Compare merge sort and quick sort algorithms in terms of storage space and time required to execute them.

Merge Sort:

• Storage Space: Merge sort requires additional storage space proportional to the size of the input array. This is because it creates a new array to store the sorted result. Therefore, the auxiliary space complexity is O(n), where n is the size of the array.

• Time Complexity: The time complexity of merge sort is O(n log n). This is because it recursively divides the array into smaller subarrays, sorts each subarray, and then merges them back together. The recursion depth is O(log n), and each merge operation takes O(n) time.

Quick Sort:

• Storage Space: Quick sort does not require additional storage space beyond the input array. It operates by rearranging elements in place, without the need for a new array to store the sorted result. Therefore, the auxiliary space complexity is O(1).

• Time Complexity: The average-case time complexity of quick sort is O(n log n). However, the worst-case time complexity is O(n^2), which occurs when the input array is already sorted or nearly sorted. This is because the partitioning step in quick sort can result in an unbalanced split, leading to a recursive call on a subarray of size n-1, n-2, and so on, resulting in a quadratic time complexity.

Comparison:

Feature	Merge Sort	Quick Sort
Storage Space	O(n)	O(1)
Average-Case Time Complexity	O(n log n)	O(n log n)
Worst-Case Time Complexity	O(n log n)	O(n^2)

Overall, merge sort has a guaranteed O(n log n) time complexity, regardless of the input array, while quick sort has an average-case time complexity of O(n log n) but a worst-case time complexity of O(n^2). Merge sort requires additional storage space, while quick sort does not. Depending on the specific requirements of the application, either algorithm may be more suitable.