Day 34: Matrix Chain Multiplication
Matrix Chain Multiplication #
Welcome to Day 34 of our 60 Days of Coding Algorithm Challenge! Today, we’ll explore Matrix Chain Multiplication, a classic optimization problem that demonstrates the power of dynamic programming.
What is Matrix Chain Multiplication? #
Matrix Chain Multiplication is an optimization problem that seeks to find the most efficient way to multiply a chain of matrices. The problem is not to actually perform the multiplications, but rather to decide the order in which the matrices should be multiplied.
Problem Statement #
Given a sequence of matrices, find the most efficient way to multiply these matrices together. The problem is not actually to perform the multiplications, but merely to decide in which order to perform the multiplications.
Why is this Important? #
The order in which we multiply matrices can significantly affect the total number of operations needed. For example, if we have three matrices A, B, and C with dimensions 10x30, 30x5, and 5x60 respectively:
- (AB)C = (10x30x5) + (10x5x60) = 1500 + 3000 = 4500 operations
- A(BC) = (30x5x60) + (10x30x60) = 9000 + 18000 = 27000 operations
Choosing the right order (AB)C …
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