The document discusses algorithms and their role in computing. It begins by asking what the smallest value of n is such that an algorithm running in 100n time runs faster than one running in 2n time. It then defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs, consisting of a sequence of computational steps. As an example, it discusses sorting algorithms, which take a sequence of numbers as input and output the numbers in nondecreasing order.
2. What is the smallest value of n such that an algorithm whose running time is 100n
runs faster than an algorithm whose running time is 2n on the same machine?
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3. Algorithms
• an algorithm is any well-defined computational procedure that takes some
value, or set of values, as input and produces some value, or set of values,
as output. An algorithm is thus a sequence of computational steps that
transform the input into the output.
• For example, we might need to sort a sequence of numbers into
nondecreasing order. This problem arises frequently in practice and
provides fertile ground for introducing many standard design techniques
and analysis tools. Here is how we formally define the sorting problem:
• Input: A sequence of n numbers (a1, a2, ………… ,an).
• Output: A permutation (reordering) (a`1, a`2 ,…………… , a`n) of the input
sequence such that a`1 <= a`2 <= …………… <= a`n.
