Collaborative Text Editing with Operational Transformation (OT)

Operational Transformation (OT) is a technique used in collaborative text editors to maintain consistency across multiple users editing the same document simultaneously. This challenge asks you to implement a simplified OT system in JavaScript, allowing multiple clients to concurrently modify a shared text string and resolve conflicts that arise from overlapping edits. Successfully completing this challenge demonstrates an understanding of concurrency control and conflict resolution in distributed systems.

Problem Description

You are tasked with building a basic Operational Transformation (OT) system. The system should handle insertions of characters into a shared text string. The core of the system lies in transforming operations (insertions) based on the operations that have already been applied. This ensures that each client's view of the document remains consistent with others, even when edits are made concurrently.

What needs to be achieved:

1. Operation Representation: Define a structure to represent an insertion operation. This structure should include the index (position) in the text where the character should be inserted and the character to be inserted.
2. Apply Operation: Implement a function that applies an operation to a given text string. This function should insert the character at the specified index.
3. Transform Operation: Implement a function that transforms an operation based on a list of previously applied operations. The transformation logic should adjust the index of the incoming operation to account for insertions made by other clients. Specifically, if an operation inserts characters before the index of the incoming operation, the incoming operation's index should be incremented by the number of characters inserted.
4. Consistent State: The system should ensure that applying a series of operations (in any order, after transformation) results in the same final text string across all clients.

Key Requirements:

• The system should only support insertions. Deletions and other operations are outside the scope of this challenge.
• The index in an operation is zero-based.
• The transformation function must correctly handle cases where operations overlap or are applied in reverse order.

Expected Behavior:

• When an operation is applied to a text string, the character is inserted at the specified index.
• When an operation is transformed, its index is adjusted based on the operations that have already been applied.
• Applying a series of operations, even if applied out of order, should result in the same final text string.

Edge Cases to Consider:

• Inserting at the beginning or end of the string.
• Transforming an operation based on an empty history of operations.
• Operations inserting at the same index. (While not explicitly required to handle perfectly, consider how your transformation might behave in this scenario - it's a good indicator of understanding.)
• Large numbers of operations.

Examples

Example 1:

Initial Text: "abc"
Operation 1: { index: 1, character: "x" }
Operation 2: { index: 2, character: "y" }

Applying Operation 1: "axbc"
Applying Operation 2: "axbyc"

Applying Operation 2 first, then Operation 1:
Applying Operation 2: "abc"
Transforming Operation 1 based on Operation 2: { index: 2, character: "x" } (index increased by 1)
Applying Transformed Operation 1: "axbyc"

Example 2:

Initial Text: ""
Operation 1: { index: 0, character: "a" }
Operation 2: { index: 0, character: "b" }

Applying Operation 1: "a"
Transforming Operation 2 based on Operation 1: { index: 1, character: "b" } (index increased by 1)
Applying Transformed Operation 2: "ab"

Applying Operation 2 first, then Operation 1:
Applying Operation 2: "b"
Transforming Operation 1 based on Operation 2: { index: 1, character: "a" } (index increased by 1)
Applying Transformed Operation 1: "ba"  (Incorrect!  OT is designed to avoid this.  Your transformation logic must prevent this.)

Example 3:

Initial Text: "hello"
Operation 1: { index: 2, character: "z" }
Operation 2: { index: 2, character: "w" }

Applying Operation 1: "hezllo"
Transforming Operation 2 based on Operation 1: { index: 3, character: "w" } (index increased by 1)
Applying Transformed Operation 2: "hezwllo"

Applying Operation 2 first, then Operation 1:
Applying Operation 2: "hello"
Transforming Operation 1 based on Operation 2: { index: 3, character: "z" } (index increased by 1)
Applying Transformed Operation 1: "hezwllo"

Constraints

• The text string will contain only ASCII characters.
• The index in an operation will be a non-negative integer.
• The character to be inserted will be a single ASCII character.
• The maximum length of the initial text string is 100 characters.
• The maximum number of operations to be applied in a single sequence is 10.
• Performance is not a primary concern for this challenge, but avoid excessively inefficient algorithms.

Notes

• Focus on the core transformation logic. You don't need to build a full-fledged collaborative editor.
• Think carefully about how the index of an operation changes when other operations have been applied.
• Test your implementation thoroughly with various scenarios, including overlapping operations and operations applied in different orders.
• Consider how you would handle concurrent operations arriving at different clients. The transformation function is the key to ensuring consistency.
• The goal is to understand the principles of OT, not to create a production-ready system. Simplicity and clarity are valued.