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Divide and Conquer Algorithms Quiz

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Questions and Answers

What is the time complexity of mergesort?

$\Theta(n \log n)$ (correct)

$\Theta(n)$

$\Theta(2^n)$

$\Theta(n^2)$

In the general Divide-and-Conquer recurrence $T(n) = aT(n/b) + f(n)$, what does the Master Theorem state when $a > bd$?

$T(n) \in \Theta(2^n)$

$T(n) \in \Theta(n^{\log_b a})$ (correct)

$T(n) \in \Theta(nd)$

$T(n) \in \Theta(n^{\log_b a} \log n)$

What is the time complexity of matrix multiplication using Strassen’s algorithm?

$\Theta(n^3)$

$\Theta(2^n)$

$\Theta(n^{\log_2 7})$ (correct)

$\Theta(n^2)$

If $T(n) = 4T(n/2) + n^2$, what is the time complexity according to the Master Theorem?

<p>$T(n) \in \Theta(n^2 \log n)$</p> Signup and view all the answers

What is the primary advantage of using Strassen’s algorithm for matrix multiplication?

<p>Improved time complexity compared to traditional algorithms</p> Signup and view all the answers

Study Notes

Divide and Conquer Strategy

A well-known algorithm design strategy that involves dividing an instance of a problem into two or more smaller instances
Divide the problem into smaller instances
Solve the smaller instances recursively

Examples of Decrease by a Constant

Insertion sort
Topological sorting

Examples of Decrease by a Constant Factor

Binary search
Bisection method
Exponentiation by squaring
Multiplication

Examples of Variable-Size Decrease

Euclid’s algorithm
Selection by partition

Lecture Topics

Sorting Algorithms

Mergesort
Quicksort

Binary Tree Traversals

Applications and uses of binary tree traversals

Binary Search

Applications and uses of binary search

Multiplication of Large Integers

Importance and applications of multiplying large integers

Matrix Multiplication

Strassen’s algorithm for efficient matrix multiplication

Computational Geometry

Closest-pair algorithm
Convex-hull algorithms

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Description

Test your knowledge of divide and conquer algorithms with this quiz covering topics such as decrease by a constant, decrease by a constant factor, variable-size decrease, sorting algorithms like mergesort and quicksort, and more.