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Improvement of an algorithm can reduce the bound. For example, sequential search in a sorted table: O(n), binary search in a sorted table: O(log n). Is there also a lower bound for a given algorithm? Is it possible to show that the solution of a given problem requires a certain minimum of effort? If a problem necessitates at least O(n2 ) steps, there is no point in searching for an O(n) solution. The Ω notation describes lower bounds. For example, sequential search in a table is of the order Ω(n), because each element must be looked at at least once.

Is it possible to show that the solution of a given problem requires a certain minimum of effort? If a problem necessitates at least O(n2 ) steps, there is no point in searching for an O(n) solution. The Ω notation describes lower bounds. For example, sequential search in a table is of the order Ω(n), because each element must be looked at at least once. Ω(log n) is not possible. In this case, Ω(n) = O(n). 376 ) von Strassen 1969 ) Coppersmith and Winograd 1987 (quoted in Cormen et al. 6 Auxiliary classes and functions This section briefly describes some tools which will be needed at a later stage.

Reference front() Supplies a reference to the first element of a container. const_reference front() Ditto, but cannot be used to modify container elements. reference back() Supplies a reference to the last element of a container. const_reference back() Ditto, but cannot be used to modify container elements. void push_back(t) Inserts t at the end. void pop_back() Deletes the last element. void resize(n, t = T()) Changes the container size. n size() elements t are inserted at the end or size()-n elements are deleted at the end, depending on whether n is greater or less than the current size.

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