Under uniform hashing, what is the expected number of probes for an unsuccessful search in a hash table using open addressing with load factor $\alpha < 1$?
Under the uniform-hashing assumption for open addressing, the expected number of probes for an unsuccessful search is at most 1/(1 - $\alpha$). This is a probe-count bound; the exact expectation for successful searches is different.
Which property must hold for a Binary Min-Heap?
In a Min-Heap, every parent node has a key value less than or equal to the key values of its children.
What is the primary advantage of a B+ Tree over a standard B-Tree in database indexing?
In B+ Trees, internal nodes store only index keys and all record data/pointers reside in leaf nodes, which are linked as a doubly linked list for extremely fast range queries.
Which sorting algorithm is optimal for sorting integers bounded in the range [1, K] when $K = O(N)$?
Counting Sort runs in O(N + K) time. When $K = O(N)$, its time complexity becomes linear O(N), outperforming comparison-based O(N log N) algorithms.
What is the tight worst-case time complexity of Quick Sort algorithm?
Quick Sort's worst case occurs when the pivot chosen is consistently the smallest or largest element (e.g., already sorted array with first element as pivot), yielding recurrence T(N) = T(N-1) + O(N) = O($N^2)$.