# Homework 3 - W08/CS5592 Homework Three Design and Analysis...

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W08/CS5592 Homework Three Design and Analysis of Algorithms Due: Monday, March 10, 2008, in class There are four problems 1 Find an optimal parenthesization of a matrix chain product whose sequence of dimensions is (8, 10, 6, 11, 3, 35). 2 Re-consider the domino stone problem. Suppose that a sequence of n (> 1) domino stones, s 1 , s 2 , …, s n , are placed horizontally in a row. Each stone s i (1 i n ) has two nonnegative numbers as illustrated by the following figure. 5 6 4 2 9 7 5 7 3 9 11 10 S 1 S 2 S 3 S 4 S 5 S 6 We use arrays L [ i ] and R [ i ] to store the two numbers of s i (1 i n ), where L [ i ] is the number arranged to the left side of R [ i ] in the sequence. For example, in the above sequence, we have L[1] = 5, R[1] = 6, L[2] = 4, R[2] = 2, L[3] = 9, R[3] = 7, L[4] = 5, R[4] = 7, L[5] = 3, R[5] = 9, L[6] = 11, R[6] = 10. If L [ i ] R [ i ], then we say that stone s i is in state 0, denoted by W[ i ] = 0. Otherwise, W[

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## This note was uploaded on 04/12/2008 for the course CS 592 taught by Professor Shen during the Winter '05 term at University of Missouri-Kansas City .

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Homework 3 - W08/CS5592 Homework Three Design and Analysis...

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