What are the key differences between merge sort and heap sort, and which one is more efficient in terms of time complexity and space complexity?

Merge sort and heap sort are both comparison-based sorting algorithms, but they differ in their approach to sorting.

Merge sort divides the array into two halves, sorts each half separately, and then merges them back together in sorted order. It has a time complexity of O(n log n) in all cases and a space complexity of O(n) due to the need for additional space to store the merged arrays.

Heap sort, on the other hand, uses a binary heap data structure to sort the array in place. It has a time complexity of O(n log n) in all cases and a space complexity of O(1) since it does not require additional space for merging arrays.

In terms of efficiency, both merge sort and heap sort have the same time complexity, but heap sort is more space-efficient as it does not require additional space for merging arrays.