دانلود کتاب An introduction to the analysis of algorithms

Machine generated contents note: ch. One Analysis of Algorithms --1.1. Why Analyze an Algorithm? --1.2. Theory of Algorithms --1.3. Analysis of Algorithms --1.4. Average-Case Analysis --1.5. Example: Analysis of Quicksort --1.6. Asymptotic Approximations --1.7. Distributions --1.8. Randomized Algorithms --ch. Two Recurrence Relations --2.1. Basic Properties --2.2. First-Order Recurrences --2.3. Nonlinear First-Order Recurrences --2.4. Higher-Order Recurrences --2.5. Methods for Solving Recurrences --2.6. Binary Divide-and-Conquer Recurrences and Binary Numbers --2.7. General Divide-and-Conquer Recurrences --ch. Three Generating Functions --3.1. Ordinary Generating Functions --3.2. Exponential Generating Functions --3.3. Generating Function Solution of Recurrences --3.4. Expanding Generating Functions --3.5. Transformations with Generating Functions --3.6. Functional Equations on Generating Functions --3.7. Solving the Quicksort Median-of-Three Recurrence with OGFs --3.8. Counting with Generating Functions --3.9. Probability Generating Functions --3.10. Bivariate Generating Functions --3.11. Special Functions --ch. Four Asymptotic Approximations --4.1. Notation for Asymptotic Approximations --4.2. Asymptotic Expansions --4.3. Manipulating Asymptotic Expansions --4.4. Asymptotic Approximations of Finite Sums --4.5. Euler-Maclaurin Summation --4.6. Bivariate Asymptotics --4.7. Laplace Method --4.8."Normal" Examples from the Analysis of Algorithms --4.9."Poisson" Examples from the Analysis of Algorithms --ch. Five Analytic Combinatorics --5.1. Formal Basis --5.2. Symbolic Method for Unlabelled Classes --5.3. Symbolic Method for Labelled Classes --5.4. Symbolic Method for Parameters --5.5. Generating Function Coefficient Asymptotics --ch. Six Trees --6.1. Binary Trees --6.2. Forests and Trees --6.3.Combinatorial Equivalences to Trees and Binary Trees --6.4. Properties of Trees --6.5. Examples of Tree Algorithms --6.6. Binary Search Trees --6.7. Average Path Length in Catalan Trees --6.8. Path Length in Binary Search Trees --6.9. Additive Parameters of Random Trees --6.10. Height --6.11. Summary of Average-Case Results on Properties of Trees --6.12. Lagrange Inversion --6.13. Rooted Unordered Trees --6.14. Labelled Trees --6.15. Other Types of Trees --ch. Seven Permutations --7.1. Basic Properties of Permutations --7.2. Algorithms on Permutations --7.3. Representations of Permutations --7.4. Enumeration Problems --7.5. Analyzing Properties of Permutations with CGFs --7.6. Inversions and Insertion Sorts --7.7. Left-to-Right Minima and Selection Sort --7.8. Cycles and In Situ Permutation --7.9. Extremal Parameters --ch. Eight Strings and Tries --8.1. String Searching --8.2.Combinatorial Properties of Bitstrings --8.3. Regular Expressions --8.4. Finite-State Automata and the Knuth-Morris-Pratt Algorithm --8.5. Context-Free Grammars --8.6. Tries --8.7. Trie Algorithms --8.8.Combinatorial Properties of Tries --8.9. Larger Alphabets --ch. Nine Words and Mappings --9.1. Hashing with Separate Chaining --9.2. The Balls-and-Urns Model and Properties of Words --9.3. Birthday Paradox and Coupon Collector Problem --9.4. Occupancy Restrictions and Extremal Parameters --9.5. Occupancy Distributions --9.6. Open Addressing Hashing --9.7. Mappings --9.8. Integer Factorization and Mappings.