Everything about Problem Size totally explained
In the fields of
algorithm analysis and
computational complexity theory, the running time or space requirements of an
algorithm are expressed as a function of the
problem size. The problem size measures the size, in some sense, of the input to the algorithm. The problem size has to be cleanly defined before an algorithm analysis can be attempted.
For many problems, the problem size is taken to be the number of
bits required to encode the input. For instance, if the problem is to square a given (nonzero) integer, we'd typically measure the input size as one plus the
floor of the base two
logarithm of the input integer (since that describes how many bits are needed to encode the integer in
binary notation). However, often the encoding of the input isn't canonical; if for instance the problem is one in
graph theory, then different problem sizes can be defined, since a graph can be encoded as a list of edges or alternatively as an
adjacency matrix.
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