Matrix Chain Multiplication

Matrix Chain Multiplication Problem Statement Given a chain of matrices $A 1, A 2, \dots, A n$. The dimensions of these matrices are represented by an array arr of size n+1, where arr[i 1] and arr[i] are the dimensions of matrix $A i$. Find the minimum number of scalar multiplications required to multiply these $n$ matrices. Rules of Matrix Multiplication: Two matrices $A 1$ (dimensions $p \times q$) and $A 2$ (dimensions $r \times s$) can only be multiplied if and only if $q = r$. The resulting matrix will have dimensions $p \times s$. The total number of scalar multiplications required to multiply $A 1$ and $A 2$ is $p \cdot q \cdot s$. Example: Given dimensions arr = {10, 20, 30, 40, 50}. Here, $n=4$ matrices are involved: $A 1$ of size $10 \times 20$ $A 2$ of size $20 \times 30$ $A 3$ of size $30 \times 40$ $A 4$ of size $40 \times 50$ Output: The minimum number of scalar operations. Sample Test Case: Input: arr = {10, 20, 30, 40, 50} Output: 38000