## Analysis And Design Of AlgorithmsWhat is an algorithm ? Fundamentals of algorithmic problem solving, Important problem types, Fundamental data structures.Fundamentals of the Analysis of Algorithm Efficiency : Analysis framework.Asymptotic notations and basic efficiency classes, Mathematical analysis of nonrecursive and recursive algorithms, Example - Fibonacci numbers.Brute Force : Selection sort and bubble sort, Sequential search and brute-force string matching, Exhaustive search.Divide and Conquer : Mergesort, Quicksorst, Binary search. Binary tree traversals and related properties, Multiplication of large integers and Stressen's matrix multiplication.Decrease and Conquer : Insertion sort, Depth first search, Breadth first search, Topological sorting.Algorithms for generating combinatorial objects.Transform and Conquer : Presorting, Balanced search trees, Heaps and heapsort, Problem reduction.Space and Time Tradeoffs : Sorting by counting, Input enhancement in string matching, Hashing.Dynamic Programming : Computing a binomial coefficient, Warshall's and Floyd's algorithms, The Knapsack problem and memory functions.Greedy Technique : Prim's algorithm, Kruskal's algorithm, Dujkstra's algorithm, Huffman trees.Limitations of Algorithm Power : Lower-bound arguments, Decision trees., P, NP and NP-complete problems.Coping with the Limitations of Algorithm Power : Backtracking, Branch-and-bound, Approximation algorithms for NP-hard problems. |

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### Contents

Table of Contents | 1-1 |

pter3 Mathematical Aspects and Analysis of Algorithms 3 1 to 3 | 1-3 |

Chapter3 Mathematical Aspects and Analysis of Algorithms 31 to 3 48 | 4-3 |

36 | 4-36 |

Chapter6 Decrease and Conquer 6110668 | 6-1 |

Summary 666 | 6-66 |

Chapter7 Transform and Conquer 71 to 7 86 | 7-86 |

Chapter8 Space and Time Tradeoffs 81 to 8 46 | 8-8 |

Summary 967 | 9-67 |

Chapter11 Limitations of Algorithm Power 11 1 to 11 20 | 11-3 |

Chapter9 Dynamic Programming 91 to 9 68 | 11-9 |

viii | 11-54 |

Summary 210 | 22 |

Coping with the Limitations of Algorithm Power 121 to 12 80 | P-1 |

### Common terms and phrases

adjacency matrix Algorithm Power Analysis and Design Analysis of Algorithms AVL tree basic operation binary search tree binary tree Breadth First Search Brute force bubble sort clrscr complexity compute Consider cost decrease and conquer deletion Design of Algorithms disk divide and conquer dynamic programming edge efficiency Enter The Element equation example executed Fibonacci number function getch given graph hash heap Hence implementation inorder input insertion sort integer knapsack problem left sublist linked list loop lower bound Master theorem merge sort minimum multiplication NULL obtained optimal Output pattern permutations pivot printf printf("\n Enter priority queue Problem Description queue quick sort right sublist scanf selection sort shortest path solution solved sorted list sorting algorithm sorting method space tree spanning tree stack Step subset subtree swap temp topological sorting total number traversal vertex vertices vl vl & v2 void main worst