate the left and right subtrees
After the root, if the string continues with a '(', it signals the start of a subtree. We find the first matching pair of parentheses to extract the left subtree string. Then, we check if there's another set of parentheses for the right subtree.
In 4(2(3)(1))(6(5))
, the first subtree is 2(3)(1)
, enclosed in the first pair of parentheses. The second subtree is 6(5)
, enclosed in the next pair.
step 3: Recursively construct left and right children
We recursively repeat the parsing process on each subtree string. The node 2 becomes the left child of 4. Similarly, within 2(3)(1)
, we identify 3 as the left child of 2 and 1 as the right child. For the right subtree 6(5)
, 6 becomes the right child of 4 and 5 becomes its left child.
step 4: Return the constructed tree node
Once the recursive calls return the constructed left and right subtrees, we attach them to the current node and return it. This process eventually constructs the full tree starting from the root.
Edge Cases
Case 1: Full Tree Structure (4(2(3)(1))(6(5))
)
The input string has both left and right subtrees. We parse both sets of parentheses and recursively build each part.
Case 2: Only Left Subtree (1(2)
)
There is only one set of parentheses, indicating only a left child. The right child remains null.
Case 3: Only Right Subtree (1()(3)
)
An empty set of parentheses denotes a missing left child, and the next set represents the right child.
Case 4: Single Node Tree (1
)
No parentheses means no children. The tree consists of a single root node with both children as null.
Case 5: Empty Input (""
)
An empty string means there's no tree to build. We return null immediately — this is often a base case in recursive functions.
Finally
This problem is an excellent example of recursive string parsing and tree construction. The key is to understand how to locate matching parentheses and recursively build subtrees. By addressing edge cases like missing children and empty inputs, we ensure our solution is robust and handles all possible valid inputs gracefully.
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