'Sorted sequence' presentation slideshows

Comparison Sorts

Comparison Sorts. Chapter 9.4, 12.1, 12.2. Sorting. We have seen the advantage of sorted data representations for a number of applications Sparse vectors Maps Dictionaries Here we consider the problem of how to efficiently transform an unsorted representation into a sorted representation.

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Sorting

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Algorithms Design and Analysis

Algorithms Design and Analysis. Lecturer: Jing Liu Email: neouma@mail.xidian.edu.cn Homepage: http://see.xidian.edu.cn/faculty/liujing Xidian Homepage: http://web.xidian.edu.cn/liujing. Textbook.

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Merge Sort

7 2 ? 9 4 ? 2 4 7 9. 7 ? 2 ? 2 7. 9 ? 4 ? 4 9. 7 ? 7. 2 ? 2. 9 ? 9. 4 ? 4. Merge Sort. Divide-and conquer is a general algorithm design paradigm: Divide : divide the input data S in two disjoint subsets S 1 and S 2

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Merge Sort

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Merge Sort

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Chapter 11: Sorting, Sets and Selection

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Chapter 8 Sorting

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Heaps and Priority Queues

2. 5. 6. 9. 7. Heaps and Priority Queues. A priority queue stores a collection of items An item is a pair (key, element) Main methods of the Priority Queue ADT insertItem (k, o) inserts an item with key k and element o removeMin () removes the item with the smallest key.

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Searching

Searching. data record:. sequential search ( linear search): O(n) binary search: used for sorted sequence O(log n). Example: 3, 11, 2, 9, 8, 5, 4, 6, 7. O(log N). O(1). O(log n/N). O(1). time:. EREW Searching(Sorted Sequence). N processors. n data records method:.

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MergeSort

MergeSort. Source: Gibbs & Tamassia. MergeSort. MergeSort is a divide and conquer method of sorting. MergeSort Algorithm. MergeSort is a recursive sorting procedure that uses at most O(n lg(n)) comparisons. To sort an array of n elements, we perform the following steps in sequence:

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Heaps

Heaps. 2. 5. 6. 9. 7. A priority queue stores a collection of entries Each entry is a pair (key, value) Main methods of the Priority Queue ADT insert (k, x) inserts an entry with key k and value x removeMin () removes and returns the entry with smallest key. Additional methods

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Quick-Sort

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Merge Sort

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Quick-Sort

7 4 9 6 2 ? 2 4 6 7 9. 4 2 ? 2 4. 7 9 ? 7 9. 2 ? 2. 9 ? 9. Quick-Sort. Quick-sort is a randomized sorting algorithm based on the divide-and-conquer paradigm: Divide : pick a random element x (called pivot ) and partition S into L elements less than x

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Part-G1 Merge Sort

7 2 ? 9 4 ? 2 4 7 9. 7 ? 2 ? 2 7. 9 ? 4 ? 4 9. 7 ? 7. 2 ? 2. 9 ? 9. 4 ? 4. Part-G1 Merge Sort. Divide-and conquer is a general algorithm design paradigm: Divide : divide the input data S in two disjoint subsets S 1 and S 2

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COMP20010: Algorithms and Imperative Programming

COMP20010: Algorithms and Imperative Programming. Lecture 2 Data structures for binary trees Priority queues. Lecture outline. Different data structures for representing binary trees (vector-based, linked), linked structure for general trees; Priority queues (PQs), sorting using PQs;.

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Batcher Sorting Network, n = 4

Batcher Sorting Network, n = 4. Batcher Sorting Network, n = 8. n = 4. n = 4. sorted. sorted. Lemma 1. Any subsequence of a sorted sequence is a sorted sequence. 0. 0. 0. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. sorted. Lemma 2.

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Quick-Sort

7 4 9 6 2 ? 2 4 6 7 9. 4 2 ? 2 4. 7 9 ? 7 9. 2 ? 2. 9 ? 9. Quick-Sort. Quick-sort is a randomized sorting algorithm based on the divide-and-conquer paradigm: Divide : pick a random element x (called pivot ) and partition S into L elements less than x

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Merge Sort

7 2 ? 9 4 ? 2 4 7 9. 7 ? 2 ? 2 7. 9 ? 4 ? 4 9. 7 ? 7. 2 ? 2. 9 ? 9. 4 ? 4. Merge Sort. Divide-and conquer is a general algorithm design paradigm: Divide : divide the input data S in two disjoint subsets S 1 and S 2

260 views • 9 slides