Problem Description

This problem asks you to extend JavaScript's built-in Array prototype with a custom groupBy method. The method should transform any array into a grouped object based on a provided function.

The groupBy method takes a callback function fn as its parameter. This callback function:

• Accepts each item from the array as input
• Returns a string that serves as the grouping key

The method should return an object where:

• Each key is a unique string returned by calling fn on the array items
• Each value is an array containing all items from the original array that produced that particular key when passed through fn

Key requirements:

• Items in each grouped array must maintain their original order from the source array
• The order of keys in the resulting object doesn't matter
• You cannot use external libraries like lodash's _.groupBy

For example, if you have [1, 2, 3] and use String as the grouping function:

• fn(1) returns "1", so 1 goes into the group with key "1"
• fn(2) returns "2", so 2 goes into the group with key "2"
• fn(3) returns "3", so 3 goes into the group with key "3"
• Result: {"1": [1], "2": [2], "3": [3]}

The solution uses the reduce method to iterate through the array once, building up the grouped object by either creating new arrays for new keys or appending items to existing arrays for keys that have already been encountered.

Intuition

When we need to group array elements by some criteria, we're essentially building a mapping from keys to collections of values. Think about organizing items into buckets - each bucket has a label (the key), and we place items into the appropriate bucket based on what the function tells us.

The natural data structure for this is an object (or Record<string, T[]> in TypeScript), where each property represents a bucket. As we go through the array, we need to:

1. Determine which bucket each item belongs to by calling fn(item)
2. Place the item in that bucket

This is a classic accumulation pattern - we start with an empty object and gradually build it up by processing each element. JavaScript's reduce method is perfect for this because it's designed to transform an array into a single value (in this case, an object) by iterating through elements and accumulating results.

For each item, we face two scenarios:

• The bucket (key) already exists: We simply add the item to the existing array
• The bucket doesn't exist yet: We create a new bucket with this item as its first element

The beauty of reduce is that it handles the iteration and accumulation in one clean operation. We pass an empty object {} as the initial accumulator, and for each item, we:

1. Calculate the key using fn(item)
2. Check if acc[key] exists
3. Either push to the existing array or create a new array with the current item
4. Return the updated accumulator for the next iteration

This approach ensures we only traverse the array once (O(n) time complexity) and maintain the original order of elements within each group since we process items sequentially and use push to append them.

Solution Approach

The implementation extends the Array prototype by adding a new groupBy method. Let's walk through the key components:

TypeScript Declaration:

declare global {
    interface Array<T> {
        groupBy(fn: (item: T) => string): Record<string, T[]>;
    }
}

This declaration tells TypeScript that all arrays now have a groupBy method that accepts a function returning a string and produces a Record<string, T[]> (an object with string keys and array values).

Core Implementation using reduce:

Array.prototype.groupBy = function (fn) {
    return this.reduce((acc, item) => {
        const key = fn(item);
        if (acc[key]) {
            acc[key].push(item);
        } else {
            acc[key] = [item];
        }
        return acc;
    }, {});
};

The algorithm works as follows:

1. Initialize with an empty object: The reduce method starts with {} as the initial accumulator value.

2. Process each array element: For each item in the array:

   • Call fn(item) to get the grouping key
   • Store this key for use in the next steps

3. Conditional bucket management:

   • If acc[key] exists: This means we've seen this key before, so we have an existing array. We simply push the current item to that array using acc[key].push(item).
   • If acc[key] doesn't exist: This is a new key, so we create a new array containing just the current item: acc[key] = [item].

4. Return the accumulator: After handling the current item, we return acc to pass it to the next iteration.

5. Final result: After all items are processed, reduce returns the fully populated object with all groups.

Example execution trace for [1, 2, 1].groupBy(String):

• Start: acc = {}
• Item 1: key = "1", acc["1"] doesn't exist → acc = {"1": [1]}
• Item 2: key = "2", acc["2"] doesn't exist → acc = {"1": [1], "2": [2]}
• Item 1: key = "1", acc["1"] exists → push to array → acc = {"1": [1, 1], "2": [2]}
• Return: {"1": [1, 1], "2": [2]}

This pattern ensures O(n) time complexity with a single pass through the array, while maintaining the insertion order of elements within each group.

Example Walkthrough

Let's walk through grouping an array of people by their age:

const people = [
  { name: "Alice", age: 25 },
  { name: "Bob", age: 30 },
  { name: "Charlie", age: 25 },
  { name: "David", age: 30 }
];

const result = people.groupBy(person => String(person.age));

Step-by-step execution:

1. Initialize: Start with empty accumulator acc = {}

2. Process Alice (age: 25):

   • Call fn({name: "Alice", age: 25}) → returns "25"
   • Check if acc["25"] exists → No
   • Create new array: acc["25"] = [{name: "Alice", age: 25}]
   • Accumulator becomes: {"25": [{name: "Alice", age: 25}]}

3. Process Bob (age: 30):

   • Call fn({name: "Bob", age: 30}) → returns "30"
   • Check if acc["30"] exists → No
   • Create new array: acc["30"] = [{name: "Bob", age: 30}]
   • Accumulator becomes: {"25": [{name: "Alice", age: 25}], "30": [{name: "Bob", age: 30}]}

4. Process Charlie (age: 25):

   • Call fn({name: "Charlie", age: 25}) → returns "25"
   • Check if acc["25"] exists → Yes!
   • Push to existing array: acc["25"].push({name: "Charlie", age: 25})
   • Accumulator becomes: {"25": [{name: "Alice", age: 25}, {name: "Charlie", age: 25}], "30": [{name: "Bob", age: 30}]}

5. Process David (age: 30):

   • Call fn({name: "David", age: 30}) → returns "30"
   • Check if acc["30"] exists → Yes!
   • Push to existing array: acc["30"].push({name: "David", age: 30})
   • Final result: {"25": [{name: "Alice", age: 25}, {name: "Charlie", age: 25}], "30": [{name: "Bob", age: 30}, {name: "David", age: 30}]}

The key insight is that we build up our grouped object incrementally. When we encounter a new key, we create a new array bucket. When we see an existing key, we append to that bucket. The original order is preserved within each group because we process elements sequentially and use push to maintain insertion order.

Solution Implementation

Time and Space Complexity

Time Complexity: O(n)

The reduce method iterates through each element in the array exactly once. For each element:

• Calling the provided function fn(item) takes O(1) assuming the function itself is O(1)
• Checking if acc[key] exists is O(1) for object property access
• Adding an element to an array with push() is amortized O(1)
• Creating a new array with a single element is O(1)

Since we perform constant-time operations for each of the n elements, the overall time complexity is O(n).

Space Complexity: O(n)

The space complexity consists of:

• The accumulator object acc which will store all n elements distributed across different keys: O(n)
• Each element is stored exactly once in the resulting object structure
• The number of keys in the result object is at most n (when each element maps to a unique key): O(n) in the worst case
• Temporary variables like key use O(1) space

The total space complexity is O(n) where n is the number of elements in the input array.

Common Pitfalls

1. Non-String Keys from Callback Function

The most critical pitfall is when the callback function returns non-string values. The specification explicitly states that fn should return a string, but JavaScript's dynamic typing allows any value to be used as an object key, which gets automatically coerced to a string.

Problem Example:

[1, 2, 3].groupBy(x => x); // Returns number, not string
// This "works" but violates the contract
// Result: {"1": [1], "2": [2], "3": [3]}

[{id: 1}, {id: 2}].groupBy(item => item); // Returns object
// Objects get stringified to "[object Object]"
// Result: {"[object Object]": [{id: 1}, {id: 2}]} - All items grouped under same key!

Solution: Always ensure the callback explicitly returns a string:

// Good practices:
[1, 2, 3].groupBy(x => String(x));
[{id: 1}, {id: 2}].groupBy(item => String(item.id));
[{id: 1}, {id: 2}].groupBy(item => JSON.stringify(item));

2. Mutating the Original Array

While the current implementation doesn't mutate the original array, a common mistake when modifying prototypes is accidentally changing the original data.

Problem Example:

// Bad implementation that sorts original array
Array.prototype.groupBy = function(fn) {
    this.sort(); // Mutates original array!
    // ... rest of implementation
};

Solution: Never modify this directly. If you need a sorted version, create a copy:

Array.prototype.groupBy = function(fn) {
    const sorted = [...this].sort(); // Work with a copy
    // ... rest of implementation
};

3. Callback Function Throws Errors

If the callback function throws an error for certain items, the entire groupBy operation fails.

Problem Example:

const data = [1, null, 3];
data.groupBy(x => x.toString()); // Error: Cannot read property 'toString' of null

Solution: Add error handling or validate inputs:

Array.prototype.groupBy = function(fn) {
    return this.reduce((acc, item) => {
        try {
            const key = fn(item);
            if (typeof key !== 'string') {
                throw new TypeError(`Callback must return a string, got ${typeof key}`);
            }
            acc[key] = acc[key] || [];
            acc[key].push(item);
        } catch (error) {
            // Either skip the item or handle the error appropriately
            console.warn(`Error processing item ${item}:`, error);
        }
        return acc;
    }, {});
};

4. Name Collision with Future JavaScript Features

groupBy is actually being considered for future JavaScript specifications. Your implementation might conflict with native implementations.

Problem Example:

// Your implementation
Array.prototype.groupBy = function(fn) { /* ... */ };

// Future native implementation might have different behavior
// This could break your code when browsers implement it

Solution: Use a namespaced method name or check for existing implementation:

if (!Array.prototype.groupBy) {
    Array.prototype.groupBy = function(fn) { /* ... */ };
}

// Or use a unique name
Array.prototype.customGroupBy = function(fn) { /* ... */ };

5. Python-Specific: Unhashable Keys

In the Python implementation, there's an additional pitfall where the function might attempt to return unhashable types.

Problem Example:

# This will fail if fn returns a list or dict
group_by([1, 2, 3], lambda x: [x])  # Lists can't be dictionary keys

Solution: Ensure the function returns only hashable types (strings, numbers, tuples):

def group_by(array: List[T], fn: Callable[[T], str]) -> Dict[str, List[T]]:
    accumulator = {}
    for current_item in array:
        key = fn(current_item)
        if not isinstance(key, str):
            raise TypeError(f"Callback must return string, got {type(key).__name__}")
        # ... rest of implementation