Application of recursion in C++ algorithms: efficiency improvement and complexity analysis

The application of recursion in C algorithm can improve efficiency. Taking the Fibonacci sequence calculation as an example, the function fibonacci calls itself recursively, with a complexity of O(2^n). However, for recursive problems such as tree structures, recursion can greatly improve efficiency because the size of each problem is halved. But be careful to avoid problems such as infinite recursion and insufficient stack space. For complex recursive problems, loop or iterative methods may be more effective.

Application of Recursion in C Algorithm: Efficiency Improvement and Complexity Analysis

Introduction

Recursion is a powerful programming technique that can be used to simplify algorithms and increase efficiency. In C, recursion is implemented by a function calling itself.

Code Example

Take the following Fibonacci sequence calculation as an example:

int fibonacci(int n) {
  if (n <= 1) {
    return n;
  } else {
    return fibonacci(n - 1) + fibonacci(n - 2);
  }
}

How to run

• Functionfibonacci accepts an integer parameter n, representing the nth number in the Fibonacci sequence to be calculated.
• If n is less than or equal to 1, return n directly because this is the first or second item of the sequence.
• Otherwise, the function calls itself recursively twice: once with n - 1, and once with n - 2.
• The recursive call continues until n decreases to 1 or 0.
• The function returns the final calculated Fibonacci number.

Efficiency improvement

The efficiency of the recursive algorithm depends on the size of the problem type. For recursive problems such as tree structures, recursion can significantly improve efficiency because the size of each problem is reduced by half.

Complexity Analysis

The complexity of the Fibonacci sequence algorithm is O(2^n), because each recursive call will generate two new recursions transfer. For large values ​​of n, this results in an inefficient algorithm.

Practical case

• Folder traversal
• Graph search
• Divide and conquer algorithm (such as merge sort)

Notes

• When using recursion, it is important to avoid infinite recursion.
• Recursive algorithms may require a large amount of stack space, especially if the call depth is large.
• For complex recursive problems, it may be more efficient to use a loop or iterative approach (such as dynamic programming).

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