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Design and Analysis of Algorithms Quiz

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Questions and Answers

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?

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?

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'?

<p>$Key[x] \leq Key[y]$ (B)</p> Signup and view all the answers

What class consists of problems that are solvable?

<p>$P$ (D)</p> Signup and view all the answers

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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Description

Test your knowledge of algorithms with this quiz on merge sort, heap sort, and insertion sort. Questions cover worst-case scenarios, time complexity, and max-heap elements.