a3 - Q ′′ x x n 2 P x Q x = P ′ x Q ′ x P ′ x...

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Assignment #3: Due September 18 1. Draw the permutation network for n = 16 using subnetworks for n = 8 as boxes with 8 inputs and outputs 2. Show switch settings for the following using the algorithm described in class: Show the settings for all switches. N 1 n = 4 N 2 n = 4 n = 8 1 2 3 4 5 6 7 8 2 1 3 8 6 7 5 4 3. Multiplication of polynomials: Let P ( x ) and Q ( x ) be two polynomial functions given as follows: P ( x ) = p 0 + p 1 x + p 2 x 2 + ...p n 1 x n 1 Q ( x ) = q 0 + q 1 x + q 2 x 2 + ...q n 1 x n 1 Assume that n is a power of 2 . We want to use divide-and-conquer to Fnd the product P ( x ) · Q ( x ) . ±or this purpose, let P ( x ) = p 0 + p 1 x + p 2 x 2 + ...p n 2 1 x n 2 1 P ′′ ( x ) = p n 2 + p n 2 +1 x + ...p n 1 x n 2 1 Q ( x ) = q 0 + q 1 x + q 2 x 2 + ...q n 2 1 x n 2 1 Q ′′ ( x ) = q n 2 + q n 2 +1 x + ...q n 1 x n 2 1 1
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Use the facts that P ( x ) = [ P ( x )] + [ P ′′ ( x )] x n 2 Q ( x ) = [ Q ( x )] + [
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Unformatted text preview: Q ′′ ( x )] x n 2 P ( x ) · Q ( x ) = P ′ ( x ) · Q ′ ( x ) + [ P ′ ( x ) · Q ′′ ( x ) + P ′′ ( x ) · Q ′ ( x )] x n 2 + P ′′ ( x ) · Q ′′ ( x ) · x n How do we get all these terms by doing only three multiplications of half-size polynomials? Write down the recurrence relation that we get and its solution by master theorem. Does this look similar to any one of the examples done in class? 4. Problem 4-6 (b) and (c) on page 87 5. Problem 9.3-8 (page 193) 2...
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a3 - Q ′′ x x n 2 P x Q x = P ′ x Q ′ x P ′ x...

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