Practice Analysis Of Time Complexity (12.10) - Divide and Conquer: Counting Inversions

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6 sample questions

Question 1.
Define the divide and conquer strategy in one sentence.
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Think about how to tackle a large task.
Question 2.
What is an inversion in the context of rankings?
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Consider how preferences can differ between two people.
3Question 3.
What is the time complexity of the brute force method for counting inversions?
- O(n)
- O(n log n)
- O(n²)
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Consider how many comparisons are made.
4Question 4.
True or False: Merge sort can be modified to count inversions.
- True
- False
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Reflect on what happens when sorting two halves.
Question 5.
Given the rankings [3, 1, 4, 2] and [1, 4, 2, 3], calculate the number of inversions and explain each step.
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Map each of the ranking pairs and see which are inverted.
Question 6.
Describe how you would implement a counting inversions algorithm from scratch, including planning for edge cases.
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Think about how to handle empty or very small input lists effectively.

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