Multi-Language (Coding): Matrix Chain Multiplication Test

Given a chain of matrices A1, A2, ..., An, the goal is to determine the order in which to multiply them to minimize the number of scalar multiplications needed to compute the final product.

Available in

  • English

Summarize this test and see how it helps assess top talent with:

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1 Skills measured

  • Dynamic Programming

Test Type

Coding Test

Duration

40 mins

Level

Advanced

Questions

1

Use of Multi-Language (Coding): Matrix Chain Multiplication Test

The goal of matrix chain multiplication is to find the most efficient way to multiply a sequence of matrices together. As an example, consider a chain of matrices A1, A2, A3, and A4 with dimensions 10x5, 5x20, 20x10, and 10x2, respectively.

To multiply these matrices, we have several options for the order in which to perform the multiplications. For example, we could compute (A1 A2) (A3 A4), or we could compute A1 (A2 A3) A4.

The number of scalar multiplications required to compute the final product depends on the order of the multiplications. By using dynamic programming, we can determine the most efficient order of multiplication, which in this case is A1 ((A2 A3) * A4), requiring a total of 2,600 scalar multiplications.

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