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Number of possible parentheses for n matrices increases
exponentially with n
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Let Ci..j denote the the matrix that results
from multiplying the matrices
CiCi+1...C
j
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In order to find
C1C2...Cn split the
matrix chain at any number k (1 < k < n), then calculate
C1..k and Ck+1..n and then
multiply these two matrices to get the result
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One should note that the parenthesization of the chain
C1C2...Ck should be
optimal for the whole problem to have an optimal solution. If
this is not satisfied then there exists another r (1 < r < n)which can split
the chain and give an optimal solution
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The above condition implies that only an optimal solution to
the subproblem will give an optimal solution to main problem