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In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences.
If the condition is true, then the lines of code inside the loop are executed. The advancement to the next iteration part is performed exactly once every time the loop ends. The loop is then repeated if the condition evaluates to true. Here is an example of the C-style traditional for-loop in Java.
It implicitly calls the IntoIterator::into_iter method on the expression, and uses the resulting value, which must implement the Iterator trait. If the expression is itself an iterator, it is used directly by the for loop through an implementation of IntoIterator for all Iterators that returns the iterator unchanged.
For example, the iterator method is supposed to return an Iterator object, and the pull-one method is supposed to produce and return the next value if possible, or return the sentinel value IterationEnd if no more values could be produced. The following example shows an equivalent iteration over a collection using explicit iterators:
Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), some mathematicians [citation needed] choose to use ∘ to denote the compositional meaning, writing f ∘n (x) for the n-th iterate of the function f(x), as in, for example, f ...
In this example, there is an output dependence between the jth element in S1 and the j+1th element in S2. Here, c[j+1] in statement S2 is written to in one iteration. In the next iteration, c[j] in statement S2, which is the same memory location as c[j+1] in the previous iteration, is written to again.
In computer science, a generator is a routine that can be used to control the iteration behaviour of a loop.All generators are also iterators. [1] A generator is very similar to a function that returns an array, in that a generator has parameters, can be called, and generates a sequence of values.
For example, the following code does not read from the array a, and does not update the arrays b, c. No iterations have a dependence on any other iteration. No iterations have a dependence on any other iteration.