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This lecture covers the concept of heapsort, explaining how to build a heap from an unordered array, the worst-case running time of BUILD-MAX-HEAP, and the analysis of heapsort. It also delves into priority queues, discussing operations like INSERT and extracting the maximum element. The lecture concludes with a summary of heapsort's time complexity and practicality compared to quicksort, hinting at upcoming topics on using heaps for priority queues and other data structures.