Introduction to Nested Iteration

Nested Iteration refers to a loop that is contained within another loop. It is common in programming and is a fundamental concept in Computer Science.
When a loop is nested within another loop, the inner loop will complete all of its iterations for each iteration of the outer loop.
Nested iteration often comes into play when working with multi-dimensional data structures, like arrays or lists of lists.

Basic Nested Iteration

The first stage of nested iteration is the external or outer loop. This loop starts and tracks the overall progress of the iterations.
The second stage is the internal or inner loop, which goes through its iterations for each iteration of the outer loop.
When using nested loops, one must ensure that all variables tied to each loop are correctly referred to. For example, the loop counter for the outer loop should not be confused with the one for the inner loop.

Nested iteration is particularly valuable when dealing with two-dimensional arrays. In these cases, it is common to have one loop to iterate through the rows and a nested loop to iterate through each column within those rows.
Additionally, nested loops can be used to compare elements from different arrays, or different positions within the same array.

As nested loops lead to a number of iterations equal to the product of the sizes of the loops, they can be computationally expensive. This means they can significantly slow down your program when dealing with large data sets.
Efficient use of nested iteration requires careful consideration of what calculations are necessary within the inner loop and what can be calculated in the outer loop.
Break and continue statements can be used to optimise the performance of nested loops, skipping unnecessary iterations.

Some complex problems may require multiple levels of nesting, where there is a loop within a loop within a loop and so on. While this can be a powerful tool, it should be used judiciously as it can be difficult to follow and debug.
Recursion, the practice of a function calling itself, is an alternative to nested iteration for some complex problems. However, it’s also a more advanced topic that requires careful thought and planning. In the same way as nested iteration, misuse can lead to performance issues.