*杭电1014——Uniform Generator（数学题）

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 5
15 20
63923 99999

Sample Output
3 5 Good Choice

    15        20    Bad Choice 63923     99999    Good Choice

Source
South Central USA 1996

题面上的意思是按给定的公式，seed初始值为0.可以取遍0~MOD-1之内，包括0和MOD-1的所有数，则为Good Choice ，否则为Bad Choice。实质上是求两个数是否互质，如果互质的话，则输出Good Choice，否则输出Bad Choice 。因为将产生的所有数排完序，相邻的两个数的差值为STEP和MOD的最大公约数（为什么？？？？？），要取遍多有数的话，公约数只能为1，所以两数互质。

# include<stdio.h>//辗转相除法求两个数的最大公约数int gcd(int x,int y){    int t;    if(x<y)    {        t=x;x=y;y=t;    }    int r;    while(r=x%y)    {        x=y;        y=r;    }    return y;}int main(){    int STEP,MOD;    while(scanf("%d%d",&STEP,&MOD)!=EOF)    {        if(gcd(STEP,MOD)==1)//互为质数            //printf("%10d%10d    Good Choice\n\n",STEP,MOD);            printf("%10d%10d%-15s\n\n",STEP,MOD,"    Good Choice");        else            //printf("%10d%10d    Bad Choice\n\n",STEP,MOD);            printf("%10d%10d%-14s\n\n",STEP,MOD,"    Bad Choice");    }    return 0;}