Uva 113 Power of Cryptography
| 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 ofp. In this problem, given such integers n and p, p will always be of the form for an integerk (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 integerk, such that .
The Output
For each integer pair n and p the value should be printed, i.e., the numberk such that .
Sample Input
2 16 3 27 7 4357186184021382204544
Sample Output
4 3 1234
题目大意：
,
计算
#include<stdio.h>
#include<math.h>
int main(void)
{
double n, p;
while(scanf("%lf%lf", &n, &p) != EOF)
{
printf("%.0lf\n", pow(p, 1/n));
}
return 0;
}
1. 范围
float和double的范围是由指数的位数来决定的。
float的指数位有8位，而double的指数位有11位，分布如下：
float：
1bit（符号位） 8bits（指数位）23bits（尾数位）
double：
1bit（符号位） 11bits（指数位）52bits（尾数位）
于是，float的指数范围为-127~+128，而double的指数范围为-1023~+1024，并且指数位是按补码的形式来划分的。
其中负指数决定了浮点数所能表达的绝对值最小的非零数；而正指数决定了浮点数所能表达的绝对值最大的数，也即决定了浮点数的取值范围。
float的范围为-2^128 ~+2^128，也即-3.40E+38 ~ +3.40E+38；double的范围为-2^1024 ~+2^1024，也即-1.79E+308 ~ +1.79E+308。
2. 精度
float和double的精度是由尾数的位数来决定的。浮点数在内存中是按科学计数法来存储的，其整数部分始终是一个隐含着的“1”，由于它是不变的，故不能对精度造成影响。
float：2^23 =8388608，一共七位，这意味着最多能有7位有效数字，但绝对能保证的为6位，也即float的精度为6~7位有效数字；
double：2^52 =4503599627370496，一共16位，同理，double的精度为15~16位。