By Manoochehr Azmoodeh (auth.)
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Extra info for Abstract Data Types and Algorithms
Write bad and good programs to evaluate polynomials. For instance, evaluate 2x + 4x 2 + 5x 3 + 13x4 at x =5. Design the necessary data structures and write the programs. Compare their time complexities. 9. 10. 9 by not evaluating xk more than once (for a given k). 11. 10. 12. Write a program to compute e n2 n3 n4 n10 e(n) =n +- +- +- + ... + 2! 3! 4! 10! What is the time complexity of your solution? 13. _ n logn 3 10 log 3n The Complexity of Algorithms 23 (f(n) + 10? 14. Which of the following are valid?
13, 14. So for small n, it may be best to use an exponential algorithm. Also, if an algorithm is to be executed only a few times, the efforts to find an efficient algorithm may not be justified and hence a slower algorithm may be preferred. Finally, it should be borne in mind that asymptotic complexities are only a gross measure of cost and for more exact comparisons the coefficients and constants in the complexity formulae should be found. For instance, although 1000n log nand 1/10n log n are both O(n log n), the latter is far superior to the former one.
To reverse the elements of a sequence. ' character and print the sequence in reverse order. The 'Last In First Out' property of stacks makes them suitable for this problem. As the characters are being read, they are added to a stack. When the delimiter is reached the stack is emptied by 'removing' elements one by one. 5 shows how this process works. 5 Operation of the 'reverse' program. Abstract Data Types and Program Design 35 should be a stack of characters. Thus, the elemtype as used in the definition of stack should be 'char' A Pascal program which uses an ADT stack to reverse a sequence of characters is then listed.