How Can We Calculate the Factorial of Arbitrarily Large Numbers and Display All Digits Without External Libraries?

Calculating the Factorial of Arbitrarily Large Numbers with All Digits Shown

Calculating the factorial of arbitrarily large numbers is a classic algorithm problem. However, it poses a unique challenge if we require all the digits of the answer without relying on external libraries. This article delves into a method that effectively addresses this challenge.

The Proposed Solution

The solution revolves around using an array of integers to represent the factorial and performing multiplication as we would when solving manually. Let's examine the code that implements this approach:

int max = 5000;

// Display the factorial
void display(int arr[]) {
  int ctr = 0;
  for (int i = 0; i < max; i++) {
    if (!ctr && arr[i])     ctr = 1;
    if (ctr)
      std::cout << arr[i];
  }
}

// Calculate the factorial
void factorial(int arr[], int n) {
  if (!n) return;
  int carry = 0;
  for (int i = max - 1; i >= 0; --i) {
    arr[i] = (arr[i] * n) + carry;
    carry = arr[i] / 10;
    arr[i] %= 10;
  }
  factorial(arr, n - 1);
}

int main() {
  int *arr = new int[max];
  std::memset(arr, 0, max * sizeof(int));
  arr[max - 1] = 1;
  int num;
  std::cout << "Enter the number: ";
  std::cin >> num;
  std::cout << "factorial of " << num << "is :\n";
  factorial(arr, num);
  display(arr);
  delete[] arr;
  return 0;
}

Explanation

• The arr array represents the factorial.
• factorial() progressively multiplies the factorial by the current number.
• display() ensures leading zeros are omitted.

This solution provides a comprehensive approach to calculating the factorial of large numbers without using external libraries, ensuring all digits of the result are shown.

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