Reshape Data: Concatenate

#833 Most AskedEasy

Reshape Data: Concatenate #833 Most Asked

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DataFrame df1
+-------------+--------+
| Column Name | Type   |
+-------------+--------+
| student_id  | int    |
| name        | object |
| age         | int    |
+-------------+--------+

DataFrame df2
+-------------+--------+
| Column Name | Type   |
+-------------+--------+
| student_id  | int    |
| name        | object |
| age         | int    |
+-------------+--------+

Write a solution to concatenate these two DataFrames vertically into one DataFrame.

The result format is in the following example.

Example 1:

Input:
df1
+------------+---------+-----+
| student_id | name    | age |
+------------+---------+-----+
| 1          | Mason   | 8   |
| 2          | Ava     | 6   |
| 3          | Taylor  | 15  |
| 4          | Georgia | 17  |
+------------+---------+-----+
df2
+------------+------+-----+
| student_id | name | age |
+------------+------+-----+
| 5          | Leo  | 7   |
| 6          | Alex | 7   |
+------------+------+-----+
Output:
+------------+---------+-----+
| student_id | name    | age |
+------------+---------+-----+
| 1          | Mason   | 8   |
| 2          | Ava     | 6   |
| 3          | Taylor  | 15  |
| 4          | Georgia | 17  |
| 5          | Leo     | 7   |
| 6          | Alex    | 7   |
+------------+---------+-----+
Explanation:
The two DataFramess are stacked vertically, and their rows are combined.

Try coding it in LeetCode

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 will the inputs be, and can I expect any null or empty values in the input arrays?
Are the arrays guaranteed to be of the same length, and if not, how should I handle mismatched lengths?
What is the expected output data type, and what should I return if concatenation is not possible or results in an invalid state?
Are there any memory constraints I should be aware of regarding the size of the concatenated result?
Can you provide an example of the input and expected output to clarify the desired concatenation behavior?

Brute Force Solution

Approach

The brute force method for reshaping data by concatenation involves trying every single possible combination of how to group the data. It's like rearranging blocks and testing each arrangement to see if it fits the desired shape. This is done without any clever shortcuts, simply checking every possibility.

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

Start by considering the first possible grouping: taking only the very first piece of data.
Next, try adding the second piece of data to the first grouping, then the third, and so on, expanding this initial group one piece at a time.
For each grouping you create, determine if it meets the specified length or size constraint.
If a grouping doesn't fit the constraint (e.g., it's too long), discard it and move on.
If a grouping does fit, then try all the possible ways to create the next grouping, starting from the remaining pieces of data, using the same method.
Continue this process, exploring all possible ways to create valid groupings until all the original data pieces have been used.
Keep track of every single valid combination of groupings you find.
Finally, compare all the valid combinations and choose the one that best matches any additional criteria or optimization goals you might have.

Code Implementation

def reshape_data_concatenate_brute_force(data, target_length):
    all_valid_combinations = []

    def find_combinations(current_combination, remaining_data):
        # Base case: If no data remains, check the combination
        if not remaining_data:
            all_valid_combinations.append(current_combination)
            return

        for i in range(1, len(remaining_data) + 1):
            first_group = remaining_data[:i]

            # Check if the current group is within the target length
            if len(first_group) <= target_length:

                # Recursively call to continue building combinations
                find_combinations(current_combination + [first_group], remaining_data[i:])

    # Initiate the recursive calls with an empty combination
    find_combinations([], data)

    # We want to return all possible valid combinations
    return all_valid_combinations

Big(O) Analysis

Time Complexity

O(2^n) – The described brute force approach explores all possible groupings of the data. In the worst case, it considers every possible subset of the input, leading to an exponential number of combinations. Specifically, for each element, we have the choice of including it in the current group or starting a new group, effectively doubling the search space with each element. Therefore, the number of operations grows exponentially with the input size n, approximating O(2^n).

Space Complexity

O(N!) – The algorithm explores every possible combination of groupings. In the worst-case scenario, the recursion stack will grow proportionally to the number of possible combinations. The number of possible combinations can be represented as factorial function and can grow up to N! where N is the number of elements. Storing intermediate valid combinations also contribute to the overall space usage and can also potentially reach N! in the worst case. Therefore, the auxiliary space required to store the call stack and intermediate results is O(N!).

Optimal Solution

Approach

We are given a dataset in one format, and need to transform it into another format by combining elements. The trick is to process the data sequentially, keeping track of where we are in both the original data and the new structure we are building. We avoid extra work by making simple calculations as we go.

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

Start by figuring out the total number of elements we will have in the reshaped data.
Create the new data structure, ready to hold the transformed data, with the correct size.
Move through the original data element by element.
For each element in the original data, calculate its new position in the reshaped data based on the required combination.
Place the element in its calculated new position in the reshaped data structure.
Continue moving through the original data, recalculating the positions and combining the elements until the reshaped data structure is fully populated.
Return the reshaped data structure.

Code Implementation

def concatenate_data(data_lists):
    total_elements = 0
    for data_list in data_lists:
        total_elements += len(data_list)

    # Create the new list with the correct size
    concatenated_list = [None] * total_elements

    current_index = 0
    for data_list in data_lists:
        # Placing data list elements into concatenated list
        for element in data_list:
            concatenated_list[current_index] = element
            current_index += 1

    # Returning concatenated result
    return concatenated_list

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through each element of the original data once. For each element, it performs a constant amount of calculation to determine its new position and then places it in the reshaped data structure. Since the number of operations is directly proportional to the number of elements n in the original data, the time complexity is O(n).

Space Complexity

O(N) – The plain English explanation describes creating a new data structure to hold the reshaped data, sized to contain all transformed elements. Step 2 specifically mentions allocating this new structure with the 'correct size'. If we consider N to be the number of elements in this reshaped data, the auxiliary space used to store it is directly proportional to N. Therefore, the algorithm uses O(N) auxiliary space.

Edge Cases

Case	How to Handle
One or both input lists are empty	Return the other non-empty list, or an empty list if both are empty, as there's nothing to concatenate from one or both input lists.
Input lists contain different data types	Raise a TypeError exception to indicate incompatible data types, as concatenation is generally defined for lists of the same type.
Very large input lists exceeding available memory	Consider a generator-based approach to concatenate the lists in chunks, avoiding loading the entire result into memory at once.
Nested lists of varying depths.	The prompt asks us to concatenate the inputs; assume we are concatenating two lists containing primitive data types and not nested lists.
Input lists are immutable (e.g., tuples in Python)	Convert immutable inputs to mutable lists before concatenation to allow for modification, or return a new concatenated tuple if immutability must be maintained.
Lists contain mixed data types that can be implicitly converted	Ensure consistency by explicitly converting elements to a common type before concatenation, or raise an error if implicit conversion is undesirable.
Concatenation results in integer overflow (if lists contain large numbers).	Use a language with automatic arbitrary-precision arithmetic or implement overflow checks to prevent incorrect results.
One list is significantly larger than the other.	Algorithm should still have an O(n+m) time complexity (where n and m are the sizes of the lists), with minimal performance impact from iterating a larger list.

One or both input lists are empty

How to Handle:

Return the other non-empty list, or an empty list if both are empty, as there's nothing to concatenate from one or both input lists.

Input lists contain different data types

How to Handle:

Raise a TypeError exception to indicate incompatible data types, as concatenation is generally defined for lists of the same type.

Very large input lists exceeding available memory

How to Handle:

Consider a generator-based approach to concatenate the lists in chunks, avoiding loading the entire result into memory at once.

Nested lists of varying depths.

How to Handle:

The prompt asks us to concatenate the inputs; assume we are concatenating two lists containing primitive data types and not nested lists.

Input lists are immutable (e.g., tuples in Python)

How to Handle:

Convert immutable inputs to mutable lists before concatenation to allow for modification, or return a new concatenated tuple if immutability must be maintained.

Lists contain mixed data types that can be implicitly converted

How to Handle:

Ensure consistency by explicitly converting elements to a common type before concatenation, or raise an error if implicit conversion is undesirable.

Concatenation results in integer overflow (if lists contain large numbers).

How to Handle:

Use a language with automatic arbitrary-precision arithmetic or implement overflow checks to prevent incorrect results.

One list is significantly larger than the other.

How to Handle:

Algorithm should still have an O(n+m) time complexity (where n and m are the sizes of the lists), with minimal performance impact from iterating a larger list.