Page 34Dynamic Programming

34 — Matrix Chain Multiplication

Optimal parenthesization using interval DP.

Matrix Chain Multiplication

Cost recurrence

m[i][j] = min over k from i to j-1: m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j] s[i][j] stores the best split k for parenthesization.

Time: O(n³), Space: O(n²).