杭电 1014 Uniform Generator

这题嘛，没有做，直接复制以前的代码过来，就提交了，顺利通过。

后来又看了一下。

这题我的猜想是，伪随机数在一个重复周期内的总和必然小于或等于 0 到 mod-1 的所有整数之和。（这个猜想也不知是否正确，欢迎有知情人士指出）

/* THE PROGRAM IS MADE BY PYY */
/*
   http://acm.hdu.edu.cn/showproblem.php?pid=1014
   Uniform Generator
   Author: pyy
   Begin : 16:00
   End   : 17:00
*/

#include <iostream>
#include <iomanip>
using namespace std;
inline int prand();
int seed, step, mod;
int main()
{
	int head, tail, decreasor = 0;
	while (cin >> step >> mod && mod) {
		decreasor = 0;
		seed = 0;

		// 第一个随机数
		head = prand();

                // 在 0 到 mod-1 的范围内，所以整数的总和
		for (int i = 0; i < mod; i++)
			decreasor += i;

                // 减去第一个随机数
		decreasor = decreasor - head;

                // 如果是good choice，decreasor 将在第二个重复周期前减至 0
		while (head != (tail = prand())) {
			decreasor -= tail;
		}

		cout << setw(10) << step
		     << setw(10) << mod
		     << "    ";
		if (decreasor)
			cout << "Bad Choice";
		else
			cout << "Good Choice";
		cout << endl << endl;
	}
	return 0;
}

// 随机数产生器
inline int prand()
{
	seed = (seed + step) % mod;
	return seed;
}

------------------------------ 原题如下 -------------------------------------------

Uniform Generator

Time Limit: 2000/1000 MS (Java/Others)Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5562Accepted Submission(s): 2228

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

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