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Assume that every possible way of evaluating a sequence of n such matrices (every possible way of placing parentheses) is equally likely. Design an algorithm

Assume that every possible way of evaluating a sequence of n such matrices (every possible way of placing parentheses) is equally likely. Design an algorithm that determines the average amount of work (in terms of scalar multiplications) for a given sequence of n matrices. Precisely define what is "average work"! Determine its time and space complexity.

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