Practice Insert Operation Complexity (10.1.2) - Height of the Heap - Design & Analysis of Algorithms

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9 questions

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6 sample questions

Question 1.
What is the time complexity of insert operations in heaps?
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Think about what governs the height of the tree.
Question 2.
Where is the maximum element found in a max-heap?
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Is it at the top or somewhere deeper in the tree?
3Question 3.
What is the time complexity of inserting into a heap?
- O(N)
- O(log N)
- O(N^2)
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Consider how many levels we might have in a tree with N elements.
4Question 4.
True or False? The maximum value in a max-heap can be found at any leaf node.
- True
- False
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Recall the definition of a max-heap.
Question 5.
Given an initial heap [50, 30, 20, 10], how would the heap look after inserting 40? Show the intermediate steps.
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Consider how to keep the parent node greater than its children.
Question 6.
If you start with a heap of [45, 30, 20, 10] and perform a delete max operation, what will the sequence of heaps look like? Describe each removal step.
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Focus on restoring the heap property after each deletion.

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