UVA408 Uniform Generator

随机数生成器分析

最新推荐文章于 2020-03-14 08:55:45 发布

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本文探讨了计算机模拟中伪随机数生成的方法，特别是通过特定函数形式实现均匀分布的伪随机数。文章分析了如何选择合适的STEP和MOD值来确保生成的序列在0到MOD-1范围内均匀分布，并提供了一个判断是否为好选择的算法。

Uniform Generator

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

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 ( ).

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


题目的意思就是给你两个数　前面是ｓｔｅｐ　后面是　ｍｏｄ　拿第一个样例解释，０　％　５＝０　，然后　３求余５，然后６求余５　类推。。
如果得到了　得到ｍｏｄ　－　１个余数分别是１到ｍｏｄ　－１，没有重复，就是每次加ｓｔｅｐ求余５，可以等概率出现１到　ｍｏｄ－１．。

思路就是如果两个数互质，就可以。。。。。用辗转相除。

ＡＣ代码：


#include<stdio.h>

int main () {
	long long step,mod;
	long long  big,small;
	long long r;
	while (scanf("%lld%lld",&step,&mod) != EOF) {
		r = 1;
		big = step > mod ? step : mod ;
		small = step < mod ? step : mod ;
		while (r != 0) {
		
			r = big % small;
			big = small;
			small = r;
		}
		if(big == 1)
			printf("%10lld%10lld    Good Choice\n",step,mod);
		else 
			printf("%10lld%10lld    Bad Choice\n",step,mod);
		printf("\n");

	}


return 0;
}