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  1. Practice
  2. Algorithms
  3. Implementation
  4. Extra Long Factorials
  5. Discussions

Extra Long Factorials

  • tsuda_kageyu + 7 comments

    It's beyond my capacity to implement a complete BigInteger like class in C++, but I did this:

    #include <vector>
#include <iostream>

using namespace std;

int main() {
    int n;
    cin >> n;

    vector<int> d;
    d.push_back(1);
    
    for (int i = 2; i <= n; ++i) {
        for (auto it = d.begin(); it != d.end(); ++it)
            *it *= i;
        
        for (size_t j = 0; j < d.size(); ++j) {
            if (d[j] < 10)
                continue;

            if (j == d.size() - 1)
                d.push_back(0);
            
            d[j + 1] += d[j] / 10;
            d[j] %= 10;
        }
    }

    for (auto it = d.rbegin(); it != d.rend(); ++it)
        cout << *it;
    
    return 0;
}
    • VictoriaB + 0 comments

      Wow. This is nice!

    • aaron_coltrane + 0 comments

      Almost same as me

    • ashekhar + 1 comment

      Could you please explain the approach and why we are doing: d[j + 1] += d[j] / 10; d[j] %= 10;

      • squirrelwhisky + 0 comments

        He used the math multiplication method we used everyday when it's come to multiply two more-than-one-digit number: abc * ef = abc * e * 10 + abc * f . His approach is based on that but he's done it reversely. The way he did it is really clever!

    • clivic + 1 comment

      This solution is like mimicking the multiplication process in math, in other words, how you multiply 12 by 5: 

      first, 2 (in 12) by 5 is 10. Because 10/10 == 1, we got a 1 here.
second, 1 (in 12) by 5. Because we got a 1 before, we get 5+1 == 6 here.

      If you write it down on a paper following this code, you will get it.

      • squirrelwhisky + 1 comment

        Thank for you explaination. Appreciate that!

        • nishu_iitadv + 0 comments

          u should upvote to show ur appreciation atleast

    • clivic + 1 comment

      A commented C++ version using the idea of "arithmatic carry" (the same idea this example used) is as following:

      void extraLongFactorials(int n) {
    if (n == 1) {
        cout << 1 << endl;
        return;
    }

    vector<int> digits(1, 1);
    for (int curr(2); curr <= n; ++curr) {
        auto digit_count = digits.size();

        // Every digit times the number.
        for (int i(0); i < digit_count; ++i) {
            digits[i] *= curr;
        }

        // From the units to tenths, hundreds...
        // Perform the carry.
        for (int i(0); i < digit_count; ++i) {
            auto carry = digits[i] / 10;
            digits[i] = digits[i] % 10;
            if (i != digit_count - 1) {
                // Add the carry to the next digit.
                digits[i + 1] += carry;
            } else {
                // New leftmost digit(s).
                if (carry > 0) {
                    int & remaining(carry);
                    do {
                        auto digit = remaining % 10;
                        remaining /= 10;
                        digits.push_back(digit);
                    } while (remaining > 0);
                }
            }
        }
    }

    // Print out the digits.
    for (auto it = digits.rbegin(); it != digits.rend(); ++it) {
        cout << *it;
    }
}
      • mailtokks290199 + 0 comments

        can you explain what is happening here

    • jtsaur + 0 comments
      [deleted]
    • ken771209 + 0 comments

      great idea