Detailed explanation of C++ function recursion: the definition and principle of recursion

Recursion is a programming technique in which a function calls itself, achieved by breaking the problem into smaller problems, setting boundary conditions, and decreasing the problem. Taking the Fibonacci sequence as an example, the recursive function uses boundary conditions (n ​​≤ 1) and the decrease problem (fib(n - 1) fib(n - 2)) to gradually solve the sequence items.

Detailed explanation of C function recursion: the definition and principle of recursion

Definition and principle

Recursion is a programming technique in which a function calls itself. The function passes in the data when it calls itself, and returns the result when it completes processing.

The core concept of recursion is:

• Function decomposition problem: decompose a large problem into a series of smaller problems.
• Boundary conditions: Define the boundary conditions that end the recursion to prevent infinite loops.
• Decreasing problem: In each recursive call, the subproblem becomes smaller, eventually reaching the boundary condition.

Practical case: Finding the Fibonacci sequence

The Fibonacci sequence is an integer sequence, the first two numbers of which are 0 and 1 , each subsequent number is the sum of the two preceding numbers. For example: 0, 1, 1, 2, 3, 5, 8, 13, ....

We can use recursive functions to solve the Fibonacci sequence:

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

Step breakdown:

1. Boundary conditions: When n is less than or equal to 1, n is returned directly.
2. Decreasing problem: When n is greater than 1, the function recursively calls itself twice to solve n - 1 and n - 2 Fibonacci numbers and add the results.
3. Final result: After multiple recursive calls, the Fibonacci sequence will be gradually calculated and finally returned to the initial function call.

Usage example:

int main() {
  int result = fib(10);
  cout << "斐波那契数列第 10 项：" << result << endl;
  return 0;
}

Output:

斐波那契数列第 10 项：55

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