Problem Description

The problem requires us to enhance the String prototype in TypeScript by adding a new method called replicate. This new method should take an integer x and return a new string where the original string is repeated x number of times. A key point in the description is that we should implement this functionality without using the built-in string.repeat method provided in JavaScript/TypeScript.

Intuition

To arrive at a solution for replicating a string x times without using the string.repeat method, we can utilize an array as an intermediary. The intuition is based on two steps:

1. Create an array with x number of elements, with each element being the original string that we want to replicate. This is done using the new Array(times) constructor which creates an array of the specified length, and fill(this) which fills it with the current string context (this refers to the string instance where the method is called).

2. Join all the array elements into a single string. The join('') method is used to concatenate all the elements of the array into a single string, with the empty string '' serving as the separator (which means there will be no characters between the repetitions of the original string).

When we put these two steps together in the replicate function, we get a new string consisting of the original string repeated x times without using the string.repeat method.

Solution Approach

The implementation of the replicate method in TypeScript involves extending the String prototype, which is a standard JavaScript object prototype pattern that allows us to add new properties or methods to all instances of the String class.

Here are the steps taken in the implementation:

1. Extending the String Interface: To add a new method to the String prototype in TypeScript, we first need to extend the String interface with our new method signature. This is done through declaration merging by declaring an expanded interface named String globally which includes our custom method replicate(times: number): string;.

   declare global {
       interface String {
           replicate(times: number): string;
       }
   }

   This tells TypeScript that every String object will now have a method called replicate that takes a number and returns a string.

2. Implementing the replicate Method: The replicate method is then added to the String prototype.

   String.prototype.replicate = function (times: number) {
       return new Array(times).fill(this).join('');
   };

   • Algorithm: The algorithm employed here is straightforward and involves the creation of an array followed by joining its elements. No complex patterns or data structures are required.

   • Creating an Array of Repetitions: We use the new Array(times) constructor to create an array of length equal to the number of times the string needs to be replicated. Then, the fill method fills up the array with the original string (this) in all positions. This effectively creates an array where each element is the string to be replicated.

   • Joining the Array: Once the array is filled, we use the join method with an empty string as a separator to concatenate all the elements of the array, effectively repeating the original string times number of times.

This solution is efficient because the heavy lifting is done by native array operations, which are highly optimized in JavaScript engines. Since we are avoiding recursion and repeated string concatenation, we minimize the risk of performance issues and potential call stack overflows for large values of times. It is a simple and elegant way to add custom repeat functionality to strings in TypeScript.

Example Walkthrough

Let's walk through a small example to illustrate the solution approach for enhancing the String prototype with a replicate method in TypeScript.

Suppose we have the string "hello" and we want to replicate it 3 times. To achieve this using our custom replicate method, we would start by calling "hello".replicate(3).

Here's what happens step by step when we call the replicate method:

1. An array with 3 elements is created using new Array(3).

2. This array is then filled with the string "hello" in all positions, making the array look like this: ["hello", "hello", "hello"].

3. Finally, we join all the array elements with no separator using join(''), which results in the string "hellohellohello".

So, if we execute the following TypeScript code:

"hello".replicate(3)

The output we expect to see would be:

"hellohellohello"

With this example, we have shown how the replicate method uses the concept of arrays to create multiple copies of a string and concatenate them to produce a final string with the original string repeated the specified number of times without using the built-in string.repeat method.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity of the replicate method can be considered as O(n * m), where n is the number of times the string is replicated, and m is the length of the source string.

This is because the .fill method instantiates an array of size n and fills it with the source string. Then, the .join method iterates over this array to concatenate the strings together. If the array .fill method is implemented in a way that performs a deep copy, the time to fill the array is O(n), but as it copies references in this case, we can consider this part O(n) for the references. However, the .join operation requires concatenating the string n times, with each concatenation operation being proportional to the length of the string, which is m. Therefore, the .join operation dominates and results in a time complexity of O(n * m).

Space Complexity

The space complexity of the replicate function is O(n * m) as well. This is because it creates an array of n elements, each of which is a reference to the source string of length m. When concatenated, the resulting string occupies space proportional to n * m.

One could argue that since .fill is using the same reference, the array does not require additional space proportional to the length of the string. However, the resulting string from .join still requires n * m space. Therefore, the overall space complexity remains O(n * m).