Analysis of Randomized Quick Sort

This lecture covers the analysis of (randomized) quick sort, focusing on the running time and number of comparisons. The instructor explains the concept of random variables and the expected total number of comparisons. The lecture also discusses the bound on the overall number of comparisons and the application of linearity of expectation. Additionally, it presents a summary of quick sort, proving its expected running time to be O(nlogn) for any input. The lower bounds for sorting and decision trees in the context of comparison sorting are also explored, highlighting the optimality of merge-sort, heapsort, and quicksort.