Graph Algorithms (III) 1 COMP9024: Data Structures and Algorithms Graphs (III) 2 Contents Shortest Paths Minimum Spanning Trees 3 Shortest Paths CB A E D F 0 328 5 8 48 7 1 2 5 2 3 9 4 Weighted Graphs In a weighted graph, each edge has an associated numerical value, […]
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COMP9024: Data Structures and Algorithms 1 COMP9024: Data Structures and Algorithms Sorting Algorithms 2 Outline Merge Sort Quick Sort Bucket-Sort Radix Sort Sorting Lower Bound 3 Merge Sort 7 2 9 4 → 2 4 7 9 7 2 → 2 7 9 4 → 4 9
Problem Set 4 Solutions Problem Set 4 Problem 1 Consider a tree storing 100,000 entries. What is the worst-case height of T in the following cases? a. T is an AVL tree. b. T is a (2,4) tree. c. T is a binary search tree. d. T is a splay tree. Solution: a. Let n(h)
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Problem Set 1-b Problem 1. Modify the stack implementation in the lecture notes (Stack.h and Stack.c) to implement a stack of integers. Problem 2. Write a test program for your stack code in Q1 that does the following: o initialise the stack o prompt the user to input a number n o check that n
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Problem Set3-a Solutions Problem 1 Show that if p(n) is a polynomial in n, then log p(n) is O(log n). Solution: Let p(n) = amnm + am-1nm-1 + … + a1n + a0 p(n) < max{|am|, |am-1|, …, |a0|} (m+1) n m log p(n) < log(max{|am|, |am-1|, …, |a0|} (m+1) + m log n Since
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COMP9024: Data Structures and Algorithms COMP9024: Data Structures and Algorithms Trees and Binary Search Trees Contents • Trees • Tree traversals • Binary search trees Maps and Dictionaries • A map (dictionary) is a collection of data items each of which is a pair (key, value), and supports the following major operations: find(item): find
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Text Processing 1 COMP9024: Data Structures and Algorithms Text Processing 2 Contents • Pattern matching • Tries • Greedy method • Text compression • Dynamic programming 3 Pattern Matching 1 a b a c a a b 234 a b a c a b a b a c a b 4 Strings • A string
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External Sorting 23/3/20 1 Why Sort? § A classic problem in computer science! § Data requested in sorted order – e.g., find students in increasing gpa order § Sorting is first step in bulk loading B+ tree index. § Sorting useful for eliminating duplicate copies in a collection of records (Why?) § Sort-merge join algorithm
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Microsoft PowerPoint – wk8-1.ppt – Compatibility Mode 1 1 COMP9024: Data Structures and Algorithms Graphs (II) 2 Contents Depth-First Search Breadth-First Search Transitive Closure Topological Sorting 1 2 2 3 Properties Notation n number of vertices m number of edges deg(v) degree of vertex v Property 1 Sv deg(v) = 2m