Merge sort and quick sort are two popular sorting algorithms used to arrange elements of an array in a specific order. The key differences between the two algorithms are:

Merge Sort:

1. Divide and Conquer: Merge sort is a divide-and-conquer algorithm that splits the input array into smaller subarrays, sorts each subarray, and then merges the sorted subarrays back together.
2. Stable Sorting: Merge sort is a stable sorting algorithm, meaning that the order of equal elements is preserved.
3. Time Complexity: The time complexity of merge sort is O(n log n), making it suitable for large datasets.
4. Space Complexity: The space complexity of merge sort is O(n), as it requires additional space to store the temporary arrays.
5. Implementation: Merge sort is relatively easy to implement, especially for small arrays.

Quick Sort:

1. In-Place Sorting: Quick sort is an in-place sorting algorithm that rearranges the elements within the original array, without requiring additional space.
2. Unstable Sorting: Quick sort is an unstable sorting algorithm, meaning that the order of equal elements may be changed during the sorting process.
3. Time Complexity: The average-case time complexity of quick sort is O(n log n), but it can degrade to O(n^2) in the worst case if the pivot selection is poor.
4. Space Complexity: The space complexity of quick sort is O(log n), as it only requires a small amount of extra space to store the recursive function calls.
5. Implementation: Quick sort can be more challenging to implement than merge sort, especially for large arrays, due to its complex logic and potential for poor pivot selection.