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Data Structures

Arrays
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Sorting
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Dynamic Programming
Greedy
Divide & Conquer

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Interactive simulations and exercises

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Prev: Edit Distance

Matrix Chain Multiplication

Choose optimal parenthesization of matrix chain to minimize scalar multiplications (classic interval DP).

Time

O(n³)

length powers

Space

O(n²)

dp + split

Difficulty

Advanced

Interval DP

State

dp[i][j]

min cost

Output

cost + parenthesis

Interactive Simulation

Iterate over chain lengths and inspect best split positions for each interval.

Theory & Recurrence

Understand the interval DP transition and how to reconstruct optimal parenthesization.

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