Allocate Unique File Names in an In-Memory Vault

An in-memory file vault must assign a unique name whenever a file is created. If the requested name already exists, append a parenthesized positive integer to obtain an unused name. Implement `allocate_names(requests: string[]) -> string[]` and return the assigned name for each request in order. ### Constraints & Assumptions - All requests target the same namespace, which starts empty. No file is deleted or renamed during the sequence. - If requested name `s` is unused, assign `s` unchanged. - Otherwise choose the smallest positive integer `x` for which `s + "(" + decimal(x) + ")"` is unused, then reserve and return that name. - Names are case-sensitive, nonempty ASCII strings of at most 100 characters. There are at most 10,000 requests. - Parentheses already present in a requested name are literal text. For example, a collision on `a(1)` tries `a(1)(1)`; do not reinterpret it as a collision on `a`. - The smallest available positive suffix and flat namespace are explicit practice choices for the reported duplicate-name behavior. ### Examples ```text requests = ["report", "report", "report", "report(1)"] result = ["report", "report(1)", "report(2)", "report(1)(1)"] ``` ```text requests = ["a(1)", "a", "a", "A"] result = ["a(1)", "a", "a(2)", "A"] ``` ```hint Remember where each repeated base can resume Once a suffix candidate is known to be occupied and names are never removed, trying the same candidate again for that base cannot succeed. ```