# chapter 1

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### chapter 1

• 1. Design and Analysis of Computer Algorithm Lecture 1 Ms P.Yatheesha.,Lecturer. . Department of Computer Science and Engineering PPG Institute of Technology
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• 18. What’s more important than performance? Design and Analysis of Computer Algorithm
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• 24. Example: What is an Algorithm? Design and Analysis of Computer Algorithm 25, 90, 53, 23, 11, 34 INPUT OUTPUT instance 11 Algorithm m:= a[1]; for I:=2 to size of input if m > a[I] then m:=a[I]; return s Data-Structure m Problem: Input is a sequence of integers stored in an array. Output the minimum.
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• 26. Example Algorithm A Design and Analysis of Computer Algorithm Problem: The input is a sequence of integers stored in array. Output the minimum. Algorithm A
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• 28. Visualize Algorithm B 8 9 5 6 11 34 7 20 6 5 8 7 5 7 5 Loop 1 Loop 2 Loop 3 Design and Analysis of Computer Algorithm
• 29. Example Algorithm C Sort the input in increasing order. Return the first element of the sorted data. Sorting black box Design and Analysis of Computer Algorithm 8 9 5 6 11 34 7 20 5 6 7 8 9 11 20 34
• 30. Example Algorithm D For each element, test whether it is the minimum. Design and Analysis of Computer Algorithm
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• 32. What do we need? Correctness: Whether the algorithm computes the correct solution for all instances Efficiency: Resources needed by the algorithm 1. Time: Number of steps. 2. Space: amount of memory used. Measurement “model”: Worst case, Average case and Best case. Design and Analysis of Computer Algorithm
• 33. Time vs. Size of Input Measurement parameterized by the size of the input. The algorihtms A,B,C are implemented and run in a PC. Algorithms D is implemented and run in a supercomputer. Let T k ( n ) be the amount of time taken by the Algorithm 1000 500 Input Size T b ( n ) T a ( n ) Design and Analysis of Computer Algorithm 4 0 2 T c ( n ) Running time (second) T d ( n )
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• 46. Running time for small inputs Design and Analysis of Computer Algorithm pp
• 47. Running time for moderate inputs Design and Analysis of Computer Algorithm
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• 60. Function of Growth rate Design and Analysis of Computer Algorithm
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