Data Str & Algorithm HW Solutions 94

Data Str & Algorithm HW Solutions 94 - 15 Limits to...

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15 Limits to Computation 15.1 This reduction provides an upper bound of O( n log n ) for the problem of maximum fi nding (that is the time for the entire process), and a lower bound of constant time for SORTING (since that is the time spent by Maximum Finding in this process). Neither bound is particularly enlightening. There is no true reduction from SORTING to Maximum Finding (in the sense that the transformations do not dominate the cost) since SORTING is an intrinsicly more dif fi cult problem than Maximum Finding. 15.2 Consider the following fact: A B 0 0 2 = A 2 AB 0 0 . Thus, if we had an algorithm that could square an n × n matrix in less time than needed to multiply two matrices, we could use a transformation based
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