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hwk5 - Fall 2011 Clyde Kruskal CMSC 451 Homework 5 Due at...

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Fall 2011 CMSC 451: Homework 5 Clyde Kruskal Due at the start of class Tuesday, November 22, 2011. Problem 1. Use the dynamic programming algorithm to find by hand an optimal paren- thesization for multiplying matrices of dimensions are given by the sequence < 6 , 3 , 10 , 5 , 8 , 4 , 20 > . Show the table. You may use a calculater. Problem 2. Write an efficient algorithm to determine an order of evaluating the matrix product M 1 × M 2 × M 3 ... × M n so as to minimize the scalar multiplications in the case where each M is of dimension 1 × 1 , 1 × d,d × 1 ,d × d for some fixed d . Problem 3. The number of combinations of n things taken m at a time ( n m ) can be com- puted using the following recurrence: parenleftBigg n m parenrightBigg = parenleftBigg
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