Recursion

Base cases. You must always have some base cases, which can be solved without recursion. Making progress. Recursive call must always be to a case that makes progress towards some base case. Design rule. Assume that all the recursive calls works.
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Subprogram implementation Recursion Designing recursive algorithms Recursion removal Backtracking Examples of backtracking and recursive algorithms: Factorial Fibonacci The towers of Hanoi Eight Queens Problem Treestructured program: Lookahead in Game
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Minimal Recursion Semantics (MRS) is the standard formalism used in largescale HPSG grammars to model underspeciﬁed semantics. We present the ﬁrst provably efﬁcient algorithm to enumerate the readings of MRS structures, by translating them into normal dominance constraints.
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Reduce problem into smaller instances ofsame problem  recursive solution Recursive algorithm has two cases: Base/stopping case Recursive case, Ensure no infinite recursion. Use criteria to determine recursion correct
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Báo cáo khoa học: "Learning Arguments and Supertypes of Semantic Relations using Recursive Patterns"
A challenging problem in open information extraction and text mining is the learning of the selectional restrictions of semantic relations. We propose a minimally supervised bootstrapping algorithm that uses a single seed and a recursive lexicosyntactic pattern to learn the arguments and the supertypes of a diverse set of semantic relations from the Web. We evaluate the performance of our algorithm on multiple semantic relations expressed using “verb”, “noun”, and “verb prep” lexicosyntactic patterns. ...
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We consider the problem of parsing nonrecursive contextfree grammars, i.e., contextfree grammars that generate ﬁnite languages. In natural language processing, this problem arises in several areas of application, including natural language generation, speech recognition and machine translation. We present two tabular algorithms for parsing of nonrecursive contextfree grammars, and show that they perform well in practical settings, despite the fact that this problem is PSPACEcomplete.
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Efficient syntactic and semantic parsing for ambiguous contextfree languages are generally characterized as complex, specialized, highly formal algorithms. In fact, they are readily constructed from straightforward recursive Iransition networks (RTNs). In this paper, we introduce LRRTNs, and then computationally motivate a uniform progression from basic LR parsing, to Earley's (chart) parsing, concluding with Tomita's parser. These apparently disparate algorithms are unified into a single implementation, which was used to automatically generate all the figures in this paper. 1.
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A purely functional implementation of LRparsers is given, together with a simple correctness proof. It is presented as a generalization of the recursive descent parser. For nonLR grammars the timecomplexity of our parser is cubic if the functions that constitute the parser are implemented as memofunctions, i.e. functions that memorize the results of previous invocations. Memofunctions also facilitate a simple way to construct a very compact representation of the parse forest.
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Introduction to java programming: Chapter 19  Recursion's Objectives is to know what is a recursive method and the benefits of using recursive methods; to determine the base cases in a recursive method; understand how recursive method calls are handled in a call stack.
43p cocacola_17 09122015 13 0 Download

Phương pháp thiết kế một giải thuật đệ quy: Tham số hoá bài toán. Phân tích trường hợp chung : đưa bài toán dưới dạng bài toán cùng loại nhưng có phạm vi giải quyết nhỏ hơn theo nghiã dần dần sẽ tiến đến trường hợp suy biến. Tìm trường hợp suy biến.
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Tham khảo tài liệu 'bài 16recursion', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả
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Chapter 3 Dynamic Programming This chapter introduces basic ideas and methods of dynamic programming. 1 It sets out the basic elements of a recursive optimization problem, describes the functional equation (the Bellman equation), presents three methods for solving the Bellman equation
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Part III Competitive equilibria and applications Chapter 7 Recursive (Partial) Equilibrium 7.1. An equilibrium concept This chapter formulates competitive and oligopolistic equilibria in some dynamic settings. Up to now, we have studied singleagent problems where components of the state vector not under the control of the agent were taken as given.
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Chapter 12 Recursive competitive equilibria 12.1. Endogenous aggregate state variable For pure endowment stochastic economies, chapter 8 described two types of competitive equilibria, one in the style of Arrow and Debreu with markets that convene at time 0 and trade a complete set of historycontingent securities
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Part V Recursive contracts Chapter 18 Dynamic Stackelberg problems 18.1. History dependence Previous chapters described decision problems that are recursive in what we can call ‘natural’ state variables, i.e., state variables that describe stocks of capital, wealth, and information that helps forecast future values of prices and quantities
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If you want to learn how to program, working with Python is an excellent way to start. This handson guide takes you through the language one step at a time, beginning with basic programming concepts before moving on to functions, recursion, data structures, and objectoriented design. Through exercises in each chapter, you’ll try out programming concepts as you learn them. Think Python is ideal for students at the high school or college level, as well as selflearners, homeschooled students, and professionals who need to learn programming basics....
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Chapter 19 Insurance Versus Incentives 19.1. Insurance with recursive contracts This chapter studies a planner who designs an eﬃcient contract to supply insurance in the presence of incentive constraints imposed by his limited ability either to enforce contracts or to observe households’ actions or incomes.
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Chapter 21 Optimal Unemployment Insurance 21.1. Historydependent UI schemes This chapter applies the recursive contract machinery studied in chapters 19, 20, and 22 in contexts that are simple enough that we can go a long way toward computing the optimal contracts by hand.
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Chapter 23 Two topics in international trade 23.1. Two dynamic contracting problems This chapter studies two models in which recursive contracts are used to overcome incentive problems commonly thought to occur in international trade. The ﬁrst is Andrew Atkeson’s model of lending in the context of a dynamic setting
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