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bosc p algorithm design 150 problems detailed solutions 2023

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Textbook in PDF format A best-seller in its French edition, the construction of this book is original and its success in the French market demonstrates its appeal. It is based on three principles: 1. An organization of the chapters by families of algorithms : exhaustive search, divide and conquer, etc. At the contrary, there is no chapter only devoted to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. 2. For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. 3. For its most part, the book details 150 problems, spanning on seven families of algorithms. For each problem, a precise and progressive statement is given. More important, a complete solution is detailed, with respect to the design principles that have been presented ; often, some classical errors are pointed at. Roughly speaking, two thirds of the book are devoted to the detailed rational construction of the solutions. Preface Mathematics and computer science: some useful notions Reasoning and proving Propositional and predicate calculus Proof by contradiction Proof by induction with one index Proof by simple induction Proof by partial induction Proof by strong induction Partition induction Foundation of the proof by induction Proof by induction with several indexes Recurrence relations Generalities, examples and closed forms Establishing and computing a recurrence relation Principles Some examples Designing the algorithm associated with a recurrence Recurrence, induction, recursion, etc Sets Basic notations Definition of sets Operations on sets Special sets Relations, functions and arrays Relations Functions Arrays Bags Cartesian product and inductive structures Strings and sequences Graphs Directed graphs Undirected graphs Weighted graphs Trees Priority queues Definition Implementations FIFO and LIFO queues Problems Solutions Complexity of an algorithm Reminders Algorithm Algorithmics, complexity of an algorithm Minimum and maximum complexity of an algorithm Orders of growth Some examples of complexity About elementary operations Practical computing time Pseudo-polynomial problems Problems Solutions Specification, invariants, and iteration Principle for the construction of loops by invariant An introductory example: the Euclidian division Useful techniques Sequential composition Predicate strengthening and weakening Strengthening by the introduction of programming variables Heuristics for the discovery of invariants Breakup of the postcondition Hypothesis of the work carried out partly Strengthening the invariant About bounded linear search An example Special case and related pattern Some key points to develop a loop Problems Solutions Reduce and conquer, recursion A few reminders about recursion Recurrence relation and recursion “Reduce and conquer” and its complexity Presentation Example : the spiral pattern Example : Hanoi towers What should be reminded for “Reduce and conquer” Problems Solutions Generate and test Fundamentals Principle Functions and related frames Total functions The case of partial functions Patterns for “Generate and test” Patterns derived from “AllSolutions” Patterns derived from “OptimalSolution” Patterns derived from “OneSolution” Conclusion An example: the optimal partition of an array The basic problem The initial problem with a strengthened precondition and a strengthened postcondition The initial problem with a strengthened precondition What should be remembered from “Generate and test” Exercises Solutions Branch and bound Introduction Branch and bound: the principle The separation phase The selection phase The evaluation phase The generic “Branch and bound” algorithm The priority queue Construction of the generic “Branch and bound” algorithm The generic “Branch and bound” algorithm itself An interesting special case for the functions f∗ and f An example: the traveling salesman Initial choices The algorithm First case study: the zero heuristic function Second case study: uniform cost What should be remembered about the “Branch and bound” approach Problems Solutions Greedy algorithms Introduction Presentation Proving that a greedy algorithm is exact or optimal An example: task scheduling on a photocopier The “lead run” method Proof a posteriori: the transformation technique What to remember about greedy methods Problems Solutions Divide and conquer Introduction Presentation and principle An example: merge-sort General pattern for “Divide and conquer” A typology of “Divide and conquer” algorithms Complexity of “Divide and conquer” Introduction to the master theorem Other types of recurrence equations About the size of the problem What to remember about the DaC approach Problems Solutions Dynamic programming Overview An example: the longest sub-sequence common to two sequences What should be remembered to apply dynamic programming Problems Cutting and sharing: one-dimensional problems Cutting and sharing: two-dimensional problems Graphs and trees Sequences Definitions The problem Images Games Pseudo-polynomial problems Solutions Notations List of problems Bibliography Index

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bosc p algorithm design 150 problems detailed solutions 2023