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upper_bound: upper_bound: Returns an iterator to the first element with a key greater than a certain value. Observers key_comp: key_comp: key_comp: key_comp: Returns the key comparison function. value_comp: value_comp: value_comp: value_comp: Returns the value comparison function. In set and multiset this function is equivalent to key_comp ...
Similarly, a function g defined on domain D and having the same codomain (K, ≤) is an upper bound of f, if g(x) ≥ f (x) for each x in D. The function g is further said to be an upper bound of a set of functions, if it is an upper bound of each function in that set.
C provides the function bsearch() in its standard library, which is typically implemented via binary search, although the official standard does not require it so. [67] C++'s standard library provides the functions binary_search(), lower_bound(), upper_bound() and equal_range(). [68]
Here is an example, in C-like pseudocode, of an integer variant computed from some upper bound on the number of iterations remaining in a while loop. However, C allows side effects in the evaluation of expressions, which is unacceptable from the point of view of formally verifying a computer program.
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil(x). [1]
By the boundedness theorem, f is bounded from above, hence, by the Dedekind-completeness of the real numbers, the least upper bound (supremum) M of f exists. It is necessary to find a point d in [a, b] such that M = f(d). Let n be a natural number. As M is the least upper bound, M – 1/n is not an upper bound for f.
To optimize this, a C++ compiler would need to: Inline the sin and operator+ function calls. Fuse the loops into a single loop. Remove the unused stores into the temporary arrays (can use a register or stack variable instead). Remove the unused allocation and free. All of these steps are individually possible.
In the C++ Standard Library, the algorithms library provides various functions that perform algorithmic operations on containers and other sequences, represented by Iterators. [1] The C++ standard provides some standard algorithms collected in the <algorithm> standard header. [2] A handful of algorithms are also in the <numeric> header.