Solving recurrences The analysis of merge sort from Lecture I required us to solve a recurrence Recurrences are like solving integrals erential equations, etc o Learn a few tricks Lecture 3: Applications of recurrences
Quicksort Proposed by C. A.R. Hoare in 1962 Divide-and-conquer algorithm Sorts“ in place”( like insertion sort, but not like merge sort Very practical(with tuning)
Order statistics Select the ith smallest of n elements(the element with rank i i=l: minimum, .i=n: marimum, i=L(n+1)/2]or[(n+1)/2 median Naive algorithm: Sort and index ith element Worst-case running time =o(n Ig n)+o(1 o(nIg n using merge sort or heapsort(not quicksort) c 2001 by Charles E Leiserson