An iterative algorithm is an algorithm that solves a problem by repeatedly executing a series of steps until a specific condition or set of conditions is met. These conditions typically involve reaching a desired level of accuracy or iterating over all elements of a data structure, such as an array or a graph.
In each iteration of the algorithm, a new solution is derived from the previous one. This is opposed to recursive algorithms, which solve problems by breaking them down into smaller instances of the same problem.
Iterative algorithms are often used when the state at a given point in the computation depends only on the state at a previous point, not on the complete history of the computation. This can make iterative algorithms more memory-efficient than their recursive counterparts.
A common example of an iterative algorithm is the ‘for’ loop in programming, where a loop iteratively performs operations on each element in a data structure. Another example is the method used to calculate factorials: n! = n * (n-1) * (n-2) * … * 1, where each multiplication can be computed in an iteration.
While iterative algorithms can often be easier to understand and implement, and more efficient in terms of memory usage, they may not be the best choice for all types of problems. For example, some problems may lend themselves more naturally to recursive solutions or other types of algorithms.