Step 4: Construct Optimal Solution

Let A = .

Call Matrix-Chain-Order then Matrix-Chain-Multiply, defined below.

Matrix-Chain-Multiply(A, s, i, j)
$\;\;\;\;\;$if i < j
$\;\;\;\;\;$then x = Matrix-Chain-Multiply(A, s, i, s[i,j])
$\;\;\;\;\;$ $\;\;\;\;\;$y = Matrix-Chain-Multiply(A, s, s[i,j]+1, j)
$\;\;\;\;\;$ $\;\;\;\;\;$return Matrix-Multiply(x, y)
$\;\;\;\;\;$else return A_i