Data Structures and Algorithms

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For an n that is a power of 2, the n n Weirdo matrix W, is defined as follows. For n = 1, Wi = [1]. For n > 1, W, is defined inductively by n/2 W where Ik denotes the k k identity matrix. For example, 1 0-110-1 1 1 1-1 -1 1 01-1 1 00 0 -1-1 1 0 1 0 0 1-1 -1 0 0 0 1 01 1 1 Give 0(n log n)-time algorithm that computes the product Wnx, where x is a vector of 0 0 1 0 0 1 length n and n is a power of 2 For an n that is a power of 2, the n n Weirdo matrix W, is defined as follows. For n = 1, Wi = [1]. For n > 1, W, is defined inductively by n/2 W where Ik denotes the k k identity matrix. For example, 1 0-110-1 1 1 1-1 -1 1 01-1 1 00 0 -1-1 1 0 1 0 0 1-1 -1 0 0 0 1 01 1 1 Give 0(n log n)-time algorithm that computes the product Wnx, where x is a vector of 0 0 1 0 0 1 length n and n is a power of 2