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
问题简述:
题目要求伪随机数,给了step和mod,利用公式 seed(x+1) = [ seed(x) + STEP ] % MOD看能否求得从0到mod-1的伪随机数。若能则输出Good Choice,否则输出Bad Choice。注意输出格式:1到10列输出step,11到20列输出mod,25列输出Good Choice或者Bad Choice,每输出一行要空一行。
分析:方法一:从给的例子分析得到,如果step是mod的因子,那么就不能产生题目所要求的伪随机数。
#include<iostream>
#include<stdio.h>
#include<algorithm>
using namespace std;
int gcd(int a,int b){
return b==0?a:gcd(b,a%b);
}
int main(){
int step,modn;
while(~scanf("%d%d",&step,&modn)){
if(gcd(step,modn)==1)
printf("%10d%10d Good Choice\n\n",step,modn);
else
printf("%10d%10d Bad Choice\n\n",step,modn);
}
return 0;
}
数论的方法还不太理解