Merge Two 2D Arrays by Summing Values

#803 Most AskedEasy

Merge Two 2D Arrays by Summing Values #803 Most Asked

Easy

Bloomberg LP

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ArraysTwo Pointers

You are given two 2D integer arrays nums1 and nums2.

nums1[i] = [id_i, val_i] indicate that the number with the id id_i has a value equal to val_i.
nums2[i] = [id_i, val_i] indicate that the number with the id id_i has a value equal to val_i.

Each array contains unique ids and is sorted in ascending order by id.

Merge the two arrays into one array that is sorted in ascending order by id, respecting the following conditions:

Only ids that appear in at least one of the two arrays should be included in the resulting array.
Each id should be included only once and its value should be the sum of the values of this id in the two arrays. If the id does not exist in one of the two arrays, then assume its value in that array to be 0.

Return the resulting array. The returned array must be sorted in ascending order by id.

Example 1:

Input: nums1 = [[1,2],[2,3],[4,5]], nums2 = [[1,4],[3,2],[4,1]]
Output: [[1,6],[2,3],[3,2],[4,6]]
Explanation: The resulting array contains the following:
- id = 1, the value of this id is 2 + 4 = 6.
- id = 2, the value of this id is 3.
- id = 3, the value of this id is 2.
- id = 4, the value of this id is 5 + 1 = 6.

Example 2:

Input: nums1 = [[2,4],[3,6],[5,5]], nums2 = [[1,3],[4,3]]
Output: [[1,3],[2,4],[3,6],[4,3],[5,5]]
Explanation: There are no common ids, so we just include each id with its value in the resulting list.

Constraints:

1 <= nums1.length, nums2.length <= 200
nums1[i].length == nums2[j].length == 2
1 <= id_i, val_i <= 1000
Both arrays contain unique ids.
Both arrays are in strictly ascending order by id.

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 values within the 2D arrays be, and can I expect negative values or non-integer values like floats?
What happens if a key exists in only one of the input arrays? Should it still be included in the output with the corresponding value?
If both arrays have the same key, but the values sum to zero, should that key-value pair be included in the output?
Are the input arrays guaranteed to be sorted by key, and if not, what is the expected ordering of the output array?
Can I assume the keys will be unique within each individual 2D array, or should I handle potential duplicate keys within a single input array?

Brute Force Solution

Approach

We want to combine two lists where each item has a key and a value. The brute force method involves checking all possible keys in both lists and combining values whenever the keys match.

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

Look at each item in the first list.
For each of those items, go through the entire second list to see if there's an item with the same key.
If a matching key is found in the second list, add the values of those two items together and record the key along with its summed value.
If the key from the first list doesn't exist in the second list, just keep the original key and value from the first list.
After checking all items in the first list, go through the second list again.
This time, focus only on the items whose keys were NOT found in the first list. Record these keys and values as well.
Finally, collect all the recorded keys and values into a single list.

Code Implementation

def merge_two_2d_arrays_brute_force(first_array, second_array):
    merged_array = []
    keys_from_first_array = set()

    for first_item in first_array:
        key_found_in_second = False
        for second_item in second_array:
            if first_item[0] == second_item[0]:
                # Combine values since keys match
                merged_array.append([first_item[0], first_item[1] + second_item[1]])
                keys_from_first_array.add(first_item[0])
                key_found_in_second = True
                break

        if not key_found_in_second:
            # Keep the original key value from the first array
            merged_array.append(first_item)
            keys_from_first_array.add(first_item[0])

    # Add elements from the second array whose keys are not in the first
    for second_item in second_array:
        if second_item[0] not in keys_from_first_array:
            merged_array.append(second_item)

    return merged_array

Big(O) Analysis

Time Complexity

O(n²) – The described algorithm iterates through the first list of n elements and for each element, it iterates through the second list of potentially n elements to find matching keys. This results in a nested loop structure with a cost of n * n. After processing the first list, the algorithm iterates through the second list again, but only for elements not found in the first list; in the worst-case scenario (where the first list is empty or has completely distinct keys), this second iteration also takes n time. The combination of these operations leads to approximately n*n + n which simplifies to O(n²).

Space Complexity

O(N) – The algorithm accumulates recorded keys and values into a single list. In the worst case, all items from both input lists have unique keys, leading to a new list containing all N items (where N is the total number of items across both input lists). Therefore, the auxiliary space used to store this combined list grows linearly with the input size. The recorded list dominates the space complexity.

Optimal Solution

Approach

The most efficient way to combine these arrays is to use a method that groups matching entries quickly. We want to avoid unnecessary lookups or comparisons. This method essentially sorts and then combines.

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

Create a way to store the combined information that allows quick access.
Go through the first array and put all its information into the storage.
Go through the second array. If an entry already exists in the storage, add the new value to the existing value. If it doesn't exist, add the entry to the storage.
Finally, arrange the combined information into a single, sorted list.

Code Implementation

def merge_arrays(array_one, array_two):
    combined_map = {}

    # Use a dictionary for quick lookup and merging
    for key, value in array_one:
        combined_map[key] = value

    # Add or update entries from the second array
    for key, value in array_two:
        if key in combined_map:
            combined_map[key] += value

        # Add this key if it's not already present
        else:
            combined_map[key] = value

    # Convert the dictionary to a sorted list of lists
    sorted_combined_list = sorted(combined_map.items())

    result = []

    # Restructure the output into the desired format.
    for key, value in sorted_combined_list:
        result.append([key, value])

    return result

Big(O) Analysis

Time Complexity

O(n log n) – The algorithm involves iterating through both arrays, which together contribute to 'n' elements where n represents the total number of entries in both arrays. Inserting and updating a hash map takes O(1) on average, so the iterations themselves are O(n). The final step involves sorting the combined information, which typically uses an efficient algorithm like merge sort or quicksort, leading to a time complexity of O(n log n). Therefore, the overall time complexity is dominated by the sorting step, resulting in O(n log n).

Space Complexity

O(N) – The algorithm uses a storage mechanism (likely a hash map or dictionary) to hold the combined information from the two input arrays. In the worst-case scenario, where all entries in both arrays have unique keys, the storage will need to hold all N entries, where N is the total number of unique entries across both input arrays. Additionally, a sorted list to hold the combined information is created, which can also grow up to size N in the worst case. Therefore, the auxiliary space complexity is O(N).

Edge Cases

Case	How to Handle
Both input arrays are null or empty	Return an empty array as there's nothing to merge or sum.
One array is null or empty while the other is not	Return a copy of the non-null and non-empty array.
Arrays contain duplicate IDs with differing values	The solution should correctly sum values for duplicate IDs, prioritizing later occurrences if a conflict exists in the input.
Arrays contain large IDs potentially causing integer overflow if IDs are used directly as array indices.	Use a hash map (dictionary) to store the summed values, avoiding direct array indexing and potential overflow.
Summed values may exceed maximum integer value resulting in overflow	Use a data type with a larger range (e.g., long) to store the sums to prevent integer overflow.
Arrays contain negative values	The summing logic should correctly handle negative values without introducing errors.
Arrays are very large, impacting performance	The solution should use an efficient data structure like a hash map to ensure reasonable time complexity (O(n+m) where n and m are the sizes of the input arrays).
Input arrays are not sorted by ID	The solution should correctly handle unsorted arrays, typically using a hash map to aggregate values by ID.

Both input arrays are null or empty

How to Handle:

Return an empty array as there's nothing to merge or sum.

One array is null or empty while the other is not

How to Handle:

Return a copy of the non-null and non-empty array.

Arrays contain duplicate IDs with differing values

How to Handle:

The solution should correctly sum values for duplicate IDs, prioritizing later occurrences if a conflict exists in the input.

Arrays contain large IDs potentially causing integer overflow if IDs are used directly as array indices.

How to Handle:

Use a hash map (dictionary) to store the summed values, avoiding direct array indexing and potential overflow.

Summed values may exceed maximum integer value resulting in overflow

How to Handle:

Use a data type with a larger range (e.g., long) to store the sums to prevent integer overflow.

Arrays contain negative values

How to Handle:

The summing logic should correctly handle negative values without introducing errors.

Arrays are very large, impacting performance

How to Handle:

The solution should use an efficient data structure like a hash map to ensure reasonable time complexity (O(n+m) where n and m are the sizes of the input arrays).

Input arrays are not sorted by ID

How to Handle:

The solution should correctly handle unsorted arrays, typically using a hash map to aggregate values by ID.