Array Data Structure Questions

Heap Sort operates in-place, meaning it only requires a constant amount of additional memory regardless of the input size. Merge Sort typically needs O(n) extra space, while Quick Sort's space complexity depends on the recursion depth.

Adaptive search algorithms modify their behavior based on the information gathered during the search process. For example, they might reorder elements based on access frequency to potentially improve future searches.

In the worst case, we need to compare elements from both subarrays one by one until only one element is left. We perform 'm + n - 1' comparisons in this scenario.

Binary search halves the search space in each step. With 1000 elements, you can divide the search space in half roughly 10 times (log₂1000 ≈ 10) before reaching a single element.

While many stable sorting algorithms like Merge Sort have O(n log n) complexity, stability itself is not tied to a specific time complexity. There can be stable algorithms with other complexities.

Heap Sort utilizes a binary heap to efficiently organize the data. The algorithm repeatedly extracts the maximum (or minimum) element from the heap and rebuilds it to maintain the heap property.

Merge sort is a sorting algorithm, not inherently designed for array rotation. The other options are established array rotation techniques.

Inserting into a heap involves adding the element at the end and then performing a 'heapify' operation, which has a logarithmic time complexity due to traversing the height of the heap.

Sparse arrays efficiently store only the non-zero elements and their indices, saving memory for matrices with a high proportion of zeros.

A circular array's wrap-around nature is ideal for managing a fixed-size buffer, efficiently overwriting older data as new data arrives.