Challenge: Matrix Chain Reconstruction

The DP gives minimum cost, but what's the optimal order? Track the split point. When computing $dp[i][j]$, record $split[i][j] = k$ where the minimum occurs.

Reconstruct recursively: $parenthesize(i, j)$ = "(" + $parenthesize(i, split[i][j])$ + $parenthesize(split[i][j]+1, j)$ + ")". For our example: $split[1][3] = 2$, so optimal is $(A_1 \cdot A_2) \cdot A_3$. Store the split point in a separate array. Reconstruct by recursively printing the optimal parenthesization.