Dynamic Programming

Matrix-Chain Multiplication


•	Restatement: Given matrices

	M₁,M₂,...,M_n where M_i has r_i
	rows and r_i+1 columns, find
	the way to compute the

	product of the matrices that

	uses the smallest number of
	scalar multiplies

A recursive solution:

best (i,j):

// Least cost for M[i]...M[j] //

if (i = j) return 0;

min = infinity;

for k = i to j-1 do

cost = best(i,k) + best(k+1,j)

+ r[i]*r[k+1]*r[j+1];

if (cost < min) min = cost;

return min;

end best.

CS409 - Spring 2000

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