01-Analysis-of-Algorithms

01-Analysis-of-Algorithms - Algorithms LECTURE 1 Analysis...

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Algorithms Professor Ashok Subramanian L ECTURE 1 Analysis of Algorithms Insertion sort Asymptotic analysis Merge sort Recurrences
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Algorithms L1.2 Analysis of algorithms The theoretical study of computer- program performance and resource usage. What’s more important than performance? modularity correctness maintainability functionality robustness user-friendliness programmer time simplicity extensibility reliability
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Algorithms L1.3 Why study algorithms and performance? Algorithms help us to understand scalability . Performance often draws the line between what is feasible and what is impossible. Algorithmic mathematics provides a language for talking about program behavior. Performance is the currency of computing. The lessons of program performance generalize to other computing resources. Speed is fun!
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Algorithms L1.4 The problem of sorting Input: sequence a , a , …, a of numbers. Example: Input: 8 2 4 9 3 6 Output: 2 3 4 6 8 9 Output: permutation a' , a' , , a' such
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Algorithms L1.5 Insertion sort I NSERTION -S ORT ( A , n ) A [1 . . n ] for j ← 2 to n do key ← A [ j ] i ← j – 1 while i > 0 and A [ i ] > key do A [ i+ 1] ← A [ i ] i ← i – 1 A [ i+ 1] = key “pseudocode”
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Algorithms L1.6 Insertion sort I NSERTION -S ORT ( A , n ) A [1 . . n ] for j ← 2 to n do key ← A [ j ] i ← j – 1 while i > 0 and A [ i ] > key do A [ i+ 1] ← A [ i ] i ← i – 1 A [ i+ 1] = key “pseudocode” sorted i j key A : 1 n
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Algorithms L1.7 Example of insertion sort 8 2 4 9 3 6
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Algorithms L1.8 Example of insertion sort 8 2 4 9 3 6
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Algorithms L1.9 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6
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Algorithms L1.10 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6
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Algorithms L1.11 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6
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Algorithms L1.12 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6
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Algorithms L1.13 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6 2 4 8 9 3 6
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Algorithms L1.14 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6 2 4 8 9 3 6
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Algorithms L1.15 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6 2 4 8 9 3 6 2 3 4 8 9 6
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Algorithms L1.16 Example of insertion sort 8 2 4 9 3 6 2 8 4 9 3 6 2 4 8 9 3 6 2 4 8 9 3 6 2 3 4 8 9 6
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This note was uploaded on 04/29/2011 for the course IT 201 taught by Professor K.v.arya during the Spring '11 term at IIT Kanpur.

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01-Analysis-of-Algorithms - Algorithms LECTURE 1 Analysis...

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