When deciding between using recursive and iterative algorithms, there are several situations where recursion is a better choice, especially for students. Knowing when to use recursion can help students understand the basics of complexity analysis, especially when using tools like the Master Theorem.

First, readability and clarity often make recursion more appealing than iteration. Recursive algorithms can break problems into smaller, easier parts. A great example is the Merge Sort algorithm. It uses recursion to divide the array into two halves, sort those halves, and then combine the results. This makes the code easier to read and understand for students and developers.

On the other hand, iterative versions can become confusing, especially when they involve many nested loops or complicated structures. For students new to working with data, easier-to-read recursive solutions can help them learn better. In academic settings, where understanding is essential, recursion can really shine.

Another area where recursion works well is with overlapping subproblems. A good example is calculating the Fibonacci sequence. While the simple recursive approach is easy to understand, it can be slow for larger numbers because it keeps recalculating the same values. By using memoization, we can make this recursive method more efficient, allowing us to work in linear time ($O(n)$) while still keeping it simple to understand. This shows how recursion can work well with dynamic programming to improve performance without making the code hard to read.

Recursion is especially useful for tree and graph algorithms. Many data structures, like trees, are naturally recursive. For example, when calculating the height of a binary tree, a recursive function can easily show how the heights of the left and right branches relate to each other. This makes recursion a straightforward way to represent the tree's structure.

In contrast, using iteration for these tasks might require extra data structures, like stacks, which can make the code more complex. Recursion often leads to cleaner, more understandable code, letting students focus on how the algorithm works instead of getting lost in complicated code.

Additionally, backtracking algorithms also benefit from recursion. These problems, which involve searching and exploring options, work well with recursive functions. They can easily try out solutions and backtrack when necessary. Examples include Sudoku solvers and the N-Queens problem. Using iteration here can become complicated and less efficient.

When it comes to navigating complex data, recursion has its advantages, especially with structures like nested lists. For instance, if you have a nested JSON or XML structure with nodes containing more nodes, recursion allows you to go through these nested structures easily. Trying to do this with an iterative approach might require extra manual steps, making it harder to understand.

However, students need to be careful about performance issues with recursion. If a recursive function goes too deep, it can cause stack overflow errors. This is common with poorly designed recursive functions, such as trying to walk through deeply nested structures without the right base cases. In such cases, it might be better to switch to iteration to avoid these issues.

That said, using tail recursion can help with some of these problems. Some compilers can optimize tail recursion, making it work like an iterative function. This allows for more efficient use of stack space and keeps the clear structure that recursion provides.

Finally, when we talk about complexity analysis and concepts like the Master Theorem, recursion is very important. Students learn how to analyze algorithms by looking at recurrence relations, which are equations that describe the total cost of recursive functions. A common example is:

$T(n) = aT\left(\frac{n}{b}\right) + f(n)$

In this equation, $a$ stands for the number of subproblems, $b$ indicates the size of each subproblem, and $f(n)$ is the work done outside the recursive calls.

By studying these relations, students can learn how to determine the time complexity of their algorithms, improving their knowledge of computer science principles. Tools like the Master Theorem help resolve these recurrences and give important insights into how algorithms perform in different situations.

In summary, there are many reasons why recursion is a good choice over iteration. From being easier to read and understand to handling overlapping subproblems, tree structure, and backtracking algorithms, recursion shows its strengths. But students must also be aware of its downsides, like stack overflow issues. Balancing the beauty of recursion with the challenges of real-world applications is key. Understanding both recursion and iteration, along with complexity analysis, prepares students to solve various problems in computer science.