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Design and analysis of algorithms: Introduction

Design and analysis of algorithms: Introduction. DESIGN and ANALYSIS of ALGORITHMS. ALGORITHMS. al- Khwārizmī : Persian mathematician, astronomer

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Design and analysis of algorithms: Introduction

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  1. Design and analysis of algorithms: Introduction

  2. DESIGN and ANALYSIS of ALGORITHMS

  3. ALGORITHMS • al-Khwārizmī : Persian mathematician, astronomer • “On the calculation with Hindu numerals”; 825 AD decimal positional number system ZERO (500 AD)

  4. ALGORITHMS • algorithm  recipe • an effective method expressed as a finite list of well-defined instructions for calculating a function • Formally, algorithms are Turing machines • BISI BELE BATH • • Take rice and dal, wash and soak for 10 min. • • Soak tamarind in water; extract juice• Cook the dal till it is half done• Roast the spices. Mix them with coconut; add turmeric powder,.• Grind mixture into a thick paste using a little bit of water. • • Heat oil in pan. Burst mustard seeds and add curry leaves.• Add onions and stir fry till soft.• Add tamarind juice and 2 cups of water to the onions and bring to boil.• Add rice, vegetables, tomatoes, half-cooked dal, spice mixture and salt. Cook on a low flame till done.• Garnish with coriander leaves. Source: Wikipedia

  5. ALGORITHMS In this course: • Instructions are basic instructions a computer can do. • However, we will be independent of programming languages/architectures/machines. • Imperative programming. Design & Analysis Programming Algorithm Computational problem tosolve Program

  6. DESIGN PARADIGMS Design paradigm: An underlying design principle that forms the basis of many algorithms. Example: Towers of Hanoi / Brahma cone Design principle: Recursion / divide-and-conquer When subproblems merge: dynamic programming

  7. DESIGN PARADIGMS • Brute force • Divide and conquer • Dynamic programming • Greedy method • Decrease and conquer • Transform and conquer (aka reductions)

  8. TYPES OF PROBLEMS • SORTING • SEARCHING • STRING PROCESSING • GRAPH PROBLEMS • COMBINATORIAL PROBLEMS • GEOMETRIC PROBLEMS • NUMERICAL PROBLEMS

  9. ALGORITHMS AND SOFT. ENGG. SYSTEM WEB SEARCH: google/bing key algorithms: indexing for fast search; ranking. THIS MEC SYSTEM: video key algorithms: mp4 compression

  10. ALGORITHM DESIGN AND ANALYSIS  CORE OF COMPUTATIONAL THINKING Useful for your entire career as a computer engineer.

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