Algorithms and Data Structures Winter TermExercises for Unit 5 1. Use the Akkra-Bazi Theorem to derive closed form expressions for the following recursively defined functions:

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Algorithms and Data Structures Winter TermExercises for Units 29 & 30 1. Let G = (V, E) be an undirected graph with vertices V = {v1 , . . . , vn }. Give an efficient algorithm that, given a sequence of non-nega

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Algorithms and Data Structures Winter TermExercises for UnitLet U = {0, 1, . . . , K − 1}, let p ≥ K be a prime number, and let 0 < t < K. For 0 ≤ a, b < p define

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• Information retrieval
• Search algorithms
• Information science
• Hashing
• Cryptographic hash functions
• Error detection and correction
• Hash function
• Hash table
• Universal hashing
• Locality-sensitive hashing

Algorithms and Data Structures (WS15/16) Example Solutions for Unit 4 Problem 1 skipped

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• Mathematics
• Mathematical analysis
• Mathematical induction
• Integer sequences
• Approximation theory
• Mathematical series
• Binomial coefficient
• Aurifeuillean factorization

Algorithms and Data Structures (WS15/16) Example Solutions for UnitQuestion 2 In this problem, we will not distinguish the key xi and the node which store xi . Let Xij be an indicator random variable where Xij = 1

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Adoption of Ind AS (effective April 1, 2016) 1. Background The Ministry of Corporate Affairs (MCA) has issued a notification dated 16th February 2015, announcing the Companies (Indian Accounting Standards) Rules, 2015 f

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• Economy
• Business economics
• Accounting
• Financial accounting
• Accounting systems
• Mergers and acquisitions
• Taxation
• International Financial Reporting Standards
• Financial statement
• Balance sheet
• Convergence of accounting standards
• Provision

Algorithms and Data Structures Winter TermExercises for Units 1 and 2 1. This sequence of exercises is supposed to illustrate that certain restrictions that we put on our RAM model are really necessary. If they

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• Mathematics
• Logarithms
• Multiplicative functions
• Analysis of algorithms
• Asymptotic analysis
• Big O notation
• Mathematical notation
• Prime number
• Greatest common divisor
• Prime number theorem
• Average order of an arithmetic function

to appear in TCS – www.wischik.com/lu/research/explicit-fusions.html Explicit Fusions Lucian Wischik1 and Philippa Gardner2 1 2

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• Theoretical computer science
• Mathematical logic
• Logic
• Formal methods
• Logic in computer science
• Process calculi
• -calculus
• Automated theorem proving
• Process calculus
• Lambda calculus
• Bisimulation
• Limit of a function

Algorithms and Data Structures Winter TermExercises for Units 37 & 38 1. For stable matching with incomplete lists, each man x ∈ X has a strict list x over a subset of the women Y, i.e., x is possibly incomp

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• Mathematics
• Graph theory
• Matching
• Discrete mathematics
• Combinatorics
• Cooperative games
• Game theory
• Combinatorial optimization
• Stable marriage problem
• Stable roommates problem
• 3-dimensional matching

Algorithms and Data Structures Winter TermExercises for Units 25 & 26 1. Suppose you are given a directed graph G = (V, E), two vertices s and t, a capacity function c : E → R+ , and another function f : E →

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• Graph theory
• Mathematics
• Network flow
• Graph connectivity
• Combinatorial optimization
• Maximum flow problem
• Cut
• Flow network
• Max-flow min-cut theorem
• Minimum-cost flow problem