JOJ-2033-Towers of Hanoi

Tomorrow is Kate's birthday,  Kate is a lovely girl aged 20. This Contest  is held for her birthday and I want everyone will be happy today. My name is sea .I'm not so good at English and Programming. But when I know that it is possible to have a personal contest on JOJ. I want to have a try. Just for her.

Kate : Wish you beauty and healthy forever

happy birthday!

Do you know the game "Towers of Hanoi"?  It is a very famous game. But people stopped moving discs from peg to peg after they know the number of steps needed to complete the entire task !  Kate loves the game. She want to know how many times she has to  move the disks at least to complete the game?

As we all know , for n disks the game takes 2^n-1 moves at least. But kate want to know the exact numble. Sea want to tell her ,but he is poor at math. So he want to write a program to help her.

Input Specification

Each line contains a numbe 'N' (0 <= N <= 500). N stand for the number of the disks.

Output Specification

Just output the least time that kate has to move the disks to complete the game. one per line.

Sample Input

7
10

Sample Output

127
1023

#include<iostream>
using namespace std;

const int MAX=501;
const int D=1000000000;
const int width=9;
void main()
{
	int fact[MAX][17]={0};//151/9==16.777
	int len[MAX]={0};
	fact[0][0]=1;
	len[0]=1;
	for(int i=1;i<MAX;++i)
	{
		int c=0;
		int idx=0;
		for(idx=0;idx<len[i-1];++idx)
		{
			int t=fact[i-1][idx]*2+c;
			fact[i][idx]=t%D;
			c=t/D;
		}
		if(c>0)
		{
			len[i]=len[i-1]+1;
			fact[i][idx]=c;
		}
		else
			len[i]=len[i-1];
	}
	int n;
	while(cin>>n)
	{
		if(len[n]==1)
		{
			cout<<fact[n][len[n]-1]-1<<endl;
			continue;
		}
		cout<<fact[n][len[n]-1];
		for(int i=len[n]-2;i>0;--i)
		{
				cout.width(width);
				cout.fill('0');
				cout<<fact[n][i];
		}
		cout.width(width);
		cout.fill('0');
		cout<<fact[n][0]-1;
		cout<<endl;
	}
}

　
　

說簡單點就是用數組計算2的乘冪　兩點教訓：第一，要計算2^0。在這道題裏可能很自然考慮到，然而在一道計算N!的程
序可難住了我，鬱悶了好久。實際上這個程序就是用計算N!的程序改。第二，不要以爲加法比乘法快。開始我是用加法，
用時0.01秒，而用乘法是0.00秒，做移位運算畢竟要比加法快多了。