So I'm stuck with this problem: Given N, print 2 lines. The first line is the number of digits in N!. In the second line, if N! number of digits >=100 then print its first 100 digits, otherwise print N!. N<=10,000.

I was thinking of using bignum and recursion to find N! but got Time Limit Exceeded.

Thanks for helping me and sorry if you feel uncomfortable.

This is my code:

#include <bits/stdc++.h>
using namespace std;
string del0(const string &s) {
    int i = 0;
    while (i < s.size()-1 && s[i] == '0') i++;
    return s.substr(i);
}

string SUM(string a, string b) {
    if(a.size() < b.size()) swap(a, b);
    while(b.size() < a.size())
        b = "0" + b;
    string res = "";
    int carry = 0;
    for (int i = a.size()-1; i >= 0; i--) {
        int sum = (a[i]-'0') + (b[i]-'0') + carry;
        res = char(sum % 10 + '0') + res;
        carry = sum / 10;
    }
    if(carry)
        res = char(carry + '0') + res;
    return del0(res);
}

string DIF(string a, string b) {
    while(a.size() < b.size())
        a = "0" + a;
    while(b.size() < a.size())
        b = "0" + b;
    string res = "";
    int carry = 0;
    for (int i = a.size()-1; i >= 0; i--) {
        int digitA = a[i] &mdash; '0';
        int digitB = b[i] &mdash; '0';
        int diff = digitA &mdash; digitB &mdash; carry;
        if(diff < 0) {
            diff += 10;
            carry = 1;
        } else {
            carry = 0;
        }
        res = char(diff + '0') + res;
    }
    return del0(res);
}

string MUL(string a, string b) {
    a = del0(a);
    b = del0(b);
    int n = max(a.size(), b.size());
    while(a.size() < n) a = "0" + a;
    while(b.size() < n) b = "0" + b;

    if(n == 1)
        return to_string((a[0]-'0') * (b[0]-'0'));

    int m = n / 2;
    string a1 = a.substr(0, n - m);
    string a0 = a.substr(n - m);
    string b1 = b.substr(0, n - m);
    string b0 = b.substr(n - m);

    string z0 = MUL(a0, b0);
    string z2 = MUL(a1, b1);
    string sumA = SUM(a0, a1);
    string sumB = SUM(b0, b1);
    string z1 = MUL(sumA, sumB);
    string mid = DIF(DIF(z1, z2), z0);
    for (int i = 0; i < 2 * m; i++) z2.push_back('0');
    for (int i = 0; i < m; i++) mid.push_back('0');

    string result = SUM(SUM(z2, mid), z0);
    return del0(result);
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    string s = "1";
    for (int i = 1; i <= n; i++){
        s = MUL(s, to_string(i));
    }
    s = del0(s);
    cout << s.size() << "\n";
    if (s.size() > 100)
        cout << s.substr(0, 100);
    else
        cout << s;

    return 0;
}