Problem Description

The problem requires us to create a function that constructs and returns an infinite-method object. An infinite-method object is a special type of object that can handle calls to any method, even if that method was not explicitly defined on the object. Whenever any method is called on this object, it should return the name of that method as a string.

For instance, if you have an object named obj and you call obj.someMethodName(), it should return the string "someMethodName". This behavior should apply universally to any method name provided when calling the object.

This problem tests one's understanding of dynamic properties and methods in object-oriented programming, as well as the implementation of such behavior in the specific programming language required by the problem, which in this case is TypeScript.

Intuition

To create this infinite-method object, we make use of the Proxy object which is a feature in JavaScript and TypeScript that allows us to define custom behavior for fundamental operations (e.g., property lookup, assignment, enumeration, function invocation, etc.). By creating a Proxy, we can control the behavior of the object when a method is called that does not exist on the object.

The intuition behind the solution is to capture all method calls on the fly and return a function that, when invoked, returns the name of the non-existent method. The get trap in the Proxy is useful for this purpose. This trap will fire every time a property on the target object is accessed. Here's how we can break down the key points of the solution:

1. We create and return a Proxy object.
2. The target object of the Proxy is an empty object {}.
3. Whenever any property (in our use case, a function name) is accessed on the Proxy object, the get trap is triggered.
4. The get trap is a function that takes the target object and the property being accessed (in our case, the method name).
5. The get trap returns a new arrow function.
6. This arrow function, when called, returns the name of the property accessed, which corresponds to the method name.

Through this approach, we are able to create an object that can catch method calls for any arbitrary method name without pre-defining any methods on the object itself.

Solution Approach

The implementation of the solution follows a distinct approach using a design pattern called Proxy, which is inherently provided in JavaScript and TypeScript languages. The Proxy pattern creates an object that wraps around another object and intercepts its fundamental operations, such as property access or function invocation. Here's how the solution is achieved step by step:

1. Create a Proxy: The solution defines a function createInfiniteObject() that returns a new Proxy object.

2. Define the target object: The Proxy is initialized with an empty object {} as its target. This object would normally not have any properties or methods.

3. Define the Proxy handlers: A handler object is provided as the second argument to the Proxy constructor. This handler object contains the get trap, a function that will be invoked every time a property on the Proxy (which includes methods) is accessed.

4. Implement the get trap: The get trap is a function that accepts two parameters: target, which is the target object, and prop, the name of the property that is being accessed. Since we want to capture function calls, prop will be the name of the method being invoked.

5. Return a function dynamically: Inside the get trap, we return an arrow function () => prop.toString(). This ensures that no matter what property name (or method name) is accessed, a function is returned that, when called, will return the name of that property as a string.

6. Leverage anonymous functions: Every time a method on the Proxy is called, like obj.someMethod(), the get trap executes and returns a new anonymous function that contains the code to simply return the prop as a string.

By following these steps, we harness the power of the Proxy pattern to dynamically intercept method calls and return the expected name of the method without explicitly defining those methods. It's a powerful way to create objects with behavior that is determined at runtime rather than compile-time. This opens up possibilities for dynamic and flexible code structures.

Here is the code of the function for reference:

function createInfiniteObject(): Record<string, () => string> {
    return new Proxy(
        {},
        {
            get: (_, prop) => () => prop.toString(),
        },
    );
}

When this function is used to create an object, it will inherently have the described infinite-method behavior, as desired.

Example Walkthrough

To better understand the solution approach described above, let's walk through a small example using the createInfiniteObject() function.

First, we call createInfiniteObject() to create a new object:

let obj = createInfiniteObject();

At this point, obj is an instance of a Proxy object that is set to respond to any method invocation using the rules defined in the get trap. Let's see what happens when we try to call a method that hasn't been defined:

console.log(obj.helloWorld());

Following the steps of the solution approach:

1. We attempt to access the property helloWorld on obj. Since obj is a Proxy, the get trap is triggered instead of a typical property access.

2. The get trap function is called with the target (which is an empty object) and the prop (which is the string "helloWorld").

3. Inside the get trap, it returns an anonymous arrow function: () => prop.toString().

4. This arrow function is immediately invoked (because we have used parentheses () after obj.helloWorld).

5. The invoked arrow function returns the string "helloWorld".

6. The console.log statement outputs the string "helloWorld" to the console.

This behavior illustrates that any method name we try to call on obj will result in the name of the method being returned as a string. It works exactly the same for any other method name:

console.log(obj.anotherMethod());  // Outputs: "anotherMethod"
console.log(obj.yetAnotherOne());  // Outputs: "yetAnotherOne"
console.log(obj['any.method']);    // Outputs: "any.method"

In each case, the Proxy intercepts the method call, the get trap provides an anonymous function, the function is called, and the method name is returned as a string. Through this example, we've seen first-hand how the Proxy pattern allowed us to handle dynamic method calls in a generic way without ever defining any actual methods on the object.

Solution Implementation

Time and Space Complexity

The time complexity of the createInfiniteObject function call itself is O(1) because it returns a proxy object without performing any computation. When any property on the resulting proxy object is accessed and the function returned is called, it performs this action in constant time, resulting in a time complexity of O(1) per property access.

The space complexity of the createInfiniteObject function is also O(1) since the proxy object does not store any properties itself and creates functions on-the-fly when a property is accessed. No additional space is used regardless of how many properties are accessed on the proxy object.