 # Matrix Chain Multiplication Using Dynamic Programming Algorithm

Subject Computer Science Data Structures and Algorithms

## Question

Use the dynamic programming technique to find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is <8, 5, 10, 30, 20, 6>.

Matrix   Dimension
A1       8x5
A2       5x10
A3       10x30
A4       30x20
A5       20x6

## Solution Preview

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The array of dimensions for the provided five matrices contains the following numbers p0=8, p1=5, p2=10, p3=30, p4=20, and p5=6.
The items from the main diagonal are initialized with 0. So m[i,i]=0, for i=1,5.
Then the recurrence we use for i<j to calculate m[i,j] entry of the matrix is given by:...

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