Problem
Matrix i has size dimensions[i] × dimensions[i+1]. Multiplying a p×q matrix by a q×r matrix costs p·q·r scalar multiplications. Choose where to put parentheses so multiplying the whole chain costs the least.
Implement min_multiplications(dimensions).
Input
dimensions: n + 1 sizes describing n matrices.
Output
Return the minimum total cost.
Constraints
2 ≤ length of dimensions ≤ 200; 1 ≤ each size ≤ 500
Examples
Input:
dimensions = [10, 30, 5, 60]
Expected output:
expected = 4500Input:
std::vector<long long> dimensions = {10, 30, 5, 60};
Expected output:
long long expected = 4500;Input:
long[] dimensions = new long[] {10, 30, 5, 60};
Expected output:
long expected = 4500;Explanation
(A×B)×C costs 10·30·5 + 10·5·60 = 4500, cheaper than A×(B×C) = 27000.
Input:
dimensions = [5, 10]
Expected output:
expected = 0Input:
std::vector<long long> dimensions = {5, 10};
Expected output:
long long expected = 0;Input:
long[] dimensions = new long[] {5, 10};
Expected output:
long expected = 0;Explanation
A single matrix needs no multiplication: 0.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
The order of multiplication changes the total cost even though the final matrix shape stays the same.
Hint 2
Try every possible split point for each interval and reuse smaller interval results.
Hint 3
Use the dimensions array carefully: each subproblem depends on the endpoints around the matrices, not the matrix count alone.
Expected complexity
O(n^3) time, O(n^2) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.