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Questions and Answers
What is the recurrence for the given algorithm?
What is the recurrence for the given algorithm?
- $T(n) = T(\frac{n}{2}) + \theta(n)$
- $T(n) = 2T(\frac{n}{2}) + \theta(n)$ (correct)
- $T(n) = 2T(n-1) + \theta(n)$
- $T(n) = T(n-1) + \theta(n)$
What is the worst-case scenario for insertion sort?
What is the worst-case scenario for insertion sort?
- When the input array is reversed
- When the input array has random elements
- When the input array is partially sorted
- When the input array is sorted (correct)
In a max-heap, where is the largest element stored?
In a max-heap, where is the largest element stored?
- At the leaf nodes
- In the middle of the heap
- At the root (correct)
- At the bottom of the heap
In a binary search tree (BST), what condition must hold true if 'y' is a node in the right subtree of 'x'?
In a binary search tree (BST), what condition must hold true if 'y' is a node in the right subtree of 'x'?
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What class consists of problems that are solvable?
What class consists of problems that are solvable?
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Study Notes
Algorithms
- The recurrence for the given algorithm is not specified, but it depends on the type of algorithm and its implementation.
Insertion Sort
- The worst-case scenario for insertion sort is O(n^2), which occurs when the input is in reverse order.
Heaps
- In a max-heap, the largest element is stored at the root node.
Binary Search Trees (BSTs)
- If 'y' is a node in the right subtree of 'x' in a BST, then the value of 'y' must be greater than the value of 'x'.
Complexity Theory
- The class of problems that are solvable is called recursive or R.
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