Matrix Chain Multiplication - The Setup

The input is an array of dimensions. If dims = [$10$, $20$, $30$, $40$], you have $3$ matrices: $A_1$ is $10 \times 20$, $A_2$ is $20 \times 30$, $A_3$ is $30 \times 40$.

Matrix i has dimensions $dims[i-1] \times dims[i]$. The number of matrices is n = dims.length - $1$. Multiplying matrices i through j (after optimal parenthesization) produces a matrix of size $dims[i-1] \times dims[j]$. This fact is key for computing dp[i][j] from smaller ranges. Understanding the problem structure is half the battle.