HDU 1014 G题

Uniform Generator

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 26820 Accepted Submission(s): 10629

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

这题代码不难，关键是理解题目：seed(x+1) = [seed(x) + STEP] % MOD 这个公式是非常重要的，首先定义seed(0)等于零，然后使用公式递推，如何判断是Bad Choice和Good Choice在于0到mod-1每个数都存在与之相等的种子，写入代码就是循环的次数是否与mod相等，还有要注意输出格式，10个间距，字母前有4个空格

AC代码：

#include <stdio.h>
int seed[1000005]={0};
int main (){
    long long   i,step,mod;
    while (scanf("%I64d%I64d",&step,&mod)!=EOF) {
        i=0;
        do{

            seed[i+1]=(seed[i]+step)%mod;
            i++;
        }while(seed[i]);
        if(i==mod)
           printf("%10I64d%10I64d    Good Choice\n\n",step,mod);
        else
           printf("%10I64d%10I64d    Bad Choice\n\n",step,mod);
    }
    return 0;
}