Web Reference: Jan 26, 2026 · By incorporating random choices into their processes, randomized algorithms can often provide faster solutions or better approximations compared to deterministic algorithms. Hash tables with universal hash functions are randomized data structures that have high performance due to randomness. Recall from last time: the selection problem is to find the kth largest element in an unsorted array. Can solve in O(n log n) time by sorting and taking the kth largest element. Assume all input elements are distinct. In practice, there are better partitioning algorithms for when duplicate input elements may exist. Let T(n) = worst-case running time on an array of n elements.
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