poj2109 Power of Cryptography
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Description
This problem involves the efficient computation of integer roots of numbers.
Given an integer n>=1 and an integer p>= 1 you have to write a program that determines the n th positive root of p. In this problem, given such integers n and p, p will always be of the form k to the nth. power, for an integer k (this integer is what your program must find).
Input
Output
Sample Input
2 163 277 4357186184021382204544
Sample Output
431234
这题可以用double型做,类型 长度 (bit) 有效数字 绝对值范围
float 32 6~7 10^(-37) ~ 10^38
double 64 15~16 10^(-307) ~10^308
long double 128 18~19 10^(-4931) ~ 10 ^ 4932
因为k^n=p,所以k=p^(1.0/n);
#include<stdio.h>#include<math.h>int main(){double n,m;while(scanf("%lf%lf",&n,&m)!=EOF) { printf("%.0f\n",pow(m,(1.0)/n)); } return 0;}
也可以用二分法做
#include<stdio.h>#include<string.h>#include<math.h>#define eps 1e-8int main(){double n,m,i,j,h,temp;int l,r,mid;while(scanf("%lf%lf",&n,&m)!=EOF){r=1000000000;l=1;while(l<=r){mid=(l+r)/2;temp=pow(mid,n);//printf("%lf %lf\n",temp,pow(mid,n));if(fabs(pow(mid,n)-m)<eps){printf("%d\n",mid);break; //因为这里求的是一个确定的整数,所以可以直接输出}else if(pow(mid,n)<m){l=mid+1;}else if(pow(mid,n)>m){r=mid-1;}}}return 0;}
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