Practice Recursive Expression And Solution (8.6.3) - Design and Analysis of Algorithms

Practice: Recursive Expression and Solution

Lesson 8.6.3Design and Analysis of Algorithms

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8 questions

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3 cards from this section. Quick, good the night before a test.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the time complexity for finding the maximum element in an array of size n?
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Think about the number of comparisons you must make.
Question 2.
What does the Towers of Hanoi question require you to do in essence?
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Consider the rules around disk size.
3Question 3.
What is the time complexity of a simple loop iterating through an array of size n?
- O(n)
- O(n²)
- O(1)
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Think about how you check each element.
4Question 4.
True or False: The Towers of Hanoi requires exponentially increasing moves for additional disks.
- True
- False
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Recall the recursive definition of moves.
Question 5.
Propose an original recursive problem where the solution resembles the Towers of Hanoi and discuss its potential time complexity.
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Think about the layering involved in organizing the balls.
Question 6.
Analyze the following pseudocode that implements a nested looping structure and determine its time complexity: for i from 1 to n, for j from i to n { operation } What is the time complexity?
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Draw out the iterations to better understand how often the inner loop executes.

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