This article focuses on the comparison of the temporal and spatial algorithmic complexities of iterative and recursive structures, through the analysis of classic cases (factorial, Fibonacci sequence, tree traversal).
We demonstrate in this study that on the one hand iteration generally offers better memory efficiency (O (1) in many cases) and avoids the risks of stack overflow, and on the other hand that recursion, although more elegant and intuitive for certain problems (such as tree traversals), can generate a memory overload (O (n) in call stack) and degraded time complexity in non-optimized cases (eg: naive Fibonacci in O (2ⁿ)).
The results obtained here highlight that the choice between these two approaches depends on the context the developer is in. It is therefore worth noting that iteration is better suited to linear and memory-constrained problems, and recursion to nested structures (trees, divide-and-conquer), especially if the language supports tail call optimization.
This comparison provides objective criteria to guide developers in selecting the most effective approach based on needs.
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