Grammar String Representation (TypeSystem)

Overview

The problem asks us to build a string representation for a simplified type system. The core challenge lies in the recursive nature of tuple types, which can contain primitives, generics, or other tuples.

The task effectively requires two things:

1. A recursive helper function to handle the arbitrary nesting of lists (tuples).
2. A formatting method to join these components into the specific function signature format: [param1,param2,...] -> returnType.

Since Python's isinstance(x, list) or type(x) == list can easily distinguish between a single type (string) and a tuple (list), a recursive approach is the most natural fit.

Brute Force

The "brute force" approach in this context is a direct recursive implementation. We traverse the input structure and concatenate strings. While straightforward, manual string concatenation in some languages can be inefficient due to string immutability; however, for the constraints of a typical interview, this is the standard logical path.

class TypeSystem:
    def __init__(self) -> None:
        pass

    def _resolve_type(self, t) -> str:
        # Base case: Primitive or Generic (represented as strings)
        if isinstance(t, str):
            return t
        
        # Recursive case: Tuple (represented as a list)
        # We process each element in the list recursively
        parts = [self._resolve_type(item) for item in t]
        return "[" + ",".join(parts) + "]"

    def toString(self, class_sequence: dict) -> str:
        params = class_sequence.get("params", [])
        return_type_raw = class_sequence.get("returnType", "")
        
        # Format parameters: [p1,p2,...]
        param_strings = [self._resolve_type(p) for p in params]
        params_str = "[" + ",".join(param_strings) + "]"
        
        # Format return type
        return_type_str = self._resolve_type(return_type_raw)
        
        return f"{params_str} -> {return_type_str}"

Time complexity: O(N) — Where N is the total number of elements (strings and list markers) in the input structure, as we visit each node exactly once. Space complexity: O(D) — Where D is the maximum depth of the nested tuples, representing the maximum height of the recursion stack.

Optimal Approach

The optimal approach follows the same recursive logic but focuses on memory efficiency and idiomatic Python. Instead of creating many intermediate strings through concatenation (which creates new string objects in memory), we can use a generator or a list-based buffer to collect parts and join them once at the end.

In Python, ",".join() is highly optimized. We ensure the _resolve_type logic handles empty lists and deep nesting correctly according to the problem's grammar rules.

class TypeSystem:
    def __init__(self) -> None:
        """
        Initializes the TypeSystem. No internal state is required 
        for the current toString requirements.
        """
        pass

    def _format_node(self, node) -> str:
        """
        Recursively converts a type node (string or list) into its 
        string representation.
        """
        if isinstance(node, str):
            return node
        
        # Process children and join with commas, wrapped in square brackets
        # Works for nested tuples and empty lists
        children = (self._format_node(child) for child in node)
        return f"[{','.join(children)}]"

    def toString(self, class_sequence: dict) -> str:
        """
        Constructs the full function type signature.
        """
        params = class_sequence.get("params", [])
        ret = class_sequence.get("returnType", "")

        # Generate parameter list string
        param_list = [self._format_node(p) for p in params]
        formatted_params = f"[{','.join(param_list)}]"
        
        # Generate return type string
        formatted_return = self._format_node(ret)

        return f"{formatted_params} -> {formatted_return}"

Time complexity: O(N) — Every primitive, generic, and tuple boundary is visited exactly once to build the final string. Space complexity: O(N) — In the worst case, the recursion stack and the list of processed strings will scale linearly with the input size.

Edge Cases

• Empty Params: The problem states params can be empty. The logic ",".join([]) correctly produces an empty string, resulting in [].
• Empty Return Tuple: If returnType is [], it should render as [].
• Deep Nesting: The recursive approach handles types like [[[int]]] by unwinding the stack level by level.
• Mixed Types: A tuple containing a primitive, a generic, and another tuple (e.g., ["int", "T1", ["float"]]) is handled uniformly by the recursive _format_node call.

Fast