Matrix Chain Multiplication - Walkthrough

Multiply matrices $A_1(10 \times 30)$, $A_2(30 \times 5)$, $A_3(5 \times 60)$. Find minimum multiplications.

Dimensions array: $[10, 30, 5, 60]$. $dp[i][j]$ = min cost for $A_i..A_j$. $dp[1][2] = 10 \cdot 30 \cdot 5 = 1500$. $dp[2][3] = 30 \cdot 5 \cdot 60 = 9000$. $dp[1][3] = \min(dp[1][1] + dp[2][3] + 10 \cdot 30 \cdot 60,\ dp[1][2] + dp[3][3] + 10 \cdot 5 \cdot 60) = \min(18000 + 0, 1500 + 3000) = 4500$.