Introduction Topical Formulations Intranasal Formulations Summary and Questions.
INTRODUCTION TO RECURSIVE FORMULATIONS FOR …
Transcript of INTRODUCTION TO RECURSIVE FORMULATIONS FOR …
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INTRODUCTION TO RECURSIVEFORMULATIONS FOR ALGORITHM DESIGN: IV
Partha P ChakrabartiIndian Institute of Technology Kharagpur
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Algorithm Design by Recursion Transformation1. Initial Solution
a. Recursive Definition – A set of Solutionsb. Inductive Proof of Correctnessc. Analysis Using Recurrence Relations
2. Exploration of Possibilitiesa. Decomposition or Unfolding of the Recursion Treeb. Examination of Structures formedc. Re-composition Properties
3. Choice of Solution & Complexity Analysisa. Balancing the Split, Choosing Pathsb. Identical Sub-problems
4. Data Structures & Complexity Analysisa. Remembering Past Computation for Futureb. Space Complexity
5. Final Algorithm & Complexity Analysisa. Traversal of the Recursion Treeb. Pruning
6. Implementationa. Available Memory, Time, Quality of Solution, etc
Algorithms and Programs Pseudo-Code Algorithms + Data Structures = Programs Initial Solutions + Analysis + Solution
Refinement + Data Structures = FinalAlgorithm
Use of Recursive Definitions as InitialSolutions
Recurrence Equations for Proofs andAnalysis
Solution Refinement through RecursionTransformation and Traversal
Data Structures for saving pastcomputation for future use
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Coin Selection Problem
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First Recursive Definition
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Example
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Improved Recursive Definition
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Alternative Recursive Definition
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Example
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Traversal and Potential Pruning
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Finalizing the Algorithm
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Special Case
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Summary
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Overview of Algorithm Design 1. Initial Solution
a. Recursive Definition – A set of Solutionsb. Inductive Proof of Correctnessc. Analysis Using Recurrence Relations
2. Exploration of Possibilitiesa. Decomposition or Unfolding of the Recursion Treeb. Examination of Structures formedc. Re-composition Properties
3. Choice of Solution & Complexity Analysisa. Balancing the Split, Choosing Pathsb. Identical Sub-problems
4. Data Structures & Complexity Analysisa. Remembering Past Computation for Futureb. Space Complexity
5. Final Algorithm & Complexity Analysisa. Traversal of the Recursion Treeb. Pruning
6. Implementationa. Available Memory, Time, Quality of Solution, etc
1. Core Methodsa. Divide and Conquerb. Greedy Algorithmsc. Dynamic Programmingd. Branch-and-Bounde. Analysis using Recurrencesf. Advanced Data Structuring
2. Important Problems to be addresseda. Sorting and Searchingb. Strings and Patternsc. Trees and Graphsd. Combinatorial Optimization
3. Complexity & Advanced Topicsa. Time and Space Complexityb. Lower Boundsc. Polynomial Time, NP-Hardd. Parallelizability, Randomization
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Thank you
Any Questions?