杭电1014Uniform Generator

题目：

Problem Description

Computer simulations often require random numbers. One way to generate pseudo-random numbers is via a function of the form

seed(x+1) = [seed(x) + STEP] % MOD

where '%' is the modulus operator.

Such a function will generate pseudo-random numbers (seed) between 0 and MOD-1. One problem with functions of this form is that they will always generate the same pattern over and over. In order to minimize this effect, selecting the STEP and MOD values carefully can result in a uniform distribution of all values between (and including) 0 and MOD-1.

For example, if STEP = 3 and MOD = 5, the function will generate the series of pseudo-random numbers 0, 3, 1, 4, 2 in a repeating cycle. In this example, all of the numbers between and including 0 and MOD-1 will be generated every MOD iterations of the function. Note that by the nature of the function to generate the same seed(x+1) every time seed(x) occurs means that if a function will generate all the numbers between 0 and MOD-1, it will generate pseudo-random numbers uniformly with every MOD iterations.

If STEP = 15 and MOD = 20, the function generates the series 0, 15, 10, 5 (or any other repeating series if the initial seed is other than 0). This is a poor selection of STEP and MOD because no initial seed will generate all of the numbers from 0 and MOD-1.

Your program will determine if choices of STEP and MOD will generate a uniform distribution of pseudo-random numbers.

 

 

Input

Each line of input will contain a pair of integers for STEP and MOD in that order (1 <= STEP, MOD <= 100000).

 

 

Output

For each line of input, your program should print the STEP value right- justified in columns 1 through 10, the MOD value right-justified in columns 11 through 20 and either "Good Choice" or "Bad Choice" left-justified starting in column 25. The "Good Choice" message should be printed when the selection of STEP and MOD will generate all the numbers between and including 0 and MOD-1 when MOD numbers are generated. Otherwise, your program should print the message "Bad Choice". After each output test set, your program should print exactly one blank line.

 

 

Sample Input

3 515 2063923 99999

 

 

Sample Output

         3         5    Good Choice        15        20    Bad Choice     63923     99999    Good Choice

 

 

解题分析：

根据随机数的产生式，，如果step和mod的最大公约数为1，则会产生从0到mod-1之内的所有数。

证明：如果step和mod有非1的公约数，step%mod的结果是0或是公约数，如果解果是公约数，则其后的结果每次递增公约数的梯度，所以取不到所有的数。

 

代码：

#include<iostream>#include<cmath>#include<iomanip>using namespace std;//判断函数，判断两个数的最大公约数是否为1bool Isprim(long m,long n)   {long temp;if(m<n){temp=m;m=n;n=temp;}if(m%n==0){if(n==1)return true;elsereturn false;}while(m%n){long t=m%n;m=n;n=t;}if(n==1)return true;else return false;cout<<endl;}int main(){long step,mod;while(cin>>step>>mod){if(Isprim(step,mod))cout<<setw(10)<<step<<setw(10)<<mod<<"    "<<"Good Choice"<<endl;elsecout<<setw(10)<<step<<setw(10)<<mod<<"    "<<"Bad Choice"<<endl;cout<<endl;}return 0;}

 

题目总结：

掌握数据运算的规律，总结规律！