Practice Optimal Computation Order (44.1.3) - Matrix multiplication - Data Structures and Algorithms in Python
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Optimal Computation Order

Practice - Optimal Computation Order

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the resulting size when multiplying a 2x3 matrix with a 3x4 matrix?

💡 Hint: Think about the rows of the first matrix and the columns of the second.

Question 2 Easy

State the associative property in your own words.

💡 Hint: Think of the order of numbers in multiplication.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the time complexity of multiplying two matrices of size m x n and n x p using the naive method?

O(n^2)
O(mnp)
O(n^3)

💡 Hint: Think about how many operations are needed in total.

Question 2

True or False: Associative property guarantees optimal multiplication cost regardless of order taken.

True
False

💡 Hint: Remember the example involving A, B, and C.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given four matrices of warm sizes A (10x20), B (20x30), C (30x40), and D (40x50), calculate the cost of multiplying them in every possible order and find the most efficient.

💡 Hint: Keep track of both the computational costs and the structure of how matrices combine!

Challenge 2 Hard

Create a dynamic programming solution to calculate the optimal order for multiplying organizations of matrices and explain the rationale behind this design.

💡 Hint: Analyzing costs recursively gives an edge to find minimum multiplications!

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