Matrix Chain Multiplication Practice Questions - Gurgaon

Lets first understand the problem statement:
Given a series of matrices A1, A2, A3,...An. Your task is to determine the cheapest way to multiply these matrices. The number of scalar multiplications is used to calculate the cost of matrix multiplication. A chain of matrices A1, A2, A3,...An is represented by a sequence of numbers in an array 'arr' where the dimension of the first matrix is arr[0] * arr[1] , 2nd matrix is arr[1] * arr[2], and so on
Example:
For arr[ ] = { 10, 20, 50, 30}, matrix A1 = [10 * 20], A2 = [20 * 50], A3 = [40 * 50]

Scalar multiplication of matrix with dimension 10 * 20 is equal to 200.
This problem can be done in various ways. The goal is to try out all possible parentheses combinations from left to right while avoiding the computation of repetitive subproblems with memoization.

- Place parentheses wherever they are possible, calculate the cost for each placement, and return the lowest value.

- The first set of parentheses in a chain of matrices of size 'n' can be placed in a 'n' - 1 way.

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