G - Plant

本文介绍了一个有趣的数学问题:一种特殊三角形植物每年分裂生长的规律,并提供了一种使用快速幂运算来高效计算任意年份朝上三角形植物数量的方法。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

G - Plant
Crawling in process...

Description

Dwarfs have planted a very interesting plant, which is a triangle directed "upwards". This plant has an amusing feature. After one year a triangle plant directed "upwards" divides into four triangle plants: three of them will point "upwards" and one will point "downwards". After another year, each triangle plant divides into four triangle plants: three of them will be directed in the same direction as the parent plant, and one of them will be directed in the opposite direction. Then each year the process repeats. The figure below illustrates this process.

Help the dwarfs find out how many triangle plants that point "upwards" will be in n years.

Input

The first line contains a single integer n(0 ≤ n ≤ 1018) — the number of full years when the plant grew.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cincout streams or the %I64dspecifier.

Output

Print a single integer — the remainder of dividing the number of plants that will point "upwards" in n years by 1000000007(109 + 7).

Sample Input

Input
1
Output
3
Input
2
Output
10

Hint

The first test sample corresponds to the second triangle on the figure in the statement. The second test sample corresponds to the third one.


题意:求出朝上的三角的个数。。。。

思路:1,1+2,1+2+3+4,1+2+3+4+5+6+7+8.。。。。。以此类推,第n个就为(2^n+1)*(2^(n-1))%mod......快速幂一发即可。。。

下面附上代码:

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#define mod 1000000007
using namespace std;
typedef long long ll;
ll Quickmod(ll a,ll b,ll c)
{
	ll ans=1;
	a=a%c;
	while(b)
	{
		if(b&1)
			ans=(ans*a)%c;
		b>>=1;
		a=(a*a)%c;
	}
	return ans;
}
int main()
{
	ll n;
	while(cin>>n)
	{
		if(n==0) puts("1");
		else
		{
			ll res=((Quickmod(2,n,mod)+1)%mod)*(Quickmod(2,n-1,mod)%mod);
			printf("%lld\n",res%mod);
		}
	}
}







评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值