Construct Binary Tree from Parent-Child Pairs and Return S-Expression

Problem: Construct a Binary Tree from Parent-Child Pairs and Return an S-Expression You are given a string containing multiple parent-child pairs. Each pair has the format: (P,C) where P is the parent node and C is the child node. Each node label is a single uppercase English letter from A to Z. For example: (A,B) (B,C) (A,D) means A is the parent of B, B is the parent of C, and A is the parent of D. Validate whether the input can form a valid binary tree: The input must consist only of valid pairs. Pairs must be separated by exactly one space. Each node can have at most 2 distinct children. The whole graph must have exactly one root. The graph must not contain a cycle. If multiple errors exist, output the highest-priority error. Error Types and Priority From highest to lowest priority: E1: Invalid Input String E2: Duplicate Pair E3: Parent Has More than 2 Children E4: Multiple Roots E5: Cycle In The Tree As soon as a higher-priority error is found, output that error code. Output When Valid If the input is valid, output the S-expression of the tree. Definition: S-expression(node) = "(" + node.val + S-expression(child1) + S-expression(child2) + ")" If a child does not exist, omit that subtree. If a node has two children, output them in ascending lexicographical order by node label. Example: Input: (A,B) (B,C) (A,D) Output: (A(B(C))(D)) Input Format Read the entire input string from standard input. It may be any string. Output Format If an error exists, print the error code, e.g. E1. Otherwise, print the S-expression. Constraints Input length is at most 10^4. Node labels are single uppercase letters, so there are at most 26 distinct nodes. Example Input (A,B) (B,C) (A,D) Output (A(B(C))(D))