数论：zoj 1526 Big Number

【转】http://blog.youkuaiyun.com/wmbol/article/details/5454093

 

∵N! = N * (N - 1) * ( N - 2)····*2

∴log(N!) = log(N) + log(N - 1) + ······ + log2

所以阶乘的位数n = 1 + log(N) + log(N - 1) + ······ + log2;

 

/*
 * 1526.cpp
 *
 *  Created on: Apr 2, 2010
 *      Author: wyy
 */
#include<iostream>
#include<cmath>
using namespace std;

int main()
{
	int T, num;
	double ans;
	cin >> T;
	while(T--)
	{
		cin >> num;
		ans = 0.0;
		for(int i = 2; i != num + 1; ++i)
			ans += log10(1.0 * i);
		cout << (int)ans + 1 << endl;
	}
}