## Design and Analysis of Algorithms"All aspects pertaining to algorithm design and algorithm analysis have been discussed over the chapters in this book-- Design and Analysis of Algorithms"--Resource description page. |

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### Contents

Algorithm Design | 3 |

Introduction | 4 |

Algorithm Analysis 368 | 12 |

Problem Solving with a Computer | 16 |

Predicates | 17 |

A 3 | 26 |

Problem Solving with a Computer | 29 |

TopDown Design | 46 |

Efficiency of Algorithms | 370 |

Efficiency of Algorithms | 373 |

Examples of Complexity Calculation | 404 |

TimeSpace TradeOff | 424 |

Tractable and NonTractable Problems | 462 |

Some NP and NPComplete Problems | 504 |

Randomized and Approximate Algorithms | 524 |

A 6 | 536 |

Iterative Algorithm Design Issues | 64 |

Computation Models and Design by Refinement | 88 |

Proof RulesBasics | 120 |

Proof RulesBasics 120 Proof RulesBasics | 123 |

Design by Proof Rules | 152 |

Design using Recursion | 180 |

Design using Recursion 180 | 197 |

Abstract Algorithms1 DivideandConquer | 200 |

Abstract Algorithms 2Greedy Methods | 236 |

Abstract Algorithms 3Dynamic Programming | 268 |

Abstract Algorithms 4Backtracking | 310 |

A 4 | 313 |

A 5 | 323 |

Natural AlgorithmsGA SA ANN TS | 340 |

Formal Specifications1 Model Oriented | 558 |

Formal | 559 |

Formal Specifications2 Algebraic | 588 |

Appendix A Essential Mathematical Background | 611 |

A 7 | 633 |

Appendix B Some Useful Mathematical Formulae | 642 |

Overview of Essential Data Structures | 667 |

Solutions of Recurrence Relations | 701 |

A 8 | 708 |

Appendix E Additional Exercises with Solutions | 720 |

A 9 | 728 |

794 | |

803 | |

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### Common terms and phrases

a[mid analysis array assume backtracking binary heap called complexity condition consider control construct cost data structure defined denote discussed dynamic programming edges efficiency elements example execution expression Fibonacci Fibonacci heap given graph greedy heap implementation input integer Key Terms Kruskal's algorithm loop invariant matrix mergesort method minimum minimum spanning tree multiplications NIL NIL NIL node notation Note NP-Complete NP-hard operations optimal solution optimal substructure output parameters partition permutation polynomial possible post-condition pre-condition prime numbers problem procedure program segment programming language proof rule prove Quicksort random numbers randomized algorithm recursive algorithm recursive function result satisfied sequence shortest path solve sorted space spanning tree specification square root statement steps strategy structured programming sub-problems termination Terms in Chapter tour traveling salesman problem true variables vertex vertices