Codeforces--630C--Lucky Numbers（快速幂）



C -
Lucky Numbers

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Time Limit:500MS    
Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

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Description

The numbers of all offices in the new building of the Tax Office of IT City will have lucky numbers.

Lucky number is a number that consists of digits 7 and
8 only. Find the maximum number of offices in the new building of the Tax Office given that a door-plate can hold a number not longer than
n digits.

Input

The only line of input contains one integer n (1 ≤ n ≤ 55) — the maximum length of a number that a door-plate can hold.

Output

Output one integer — the maximum number of offices, than can have unique lucky numbers not longer than
n digits.

Sample Input

Input

2

Output

6

数字中只含有7或者8的成为Lucky Numbers，问n位以内的数字有多少个Lucky Numbers，总数应该就是2+2^2+....+2^n,数学公式变形之后就是2^(n+1)-2个，n+1可能比较大，所以快速幂解决

#include<iostream>
using namespace std;
#define LL long long
LL  p(LL x, LL n)
{
    LL pw = 1;
    while (n > 0)
    {
        if (n & 1)
            pw *= x;
        x *= x;
        n >>= 1;
    }
    return pw;
}
int main()
{
    LL n;
    LL num;
    cin>>n;
    cout<<p(2,n+1)-2<<endl;
    return 0;
}