Codeforces--630C--Lucky Numbers(快速幂)
2024-09-06 09:06:27
C -
Lucky Numbers
Lucky Numbers
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Time Limit:500MS
Memory Limit:65536KB 64bit IO Format:%I64d & %I64u
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;
}
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