Solution Approach

The implementation consists of two main parts: extending the TypeScript type system and implementing the actual method.

Step 1: Type Declaration

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

This TypeScript declaration extends the global String interface to include our new replicate method. This tells TypeScript that all strings will have this method available, preventing type errors when we call it.

Step 2: Method Implementation

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

The implementation breaks down into three operations:

1. Array Creation: new Array(times) creates an array with a length equal to the times parameter. Initially, this array contains empty slots.

2. Array Filling: .fill(this) populates every position in the array with the current string value. In the context of a prototype method, this refers to the string instance on which the method is called.

3. String Concatenation: .join('') merges all array elements into a single string. By using an empty string '' as the separator, the strings are concatenated directly without any characters between them.

Example Walkthrough: When calling "cat".replicate(3):

• new Array(3) → [empty, empty, empty]
• .fill("cat") → ["cat", "cat", "cat"]
• .join('') → "catcatcat"

This approach efficiently handles edge cases:

• If times is 0, it creates an empty array, resulting in an empty string
• If times is 1, it returns the original string
• The method works for any positive integer value of times

Example Walkthrough

Let's walk through the solution with the example "hi".replicate(4):

Step 1: Method Call When we call "hi".replicate(4), the method executes with this = "hi" and times = 4.

Step 2: Create Empty Array

new Array(4) // Creates: [empty, empty, empty, empty]

We now have an array with 4 empty slots.

Step 3: Fill Array with String

[empty, empty, empty, empty].fill("hi") // Results in: ["hi", "hi", "hi", "hi"]

Each empty slot is replaced with our original string "hi".

Step 4: Join Array Elements

["hi", "hi", "hi", "hi"].join('') // Results in: "hihihihi"

The join('') method concatenates all array elements with no separator between them.

Final Result: "hihihihi"

Edge Case Example: "test".replicate(0)

• new Array(0) creates an empty array []
• .fill("test") has nothing to fill, remains []
• .join('') on an empty array returns ""
• Result: empty string

This demonstrates how the solution elegantly handles both normal cases and edge cases without explicit conditional logic.

Time and Space Complexity

Time Complexity: O(n) where n is the value of the times parameter.

The time complexity breaks down as follows:

• new Array(times) creates an array of size times - O(n)
• .fill(this) iterates through the array to fill each element with the string reference - O(n)
• .join('') iterates through the array to concatenate all elements into a single string - O(n)

Since these operations are sequential, the overall time complexity is O(n) + O(n) + O(n) = O(n).

Space Complexity: O(n * m) where n is the value of the times parameter and m is the length of the original string.

The space complexity analysis:

• new Array(times) creates an array with times elements - O(n) space
• .fill(this) populates the array with references to the string (not copies), so no additional space beyond the references
• .join('') creates a new string of length times * m where m is the length of the original string - O(n * m) space
• The intermediate array also holds n references - O(n) space

The dominant factor is the final string of size O(n * m), making the overall space complexity O(n * m).

Common Pitfalls

1. Not Handling Negative or Non-Integer Input

The implementation doesn't validate the times parameter. Passing negative numbers or non-integers can cause unexpected behavior:

• In TypeScript: new Array(-1) throws a RangeError
• In Python: Negative multiplication returns an empty string, which might not be the intended behavior

Solution:

String.prototype.replicate = function (times: number) {  // Validate input  if (times < 0 || !Number.isInteger(times)) {  throw new Error('Parameter must be a non-negative integer');  }  return new Array(times).fill(this).join(''); };

def replicate(self, times: int) -> str:  if not isinstance(times, int) or times < 0:  raise ValueError('Parameter must be a non-negative integer')  return self * times

2. Memory Overflow with Large Numbers

Creating very large arrays or strings can cause memory issues. For example, "hello".replicate(1000000000) would attempt to create an enormous string.

Solution: Add a reasonable upper limit:

String.prototype.replicate = function (times: number) {  const MAX_REPLICATIONS = 1000000; // Set reasonable limit  if (times > MAX_REPLICATIONS) {  throw new Error(`Cannot replicate more than ${MAX_REPLICATIONS} times`);  }  return new Array(times).fill(this).join(''); };

3. Type Safety Issues in TypeScript

Without proper type declaration, TypeScript will throw compilation errors when trying to use the replicate method. Forgetting the declare global block is a common mistake.

Solution: Always include the type declaration before implementation:

declare global {  interface String {  replicate(times: number): string;  } } export {}; // Make this file a module

4. Mutating Built-in Prototypes (Python)

Monkey-patching built-in types like str in Python can lead to:

• Conflicts with third-party libraries
• Unexpected behavior in other parts of the codebase
• Difficulty in debugging

Solution: Use a wrapper class or utility function instead:

def replicate_string(s: str, times: int) -> str:  """Standalone function that doesn't modify built-in types"""  if not isinstance(times, int) or times < 0:  raise ValueError('Times must be a non-negative integer')  return s * times  # Or use a wrapper class class ReplicableString(str):  def replicate(self, times: int) -> str:  return self * times

5. Performance Issues with Array Join Approach

In TypeScript, creating an array and then joining it has overhead compared to simple string concatenation for small repetitions.

Solution: Use a more efficient approach for small values:

String.prototype.replicate = function (times: number) {  if (times <= 0) return '';  if (times === 1) return this.toString();   // For small numbers, use simple concatenation  if (times < 10) {  let result = '';  for (let i = 0; i < times; i++) {  result += this;  }  return result;  }   // For larger numbers, use array join  return new Array(times).fill(this).join(''); };