Competitive ProgrammingEasy

Matrix Chain Multiplication

Detailed guide and Python implementation for the 'Matrix Chain Multiplication' problem.

Problem Statement

Easy

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.

Constraints
  • 2 <= len(p) <= 100
  • 1 <= p[i] <= 500

Examples

Example 1
Input
matrix_chain_order([40, 20, 30, 10, 30])
Output
26000
Explanation

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).

Example 2
Input
matrix_chain_order([10, 20, 30, 40, 30])
Output
30000
Explanation

The minimum number of scalar multiplications is 30000.

Need a Hint?
Consider using Dynamic Programming-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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