Recursion is often preferred over loops in the following cases:
1). Recursive data structures: Recursive data structures such as linked lists, trees, and graphs can be more easily processed using recursion than using loops. Recursive functions can traverse and manipulate these data structures more elegantly, without having to manage complex loop conditions.
2). Divide-and-conquer algorithms: Divide-and-conquer algorithms such as quicksort, mergesort, and binary search are often easier to implement using recursion than using loops. The recursive structure of these algorithms can more easily express the divide-and-conquer approach, which involves breaking down a problem into smaller sub-problems and combining their solutions.
3). Backtracking algorithms: Backtracking algorithms such as the N-Queens problem and the Sudoku solver are often implemented using recursion. These algorithms require exploring multiple possible paths or solutions, which can be more easily managed using recursive function calls.
4). Dynamic programming: Some dynamic programming problems, such as the Fibonacci sequence or the Towers of Hanoi, can be elegantly solved using recursion. In these cases, a recursive solution can provide a clear and concise solution to the problem, even if it is not the most efficient.
In summary, recursion is often preferred over loops in cases where a problem can be more elegantly expressed using a recursive structure, such as with recursive data structures, divide-and-conquer algorithms, backtracking algorithms, and certain dynamic programming problems.