第04章_排序集合和选择Sorting_Sets_and_Selection.ppt

Chapter 4 Merge Sort Merge Sort Outline and Reading Divide-and-conquer paradigm, MergeSort (§4.1) Sets (§4.2);Generic Merging and set operations (§4.2.1) Note: Sections 4.2.2 and 4.2.3 are Optional Quick-sort (§4.3) Analysis of quick-sort ((§4.3.1) A Lower Bound on Comparison-based Sorting (§4.4) QuickSort and Radix Sort (§4.5) In-place quick-sort (§4.8) Comparison of Sorting Algorithm (§4.6) Selection (§4.7) Divide-and-Conquer Divide-and conquer is a general algorithm design paradigm: Divide: divide the input data S in two disjoint subsets S1 and S2 Recur: solve the subproblems associated with S1 and S2 Conquer: combine the solutions for S1 and S2 into a solution for S The base case for the recursion are subproblems of size 0 or 1 Merge-sort is a sorting algorithm based on the divide-and-conquer paradigm Like heap-sort It uses a comparator It has O(n log n) running time Unlike heap-sort It does not use an auxiliary priority queue It accesses data in a sequential manner (suitable to sort data on a disk) Merge-Sort Merge-sort on an input sequence S with n elements consists of three steps: Divide: partition S into two sequences S1 and S2 of about n/2 elements each Recur: recursively sort S1 and S2 Conquer: merge S1 and S2 into a unique sorted sequence Merging Two Sorted Sequences The conquer step of merge-sort consists of merging two sorted sequences A and B into a sorted sequence S containing the union of the elements of A and B Merging two sorted sequences, each with n/2 elements and implemented by means of a doubly linked list, takes O(n) time Merge-Sort Tree An execution of merge-sort is depicted by a binary tree each node represents a recursive call of merge-sort and stores unsorted sequence before the execution and its partition sorted sequence at the end of the execution the root is the initial call the leaves are calls on subsequences of size 0 or 1 Execution Example Partition Execution Example (cont.) Recursive call, partition Execution Example (cont.) Recu