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Problem 2. (18 points) We have a set of n numbers S= {x1, x2, x3, . . . xn} where each number is represented using b bits. We want to partition the elements in Sinto two disjoint sets U and V so that the sum of the elements in U equals the sum of the elements in V. Example 1 If S= {5, 1, 4, 2, 6}, then U= {5, 4}and V= {1, 2, 6}. (a) What is the largest possible value forn i=1 xi expressed in terms of b and n? (b) What algorithm that was taught in class does this problem remind you of? (Give a brief description of the problem and the name to get credit. You can use an example.) (c) What is the running time for the algorithm from class? Make sure to define whatever parameters you use to describe the running time. (d) Explain your algorithm for partitioning Sinto Uand V. Use parts (a), (b), and (c).

          Problem 2. (18 points) We have a set of n numbers S= {x1, x2, x3, . . . xn} where each number is represented using b bits. We want to partition the elements in Sinto two disjoint sets U and V so that the sum of the elements in U equals the sum of the elements in V. Example 1 If S= {5, 1, 4, 2, 6}, then U= {5, 4}and V= {1, 2, 6}. (a) What is the largest possible value forn i=1 xi expressed in terms of b and n? (b) What algorithm that was taught in class does this problem remind you of? (Give a brief description of the problem and the name to get credit. You can use an example.) (c) What is the running time for the algorithm from class? Make sure to define whatever parameters you use to describe the running time. (d) Explain your algorithm for partitioning Sinto Uand V. Use parts (a), (b), and (c).

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