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
1 #include <iostream>
2 #include <cstring>
3 #include <set>
4 #include <cstdio>
5
6 using namespace std;
7
8
9 int main(){
10 int step,mod,v=0,n;
11 set<int> s;
12 set<int>::iterator it;
13 while(cin>>step>>mod){
14 printf("%10d%10d",step,mod);
15 n = mod-1;
16 s.insert(v);
17 while(n--){
18 v = (v+step)%mod;
19 it = s.find(v);
20 if(it!=s.end()){
21 break;
22 }
23 s.insert(v);
24 }
25 if(s.size()== mod)printf(" Good Choice\n\n");
26 else printf(" Bad Choice\n\n");
27 s.clear();
28 }
29 }