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Homework # 1~4(5) Review

Homework # 1~4(5) Review. Grading. 10 points for each homework. Exercise 5.1. Recurrence equation Master theorem Substitution method Lower bound for kd -tree query time :. Exercise 5.1. An example for the lower bound. Query range. Exercise 5.3. Kd-tree in d-dimensional space.

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Fibonacci Heaps

Fibonacci Heaps. Lecture slides adapted from: Chapter 20 of Introduction to Algorithms by Cormen , Leiserson , Rivest , and Stein. Chapter 9 of The Design and Analysis of Algorithms by Dexter Koze. Fibonacci Heaps. History. [Fredman and Tarjan, 1986]

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Chapter 6 Heapsort

Chapter 6 Heapsort. About this lecture. Introduce Heap Shape Property and Heap Property Heap Operations Heapsort : Use Heap to Sort Fixing heap property for all nodes Use Array to represent Heap Introduce Priority Queue. Heap.

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Fibonacci Heap

Fibonacci Heap. BH&FH. Why BH&FH -- ????. MaxPQ. MinPQ. Symmetric Max Data Structures. Min Heap. DEPQ. Deap. MinMax. Mergeable MinPQ. Min-Leftist. Min-Skew. Min-B-Heap. Min-F-Heap. Inheritance. ADT. ????. Why BH&FH -- ??. Server for one priority shuts down ?

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2IL05 Data Structures

2IL05 Data Structures. Fall 2007 Lecture 13: Minimum Spanning Trees. Motivation. What is the cheapest network that connects a group of computers?. 1. 1. 2. 1. 1. 1. 3. 3. 0.5. 0.5. 12. 2. 3. 2. 3. 1. 1. 1. 1. 11. Minimum spanning graph.

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Shortest Path Algorithms

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CS38 Introduction to Algorithms

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Single-Source Shortest Paths (25/24)

Single-Source Shortest Paths (25/24). HW: 25-2 and 25-3 p. 546/24-2 and 24-3 p.615 Given a graph G=(V,E) and w: E ? ? weight of <v[1],...,v[k]> is w(p) = ? w(v[i],v[i+1]) Single-source shortest-paths: find a shortest path from a source s to every vertex v ?V

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Greedy Algorithms

Greedy Algorithms. Greedy Algorithm Design. Comparison:. Dynamic Programming. Greedy Algorithms. At each step, the choice is determined based on solutions of subproblems. At each step, we quickly make a choice that currently looks best. --A local optimal (greedy) choice.

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