Build Binary Tree from Edges / S-Expression

An OA coding problem (experienced-SWE rotation): given parent-child pairs as raw strings, validate the input against a priority-ordered list of error types and, if valid, output the tree's S-expression. The input validation is deliberately fiddly. Requirements Input is a set of (parent, child) pairs (parent first in each pair), supplied as arbitrary strings that must be parsed and validated. If the input is malformed or doesn't describe a valid binary tree, output the highest-priority error among: E1: Invalid Input String E2: Duplicate Pair E3: A parent has more than 2 children E4: Multiple Roots E5: Cycle in the Tree If there is no error, output the S-expression of the tree: S(node) = "(" + node.val + S(node.first_child) + S(node.second_child) + ")", e.g. (A(B(C))(D)). Examples Input pairs (A,B) (B,C) (A,D) → (A(B(C))(D)). Input A,B A,C C,D D,B → contains a cycle / multiple-root style violation (report the highest-priority error). Notes Input is "any string", so the E1 validation (well-formed pairs, allowed characters) is the laborious part — handle it before building the tree. Children ordering for the S-expression follows the order pairs are given / sorted as the prompt specifies; confirm whether output uses first-seen or sorted child order. In the experienced-SWE OA this is the second problem, paired with a "days between two dates" warm-up; tests are sparse with many hidden cases, so validate aggressively. The OA window is generous (up to 72 hours) but submitting too slowly has correlated with rejection. Preparation Write the parser/validator first with explicit checks per error type, ordered by priority, then the tree build + recursive S-expression. Stress-test malformed inputs (bad tokens, duplicate pairs, 3-child parents, two roots, cycles) since hidden tests target exactly these.