高精原理详细精准介绍见：详情

#include<iostream>
using namespace std;

int a[3000] = { 1 }, b, c[3000];  //a[3000] i-1阶乘 //b i //c[3000] i阶乘
int f[3000];              //f[3000] 阶乘累加
int lena = 1, lenc, lenf, temp;
int flag, flag2;

int get_length(int a)
{
	int cnt = 0;
	while (a > 0)
	{
		a /= 10;
		cnt++;
	}
	return cnt;
}

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


	for (int i = 1; i <= n; i++) //i-1 阶乘已保存在 a 中
	{
		flag = 0;
		flag2 = 0;
		for (int j = 0; j < lena; j++)
		{
			c[j] = a[j] * i;
		}
		temp = get_length(i);
		for (int j = 0; j < lena + temp; j++)
		{
			if (c[j] > 10)
			{
				c[j + 1] += c[j] / 10, c[j] %= 10;
				if (j == (lena + temp - 2)) flag = 1;
			}
		}
		if (flag == 1) lenc = lena + temp;
		else lenc = lena + temp - 1;

		for (int j = 0; j < lenc; j++)
		{
			f[j] += c[j];
		}
		for (int j = 0; j < lenc + 1; j++)    //c 的长度一定大于 f //因为 c = i 个 i-1阶乘， f < i-1 个 i-1阶乘
		{
			if (f[j] >= 10)
			{
				f[j + 1] += f[j] / 10, f[j] %= 10;
				if (j == lenc - 1) flag2 = 1;
			}
		}
		if (flag2 == 1) lenf = lenc + 1;
		else lenf = lenc;

		for (int j = 0; j < lenc; j++)
		{
			a[j] = c[j];  ///准备计算 i+1 阶乘
		}
		lena = lenc;
	}
	for (int i = lenf - 1; i >= 0; i--)
	{
		cout << f[i];
	}
	printf("\n");
	return 0;
}