Flatten Deeply Nested Array

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ArraysRecursion

Given a multi-dimensional array arr and a depth n, return a flattened version of that array.

A multi-dimensional array is a recursive data structure that contains integers or other multi-dimensional arrays.

A flattened array is a version of that array with some or all of the sub-arrays removed and replaced with the actual elements in that sub-array. This flattening operation should only be done if the current depth of nesting is less than n. The depth of the elements in the first array are considered to be 0.

Please solve it without the built-in Array.flat method.

For example:

arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
n = 0

Should return:

[1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]

As another example:

arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
n = 1

Should return:

[1, 2, 3, 4, 5, 6, 7, 8, [9, 10, 11], 12, 13, 14, 15]

Write a function to perform this flattening. What is the time and space complexity of your solution? Consider edge cases such as an empty input array or a depth of 0. How would you optimize your solution if memory usage was a major concern?

Flatten Deeply Nested Array

Medium

Amazon

1 view

Topics:

ArraysRecursion

Given a multi-dimensional array arr and a depth n, return a flattened version of that array.

A multi-dimensional array is a recursive data structure that contains integers or other multi-dimensional arrays.

A flattened array is a version of that array with some or all of the sub-arrays removed and replaced with the actual elements in that sub-array. This flattening operation should only be done if the current depth of nesting is less than n. The depth of the elements in the first array are considered to be 0.

Please solve it without the built-in Array.flat method.

For example:

arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
n = 0

Should return:

[1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]

As another example:

arr = [1, 2, 3, [4, 5, 6], [7, 8, [9, 10, 11], 12], [13, 14, 15]]
n = 1

Should return:

[1, 2, 3, 4, 5, 6, 7, 8, [9, 10, 11], 12, 13, 14, 15]

Write a function to perform this flattening. What is the time and space complexity of your solution? Consider edge cases such as an empty input array or a depth of 0. How would you optimize your solution if memory usage was a major concern?

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

What data types might the array elements contain besides nested arrays and numbers (e.g., strings, null, booleans)?
What is the maximum depth of nesting I should expect in the input array?
Should the output array contain the numbers in the order they appear when traversing the nested array from left to right?
If the input array is null or empty, what should I return (e.g., null, an empty array)?
Are all the numerical values integers or could they also be floating-point numbers?

Brute Force Solution

Approach

The brute force approach to flattening a deeply nested array involves systematically examining each element within the structure. It's like peeling an onion, layer by layer, until you get to the core. We keep going until there are no more nested structures left.

Here's how the algorithm would work step-by-step:

Start by looking at the first thing in the array.
If it's a simple value (like a number or text), then just keep it.
If it's another array inside the array, then open it up and look inside that array instead.
Repeat the previous two steps for everything inside that inner array.
Keep doing this, going deeper and deeper into any nested arrays you find.
Once you've gone through all the levels of nesting, put all the simple values you found into a single, flat array.

Code Implementation

def flatten_deeply_nested_array(nested_array):
    flattened_array = []

    for element in nested_array:
        # Need to check element type to handle nested arrays.
        if isinstance(element, list):

            flattened_array.extend(flatten_deeply_nested_array(element))

        else:
            flattened_array.append(element)

    return flattened_array

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through each element of the input array. When it encounters a nested array, it processes each element within that nested array. In the worst case, the function has to traverse all n elements. Therefore, the time complexity is directly proportional to the total number of elements, resulting in O(n).

Space Complexity

O(D) – The algorithm uses recursion to traverse the deeply nested array. In the worst-case scenario, the array has a maximum depth of nesting, D, where each level of nesting results in a new stack frame being added to the call stack. Therefore, the auxiliary space complexity is proportional to the maximum depth of nesting, D, due to the recursive call stack. This means the space required grows linearly with the maximum depth of the nested arrays. The 'pile' from the plain English explanation corresponds to these stack frames.

Optimal Solution

Approach

To flatten a deeply nested structure, we want to systematically go through each element and pull out the individual pieces until nothing is nested anymore. A great way to achieve this is by using a technique that can repeat the same actions on smaller and smaller parts of the structure until we are done.

Here's how the algorithm would work step-by-step:

Start by looking at the entire structure.
If the structure is an individual element (not another structure within), simply keep it.
If the structure is a nested structure, 'open it up' and apply the same process to each piece inside.
Keep doing this 'opening up' process on any newly discovered nested structure until everything is an individual element.
Combine all the individual elements into a single, non-nested sequence.

Code Implementation

def flatten_deeply_nested_array(nested_array):
    flattened_array = []

    def flatten_recursively(current_element):
        # Check if the current element is a list (nested structure).
        if isinstance(current_element, list):

            # Iterate through each item if it is a nested list
            for item in current_element:
                flatten_recursively(item)

        else:
            # Append the non-list element to the flattened list.
            flattened_array.append(current_element)

    # Initiate the flattening process with the input nested array.
    flatten_recursively(nested_array)

    return flattened_array

Big(O) Analysis

Time Complexity

O(n) – Let n be the total number of elements in the deeply nested array, including all nested elements. The algorithm visits each element exactly once to determine if it is an array or a non-array element. Each time a nested array is encountered, it's effectively unpacked, and each of its elements is then visited. Thus, the algorithm performs a constant amount of work for each of the n elements, leading to a linear time complexity. Therefore, the time complexity is O(n).

Space Complexity

O(D) – The algorithm uses recursion to 'open up' nested structures. In the worst-case scenario, the array is deeply nested to a depth of D, where D is the maximum nesting level. Each recursive call adds a new frame to the call stack. Therefore, the auxiliary space is determined by the maximum depth of the recursion, which is proportional to D. This recursive process generates space proportional to the depth of the nested structure, leading to a space complexity of O(D).

Edge Cases

Case	How to Handle
Null or undefined input array	Return an empty array immediately to avoid NullPointerException or undefined behavior.
Input array containing only empty arrays	The recursive calls should terminate gracefully, resulting in an empty output array.
Input array with maximum nesting depth exceeding recursion limit	Consider iterative solution or tail-recursive approach for very deep nesting to avoid stack overflow.
Input array containing non-numeric values or null/undefined elements	Filter out non-numeric, null, or undefined values during flattening, or throw an IllegalArgumentException if unexpected type is not permitted.
Input array containing extremely large numbers	The chosen data type should be able to accommodate the range of numbers without overflow issues.
Input array with deeply nested structure containing circular references	Implement a visited set to detect and prevent infinite recursion due to circular references.
Very large input array size causing memory constraints	If possible process the array in chunks or use an iterative approach with generators if the programming language supports them.
Input array containing Infinity or NaN values	Handle Infinity and NaN values by either filtering them out or explicitly converting them to suitable representations based on problem requirements.