Recursive implementation of C++ functions: How to avoid recursion explosion problem?

Strategy to avoid recursion explosion: Tail recursion optimization: Convert recursive calls at the end of the function into loops. Memoization: Store calculated results to avoid repeated calls. Iterative implementation: Use loops instead of recursive calls.

Recursive Implementation of C Functions: Avoiding Recursive Explosion

Recursion is a powerful technique in computer science that allows functions Call itself. However, overuse of recursion can lead to a condition called recursion explosion, in which a function keeps calling itself, exhausting the program's available memory and time.

In order to avoid recursion explosion, there are many strategies that can be adopted:

1. Tail recursion optimization

Tail recursion means that the function is called at its end itself. Most compilers automatically optimize tail recursions by converting them into loops, thus avoiding the ever-growing function stack. The following is an example of tail recursion:

int factorial(int n) {
  if (n == 1) {
    return 1;
  } else {
    return n * factorial(n - 1); // 尾递归调用
  }
}

2. Memoization

Memoization avoids repeated recursive calls by storing a table of calculated function results. When the function encounters the same input again, it first checks if there is a result in the table and if so, returns it, otherwise it continues the recursive call. The following is an example of using memos to implement the Fibonacci sequence:

unordered_map<int, int> memo;

int fibonacci(int n) {
  if (memo.find(n) != memo.end()) {
    return memo[n]; // 如果找到之前计算的结果，则返回
  } else {
    if (n <= 1) {
      return n;
    } else {
      int result = fibonacci(n - 1) + fibonacci(n - 2);
      memo[n] = result; // 将结果存储在备忘录中
      return result;
    }
  }
}

3. Iterative implementation

For some recursive functions, the recursive call can be completely avoided by replacing it with iteration recursion. The following is an example of using iteration to implement factorial:

int factorial(int n) {
  if (n < 0) {
    throw invalid_argument("Factorial is not defined for negative numbers.");
  }

  int result = 1;
  for (int i = 1; i <= n; i++) {
    result *= i;
  }

  return result;
}

Practical case:

Suppose we are writing a program to print a layer-by-layer representation of a tree, where each Nodes have a unique ID. We can use recursion to traverse the tree and at each node print its ID and current depth. However, the recursive implementation may lead to recursion explosion if the tree is very deep.

By using tail recursion optimization, we can convert recursive calls into loops, thus avoiding recursive explosion:

void printTree(Node* root, int depth = 0) {
  if (root == nullptr) {
    return;
  }

  cout << "Node ID: " << root->id << ", Depth: " << depth << endl;

  for (Node* child : root->children) {
    printTree(child, depth + 1); // 尾递归调用
  }
}

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