What approach would you take to interleave two sorted arrays into a consolidated sorted array?

Question Analysis

The question is asking you to describe an approach to combine two sorted arrays into a single sorted array. This is a common problem in computer science, often used to teach concepts related to merging operations in sorting algorithms such as Merge Sort. When dealing with two sorted arrays, the goal is to efficiently merge them so that the resulting array maintains the sorted order.

Key aspects to consider:

• Input: Two sorted arrays.
• Output: A single sorted array containing all elements from both input arrays.
• Constraints: The input arrays are already sorted.
• Efficiency: Aim for a solution that is as efficient as possible, ideally with a time complexity of O(n + m), where n and m are the lengths of the two arrays.

Answer

To interleave two sorted arrays into a consolidated sorted array, you can use a two-pointer technique, which is both efficient and straightforward. Here's a step-by-step approach to achieve this:

1. Initialize Pointers: Start by initializing two pointers, each pointing to the first element of the two arrays.
2. Create Result Array: Prepare an empty array (or list) that will hold the sorted elements from both arrays.
3. Traverse and Compare:
   • Compare the elements at the current positions of the two pointers.
   • Append the smaller element to the result array.
   • Move the pointer of the array from which the element was taken to the next element.
4. Handle Remaining Elements:
   • Once one of the arrays is fully traversed, append the remaining elements of the other array to the result array.
5. Return the Result: The result array now contains all elements from both input arrays in sorted order.

Here is a simple implementation in Python:

def merge_sorted_arrays(arr1, arr2):
    merged_array = []
    i, j = 0, 0
    
    # Traverse both arrays
    while i < len(arr1) and j < len(arr2):
        if arr1[i] < arr2[j]:
            merged_array.append(arr1[i])
            i += 1
        else:
            merged_array.append(arr2[j])
            j += 1
    
    # Append remaining elements of arr1
    while i < len(arr1):
        merged_array.append(arr1[i])
        i += 1
    
    # Append remaining elements of arr2
    while j < len(arr2):
        merged_array.append(arr2[j])
        j += 1
    
    return merged_array

# Example usage:
arr1 = [1, 3, 5]
arr2 = [2, 4, 6]
print(merge_sorted_arrays(arr1, arr2))  # Output: [1, 2, 3, 4, 5, 6]

Key Points:

• This approach maintains the sorted order by always selecting the smallest available element from the two arrays.
• The time complexity is O(n + m), where n and m are the lengths of the two input arrays, making it efficient for large datasets.