| Power of Cryptography |
Background
Current work in cryptography involves (among other things) large prime numbers and computing powers of numbers modulo functions of these primes. Work in this area has resulted in the practical use of results from number theory and other branches of mathematics once considered to be of only theoretical interest.
This problem involves the efficient computation of integer roots of numbers.
The Problem
Given an integer 
and an integer 
you
are to write a program that determines 
, the positive 
root
of p. In this problem, given such integers n and p, p will always be of the form 
for an integer k (this
integer is what your program must find).
The Input
The input consists of a sequence of integer pairs n and p with each integer on a line by itself. For all such pairs 
,
and
there exists an integer k, 
such that 
.
The Output
For each integer pair n and p the value should be printed,
i.e., the number k such that .
Sample Input
2 16 3 27 7 4357186184021382204544
Sample Output
4 3 1234
p不是很大，可以用double(最大1.8*10^308)存儲。
k^n=p,經變換有k=p^(1/n)，可用math.h中的pow()函數，或
對兩邊取對數，有n*ln(k)=ln(p) => ln(k)=ln(p)/n =>k=e^(ln(p)/n)，求ln(p)，可以math.h中的log()函數
或者複雜一點用 二分+高精度
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
double n,p;
while(cin>>n>>p)
cout<<(int)(pow(p,1.0/n)+0.5)<<endl;//在貌似poj的數據數據較水，注意精度;
return 0;
}
#include <iostream>
#include <cmath>
using namespace std;
int main(int argc, char **argv)
{
double n,p;
while(cin>>n>>p)
cout<<(int)(exp(log(p)/n)+0.5)<<endl;
return 0;
}