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(Each chapter ends with a “Summary”.)
Preface.
1. Introduction.
The notion of algorithm.
Fundamentals of algorithmic problem solving.
Important problem types.
Fundamental data structures.
2. Fundamentals of the Analysis of Algorithm Efficiency.
Analysis framework.
Asymptotic notations and standard efficiency classes.
Mathematical analysis of nonrecursive algorithms.
Mathematical analysis of recursive algorithms.
Example: Fibonacci numbers.
Empirical analysis of algorithms.
Algorithm visualization.
3. Brute Force.
Selection sort and bubble sort.
Sequential search and brute-force string matching.
The closest-pair and convex-hull problems by brute force.
Exhaustive search.
4. Divide-and-Conquer.
Mergesort.
Quicksort.
Binary search.
Binary tree traversals and related properties.
Multiplication of large integers and Strassen's matrix multiplication.
Closest-pair and convex-hull problems by divide-and-conquer.
5. Decrease-and-Conquer.
Insertion sort.
Depth-first search and breadth-first search.
Topological sorting.
Algorithms for generating combinatorial objects.
Decrease-by-a-constant-factor algorithms.
Variable-size-decrease algorithms.
6. Transform-and-conquer.
Presorting.
Gaussian elimination.
Balanced search trees.
Heaps and heapsort.
Horner's rule and binaryexponentiation.
Problem reduction.
7. Space and Time Tradeoffs.
Sorting by counting.
Horspool's and Boyer-Moore algorithms for string matching.
Hashing.
B-trees.
8. Dynamic Programming.
Computing a binomial coefficient.
Shortest-path problems.
Warshall's and Floyd's algorithms.
Optimal binary search trees.
The knapsack problem and memory functions.
9. Greedy Technique.
Prim's algorithm.
Kruskal's algorithm.
Dijkstra's algorithm.
Huffman trees.
10. Limitations of Algorithm Power.
Lower-bound arguments.
Decision trees.
P, NP, and NP-complete problems.
Challenges of numerical algorithms.
11. Coping with the Limitations of Algorithm Power.
Backtracking.
Branch-and-bound.
Approximation algorithms for NP-hard problems.
Algorithms for solving nonlinear equations.
Epilogue.
Appendix A: Useful Formulas for the Analysis of Algorithms.
Appendix B: Short Tutorial on Recurrence Relations.
Bibliography.
Hints to Exercises.
Index.
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Greg Bensman
reviewed Introduction to the Design and Analysis of Algorithms on June 07, 2017
Introduction to the Design and Analysis of Algorithms
Pretty good introduction to algorithms. The writing style wasn't overly dry or boring. The explanations usually made sense, but occasionally felt lack in details. Some of the problem questions were quite difficult and sometimes seemed unrelated to the on page instruction material. The solutions manual helped me understand most of the difficult problems, but some were still ambiguous. This is a good textbook for use with a class, but perhaps not so great for self-learning unless you can find a community to further explain concepts and problems.
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