EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Chapter 2, Problem 10E
Program Plan Intro
Computational complexity:
- The resource used by an
algorithm is known as its complexity. - The resources required for solving computational problems or for executing an algorithm.
- Time complexity denotes the complexity expressed in terms of execution time.
- Space complexity denotes the complexity expressed in terms of memory needed for computation.
- Complexity of operations that is mathematical.
Explanation of Solution
(b) The auto increment “cnt2++” is executed exactly “n2” times
- The external for loop is executing “n” times
- The internal for loop is executin...
Explanation of Solution
(c) The auto increment “cnt3++” is executed exactly “nlogn” times
- The external for loop is executing “logn” times
- The internal for loop is executing “n” times
Explanation of Solution
(d) The auto increment “cnt4++” is executed exactly “n” times
- The external for loop is executing “logn” times
- The internal for loop is executing “2n” times
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Design a Turing machine to compute the x mod y, y>0 function. On entry, the number is represented as a unary number using |. This way, 5 will turn to |||||. When two numbers are inputted, they are placed as unary numbers separated by #. The answer must contain states, with clear instructions on what to do when finding a symbol, namely what state to go to, where to go (Stay, Left, Right) and what symbol to put in a cell.
E.g.:
q0
If found _, put _, go to q1 and Stay.
If found |, put |, go to q0 and Left.
q1
If found _, put _, go to q1 and Right
If found |, put X, go to q2 and Right.
Etc…
Feel free to use as many auxiliary symbols as you need. In the end, the program needs to output n '|' symbols without spaces('_') or anything, where n is the result of x mod y.
So, the result for input 10 and 7 and output for it would look like this:
We input numbers in the machine, and they appear on the Turing machine line like this, every symbol in its cell:
Input: ||||||||||#|||||||
Once…
Which assertion is false? CPU cycles are needed for time's complexity. Less memory is needed for space's complexity. Time complexity is measured by operations. An algorithm's worst-case scenario is the most operations.
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Chapter 2 Solutions
EBK DATA STRUCTURES AND ALGORITHMS IN C
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