Matrix Chain Multiplication
Detailed guide and Python implementation for the 'Matrix Chain Multiplication' problem.
Problem Statement
Write a function matrix_chain_order(p) that takes an array p representing the dimensions of a chain of matrices such that matrix i has dimension p[i-1] x p[i]. Find the minimum number of scalar multiplications needed to multiply the chain of matrices.
- •2 <= len(p) <= 100
- •1 <= p[i] <= 500
Examples
matrix_chain_order([40, 20, 30, 10, 30])
26000
There are 4 matrices of dimensions 40x20, 20x30, 30x10, and 10x30. The minimum operations are obtained by multiplying them in the order ((A(BC))D).
matrix_chain_order([10, 20, 30, 40, 30])
30000
The minimum number of scalar multiplications is 30000.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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