Real-world examples of recursion in algorithms you actually use

When people ask for examples of recursion in algorithms, three classics always surface: factorial, Fibonacci, and binary search. They’re popular for a reason: each one highlights a different way recursion helps you think.

Take factorial, for instance. Mathematically, n! = n × (n − 1)! with a base case of 0! = 1. In code, that becomes a function that calls itself with a smaller argument until it hits zero. It’s not the fastest way to compute large factorials in practice, but it’s a clean example of how a function can define its behavior in terms of a smaller version of the same problem.

Fibonacci is the cautionary tale. The naive recursive version mirrors the mathematical definition beautifully, but it explodes in runtime because it recomputes the same values over and over. That makes it one of the best examples of why you should pair recursion with memoization or convert to an iterative or dynamic programming approach when performance matters.

Binary search is a different flavor. You repeatedly cut a sorted array in half, deciding which half might contain your target. Here, recursion expresses a divide-and-conquer idea directly: search the left half, or search the right half, until the array slice is empty. Many developers eventually switch to an iterative version, but as a teaching tool, recursive binary search is one of the cleanest examples of recursion in algorithms that connect math, logic, and code.

Divide-and-conquer examples of recursion in algorithms

Some of the best examples of recursion in algorithms live in the divide-and-conquer family. These are problems where you:

• Split the input into smaller chunks
• Solve each chunk (often recursively)
• Combine the partial answers into a final result

Merge sort: recursion as a sorting blueprint

Merge sort is the poster child here. You break an array into two halves, recursively sort each half, then merge the two sorted halves into a single sorted array. The recursive calls keep slicing the array until you hit subarrays of size 1 (the base case), which are trivially sorted.

Why this matters in 2024–2025: merge sort and its cousins influence how standard libraries are implemented. For example, languages often use hybrid algorithms that start from merge sort or quicksort ideas and then optimize for real-world data patterns. The recursive design still shapes how we think about performance and memory, even when the production implementation is more nuanced.

Quick sort: recursion plus clever partitioning

Quick sort is another favorite example of recursion in algorithms. You:

• Pick a pivot element
• Partition the array into elements less than and greater than the pivot
• Recursively quick sort each side

The recursion ends when a subarray has zero or one element. Quick sort tends to perform very well in practice, which is why many standard library sort functions historically leaned on it or on related hybrids.

Quick sort also shows how recursion interacts with randomness and worst-case behavior. Poor pivot choices can lead to deep recursion and bad performance; randomized pivot selection and tail-call optimizations are common fixes.

Fast exponentiation: powering up with fewer multiplications

Exponentiation by squaring is a more mathematical example of divide-and-conquer recursion. To compute x^n:

• If n is 0, return 1 (base case)
• If n is even, compute (x^(n/2))^2
• If n is odd, compute x × x^(n−1)

This cuts the exponent roughly in half at each recursive step, turning a linear-time process into a logarithmic one. You’ll see this pattern in cryptography code, numerical libraries, and competitive programming solutions.

For a deeper mathematical background on recursion and induction, the open courseware from MIT is a solid starting point: MIT OpenCourseWare – Introduction to Algorithms.

Tree and graph examples include traversal, parsing, and search

If you’re looking for real examples of recursion in algorithms that show up daily in production code, tree and graph traversals are hard to beat.

Tree traversal: recursion as a natural fit

Tree structures are inherently recursive: a tree consists of a root node and zero or more subtrees. That’s why recursion feels almost tailor-made for operations like:

• Preorder traversal (visit node, then children)
• Inorder traversal (left child, node, right child) in binary trees
• Postorder traversal (children, then node)

Compilers use recursive tree traversals to walk abstract syntax trees (ASTs) when analyzing or transforming code. Modern language tooling, from Python to TypeScript, still leans heavily on these patterns.

Depth-first search (DFS): exploring graphs recursively

DFS is one of the best examples of recursion in algorithms for graphs. The idea:

• Start at a node
• Mark it as visited
• Recursively explore each unvisited neighbor

The recursion naturally mirrors the “go as deep as possible, then backtrack” strategy. In practice, large-scale systems often switch to an explicit stack to avoid stack overflow, but the recursive formulation is still how most people first understand and reason about DFS.

DFS powers:

• Cycle detection
• Topological sorting
• Connected components
• Solvers for puzzles like mazes and Sudoku

If you want a more formal view of graph algorithms, the Stanford online materials are widely used in CS courses: Stanford CS Library – Graph Algorithms.

Parsing expressions: recursive descent parsers

Another strong example of recursion is in parsing arithmetic or programming language expressions. A recursive descent parser uses one function per grammar rule, and those functions call each other recursively according to the grammar structure.

For instance, an expression grammar might say:

• An expression is a term plus or minus another expression
• A term is a factor times or divided by another term
• A factor is either a number or a parenthesized expression

Each nonterminal (expression, term, factor) becomes a function. When the parser sees parentheses, it calls the expression function recursively inside them. This pattern is everywhere in compilers, interpreters, and even configuration file parsers.

Dynamic programming: recursion with memory

Some of the best real examples of recursion in algorithms show up when you add memoization or tabulation. Dynamic programming often starts from a recursive definition of a problem and then adds caching to avoid recomputing subproblems.

Edit distance: recursive thinking behind spell check

The Levenshtein edit distance between two strings is the minimum number of edits (insertions, deletions, substitutions) to turn one string into the other. The recursive relation compares prefixes of the two strings and branches on whether the last characters match or not.

Naively, the recursive algorithm is slow, but with memoization or a bottom-up table, it becomes practical. This is the backbone of:

• Spell checkers
• DNA sequence alignment
• Fuzzy search

For a bioinformatics angle on recursive and dynamic programming patterns, the National Center for Biotechnology Information (NCBI) offers technical resources at NCBI – Algorithms in Bioinformatics.

Path counting in grids: combinatorics via recursion

Another example of recursion in algorithms is counting the number of ways to move from the top-left to the bottom-right of a grid, moving only right or down. Recursively, the number of paths to a cell is the sum of paths to the cell above it and to the cell to the left.

This turns into a classic dynamic programming table in practice, but the underlying idea is recursive: the solution to a cell depends on smaller subproblems. You’ll see this pattern in routing, logistics optimization, and even some AI planning algorithms.

Modern, real examples of recursion in algorithms (2024–2025)

Recursion isn’t just a teaching tool; it still shapes modern systems in 2024–2025. Some real examples of recursion in algorithms that matter today:

Recursive search in AI and game engines

Game-playing AI, from chess engines to Go programs, often uses recursive search trees (like minimax with alpha-beta pruning). The algorithm recursively explores possible moves, evaluates positions, and backtracks with the best found outcome.

Even with neural networks providing evaluation functions, the core search often remains recursive. The tree of possible future states is inherently recursive, and the algorithm’s logic reflects that.

Recursive neural network structures

While many deep learning models are iterative in practice, certain architectures—like recursive neural networks on tree-structured data—use recursion conceptually. They process data structures such as parse trees or scene graphs by recursively combining child representations into parent representations.

This is not the same as a function calling itself in code, but the algorithmic idea is similar: define the representation of a node in terms of its children, with a base case for leaves.

For a research-level view of algorithmic patterns in AI and machine learning, the U.S. National Institute of Standards and Technology (NIST) maintains resources on AI methods and evaluation.

File system operations and recursive directory walks

On the more everyday side, file system utilities often use recursion under the hood. When you run a command to list all files in a directory tree or back up an entire folder hierarchy, the code typically does something like:

• Process the current directory
• For each subdirectory, recursively process that subdirectory

Languages may expose this explicitly (e.g., a recursive function walking directories) or hide it behind iterators, but the algorithmic pattern is recursive.

Practical tips drawn from examples of recursion in algorithms

Looking across all these examples of recursion in algorithms, a few practical lessons keep repeating.

Always respect the base case

Every recursive algorithm needs a clear base case where it stops calling itself. In factorial, it’s when n reaches 0 or 1. In tree traversal, it’s when you hit a null child. In DFS, it’s when you see a node that’s already visited or there are no more neighbors.

Bad or missing base cases lead to stack overflows and infinite loops. When you study any example of a recursive algorithm, start by asking: what exactly makes this stop?

Watch your recursion depth

Some problems naturally produce deep recursion: very skewed binary trees, long linked lists, or worst-case quick sort partitions. On modern systems, stack size is finite, and deep recursion can blow it up.

That’s why many production implementations of DFS or quick sort switch to iterative versions with explicit stacks once the recursion depth gets large. The lesson from real examples of recursion in algorithms is simple: recursion is a tool, not a religion. Use it where it makes the code clearer, and switch approaches when the data demands it.

Combine recursion with caching or iteration when needed

Fibonacci, edit distance, and path counting all show that naive recursion can be too slow. Adding memoization or rewriting the algorithm in bottom-up form can turn a slow recursive idea into a fast solution.

When you see new examples of recursion in algorithms, especially in dynamic programming, ask:

• Am I recomputing the same subproblem?
• Can I store results in a table or map?
• Would an iterative approach be easier to optimize?

FAQ: common questions about real examples of recursion in algorithms

Q: What are some of the best examples of recursion in algorithms for beginners?
Factorial, Fibonacci (with memoization), binary search, and simple tree traversals are often the best starting points. They’re small enough to understand fully but rich enough to show how base cases and recursive calls interact.

Q: Can you give an example of recursion in everyday software?
Yes. File system tools that walk directory trees, compilers that parse nested expressions, and many search functions that explore trees or graphs are all real examples of recursion in algorithms you use indirectly every day.

Q: Is recursion always slower than iteration?
Not always. Many compilers optimize tail-recursive functions to run like loops. The performance depends on the language, compiler, and problem. That said, some naive recursive solutions (like un-memoized Fibonacci) are dramatically slower than their iterative or dynamic programming counterparts.

Q: How do I know when to use recursion versus an iterative approach?
If the problem is naturally defined in terms of smaller subproblems—like trees, divide-and-conquer sorting, or graph search—recursion often makes the code easier to reason about. For very large inputs or performance-critical paths, you might prefer an iterative version with an explicit stack.

Q: Are there examples of recursion in algorithms used in AI or data science?
Yes. Recursive search in game-playing AI, tree-based models like decision trees (where prediction walks a tree recursively), and certain neural network architectures on tree-structured data are all examples of recursion in algorithms that show up in modern AI and data science workflows.

For more formal study of algorithmic techniques, including recursion and dynamic programming, many universities publish free notes and lectures; for example, Harvard’s CS50 materials include accessible introductions to these ideas.