TAILIEUCHUNG - Lecture Analytic combinatorics (Part 1) - Chapter 6: Trees

Chapter 6: Trees investigates properties of many different types of trees, fundamental structures that arise implicitly and explicitly in many practical algorithms. Our goal is to provide access to results from an extensive literature on the combinatorial analysis of trees, while at the same time providing the groundwork for a host of algorithmic applications. | ANALYTIC COMBINATORICS PART ONE http 6. Trees Review First half of class Introduced analysis of algoritihms. Surveyed basic mathematics needed for scientific studies. Introduced analytic combinatorics. AN INTRODUCTION TO THE Analysis Algorithms SECOND EDITION ROBERT SED GEWICK PHILIPPE FLAJOLET 1 2 3 4 5 Analysis of Algorithms Recurrences Generating Functions Asymptotics Analytic Combinatorics Note Many applications beyond analysis of algorithms. 2 Orientation Second half of class Surveys fundamental combinatorial classes. Considers techniques from analytic combinatorics to study them . Includes applications to the analysis of algorithms. AN INTRODUCTION TO THE Analysis Algorithms SECOND EDITION ROBERT SED GEWICK PHILIPPE FLAJOLET chapter combinatorial classes type of class type of GF 6 Trees unlabeled OGFs 7 Permutations labeled EGFs 8 Strings and Tries unlabeled OGFs 9 Words and Mappings labeled EGFs Note Many more examples in book than in lectures.

• Kỹ thuật lập trình
• Analytic combinatorics
• Lecture Analytic combinatorics
• Combinatorial structures
• Binary trees
• Combinatorial equivalences
• Properties of trees
• Unlabelled classes
• Labelled classes
• Symbolic method for parameters
• Compare algorithms
• Analysis of algorithms
• Scientific approach
• Computing values
• Types of recurrences
• Master theorem
• Ordinary generating functions
• Exponential generating functions
• Generating functions
• Asymptotic approximation
• Asymptotic expansions
• Manipulating asymptotic expansions
• Algorithms on permutations
• Representations of permutations
• Situ permutation
• String searching
• Combinatorial properties of bitstrings
• Trie algorithms
• Hashing with separate chaining
• Birthday paradox
• Integer factorization
• Symbolic method
• Combinatorial class
• Labelled structures
• Labelled trees
• Combinatorial parameters
• Moment calculations
• Complex analysis
• Meromorphic asymptotics
• Complex functions
• Supercritical sequence schema
• Singularity analysis
• Standard function scale
• Transfer theorems
• Applications of singularity analysis
• Simple varieties of trees
• Saddle point asymptotics
• Modulus surfaces
• Saddle point bounds
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