What is the maximum number of keys contained within a node of a B-Tree of order m?
A B-Tree node of order m can have at most m children, which corresponds to holding at most m - 1 search keys.
How does a B+ Tree differ primarily from a standard B-Tree?
In a B+ Tree, internal nodes store only index keys, while all actual data pointers are stored in leaf nodes. Furthermore, leaf nodes are linked sequentially, making range queries extremely fast.
What is the time complexity to build a Max Heap from an unsorted array of n elements using Floyd's build-heap algorithm?
Floyd's bottom-up heap construction algorithm processes nodes from index ⌊n/2⌋ down to 1 using heapify. The sum of node heights converges to O(n) total time complexity.
What is the standard upper bound on the ratio of the longest root-to-leaf path length to the shortest root-to-leaf path length in a Red-Black Tree?
Every root-to-leaf path has the same number of black nodes, while red nodes cannot be adjacent. Therefore a longest path can contain at most one red node per black node and is at most twice the length of a shortest path.
Which statements correctly describe extracting the maximum element from a Max Heap?
All three statements are correct. Extract-Max removes the root, moves the last element to the root, and restores heap order by heapify-down, taking O(log n) worst-case time.