CSIS 0250B Design and Analysis of Algorithms Assignment 3 Due: 11:55 PM, Mar 12, 2009 1. Given positive integers a 1 ,a 2 , ··· ,a n , devise a dynamic programming algorithm to determine whether it is possible to divide the n integers into three disjoint subsets with equal sum (which should be equal to 1 3 ∑ n i =1 a i ). Your algorithm should run in time polynomial in n and U = ∑ n i =1 a i . 2. Consider the problem of neatly printing a paragraph on a type-writer-quality printer, which supports a character set A and prints a character a ∈ A with ﬁxed (horizontal) space f ( a ). We assume that the space character occupies 1 unit of space (i.e. f (“ ”)=1). For example, printing two words “abc” and “bca” with one space character in between requires 2( f ( a )+ f ( b )+ f ( c ))+1 units of space. The input text is a sequence of n words w 1 ,w w ,...,w n , each formed by one or more characters from A . We want to print this text neatly on a number of lines, each holds a maximum
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