C++ Practice Questions – Calculate Function Value

Time Limit: 2s Memory Limit: 192MBProblem DescriptionCalculate the function value according to the following recursive formula.When x=1, f(x)=10; when x>1, f(x)=f(x-1)+2Input FormatInteger variable xOutput Formatf(x)Sample Input10Sample Output28Code(1) Recursive Version

#include <iostream>
using namespace std;
int f(int x) {    if (x == 1) {        return 10;    } else {        return f(x - 1) + 2;    }}
int main() {    int x;    cin >> x;    cout << f(x) << endl;    return 0;}

(2) Iterative Version

#include <iostream>
using namespace std;
int f(int x) {    int result = 10;    for (int i = 2; i <= x; i++) {        result += 2;    }    return result;}
int main() {    int x;    cin >> x;    cout << f(x) << endl;    return 0;}

Output ResultProblem Analysis

The problem provides a recursively defined function:

• When x = 1, f(x) = 10

• When x > 1, f(x) = f(x-1) + 2

We need to calculate the function value corresponding to the given x.

Methodology

1. Recursive Implementation: Directly implement the function according to the recursive definition.

2. Iterative Implementation: An iterative approach can also be used to avoid excessive recursion depth.

Code Explanation

1. Recursive Version:

• Base case: When x=1, return 10.

• Recursive case: When x>1, return f(x-1)+2.

Iterative Version:

• Initialize result to 10 (corresponding to the case when x=1).

• Loop from 2 to x, adding 2 each time.

• Return the final result.

Validation Example

• Input: 10

• Calculation Process:

• f(10) = f(9) + 2

• f(9) = f(8) + 2

• …

• f(2) = f(1) + 2 = 10 + 2 = 12

• f(10) = 10 + 2 × 9 = 28

• Output: 28

Both methods can correctly calculate the function value; the recursive version is more intuitive, while the iterative version is more efficient and avoids recursion depth issues.

C++ Basic Tutorial Collection

C++ Basic Materials

1. C++ Output

2. C++ Variables

3. C++ Input

4. C++ Expressions

5. IF Statements

6. IF Applications

7. WHILE Loop Statements

8. FOR Loop Statements

9. Arrays

10. One-Dimensional Arrays

11. Two-Dimensional Arrays

12. C++ Functions

13. C++ File Operations – Writing Files

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