lecture21

Lecture21 - Alpha A final word about addition/subtraction chains(an idea due to Rob Miller Improving the 2(log 2 n 1 upper bound on the length of

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Unformatted text preview: Alpha A final word about addition/subtraction chains (an idea due to Rob Miller ) Improving the 2 (log 2 n) - 1 upper bound on the length of the shortest chain for generating n . Express n using redundant notation with as few 1 ’s and -1 ’s as possible. Examples: 31 = 0 1 1 1 1 1 31 = 1 0 0 0 0 -1 Generate powers of two: 1, 2, 4, …, 2 |log n| . Add a power of two for each 1 , subtract for each -1 . How many 1 ’s and -1 ’s are necessary? Example: 1 1 1 1 1 -1 -1 0 0 1 -1 0 1 1. Adjacent 1 ’s and -1 ’s can be eliminated, e.g., 1 -1 => 0 1 1 1 1 1 0 1 -1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 How many 1 ’s and...
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This document was uploaded on 01/17/2012.

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Lecture21 - Alpha A final word about addition/subtraction chains(an idea due to Rob Miller Improving the 2(log 2 n 1 upper bound on the length of

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