C++ Practice Problem – Calculate 1977!

Time Limit: 2s Memory Limit: 192MB

Problem Description

Write a program to calculate the value of 1977!

Input Format

None

Output Format

None

Sample Input

None

Sample Output

None

Code

#include <iostream>
using namespace std;
const int MAX_DIGITS = 10000;  // Estimate the number of digits in 1977!
void factorial(int n) {
    int result[MAX_DIGITS] = {0};
    result[0] = 1;
    int digits = 1;  // Current number of digits in the result
    for (int i = 2; i <= n; i++) {
        int carry = 0;
        for (int j = 0; j < digits; j++) {
            int product = result[j] * i + carry;
            result[j] = product % 10;
            carry = product / 10;
        }
        while (carry > 0) {
            result[digits] = carry % 10;
            carry /= 10;
            digits++;
        }
    }
    // Output result
    for (int i = digits - 1; i >= 0; i--) {
        cout << result[i];
    }
    cout << endl;
}
int main() {
    factorial(1977);
    return 0;
}

Output Result

Methodology

1. Large Number Representation: Use an array to store large numbers, with each element representing a digit.

2. Multiplication Operation: Multiply from 1 up to 1977, simulating manual multiplication.

3. Carry Handling: Handle carry after each multiplication.

4. Output Result: Output the result starting from the highest digit.

Code Explanation

1. Array Initialization: The <span>result</span> array is used to store large numbers, initialized to 1 (0! = 1).

2. Factorial Calculation:

• Outer loop: Multiply from 2 to 1977

• Inner loop: Multiply each digit of the current result array by the multiplier, adding the carry

• Handle carry: Distribute the carry to higher digits

Output Result: Output the digits from the highest position in the array.

Considerations

• The result of 1977! is extremely large, with over 5000 digits

• Use an array to simulate manual multiplication to ensure accurate calculations

• The code allocates an array space of 10000 digits, sufficient to store the result of 1977!

This method accurately calculates the factorial of 1977 by simulating large number multiplication using an array.

C++ Basic Tutorial Collection

C++ Basic Resources

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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