UVAOJ 350 基础题 伪随机数 数论

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=5&page=show_problem&problem=286

 Pseudo-Random Numbers 

Computers normally cannot generate really random numbers, but frequently are used to generate sequences of pseudo-random numbers. These are generated by some algorithm, but appear for all practical purposes to be really random. Random numbers are used in many applications, including simulation.

 

A common pseudo-random number generation technique is called the linear congruential method. If the last pseudo-random number generated was L, then the next number is generated by evaluating (  , where Z is a constant multiplier, I is a constant increment, and M is a constant modulus. For example, suppose Z is 7, I is 5, and M is 12. If the first random number (usually called the seed) is 4, then we can determine the next few pseudo-random numbers are follows:

 

 

As you can see, the sequence of pseudo-random numbers generated by this technique repeats after six numbers. It should be clear that the longest sequence that can be generated using this technique is limited by the modulus, M.

 

In this problem you will be given sets of values for Z, I, M, and the seed, L. Each of these will have no more than four digits. For each such set of values you are to determine the length of the cycle of pseudo-random numbers that will be generated. But be careful: the cycle might not begin with the seed!

 

Input

Each input line will contain four integer values, in order, for Z, I, M, and L. The last line will contain four zeroes, and marks the end of the input data. L will be less than M.

 

Output

For each input line, display the case number (they are sequentially numbered, starting with 1) and the length of the sequence of pseudo-random numbers before the sequence is repeated.

 

Sample Input

 

7 5 12 4
5173 3849 3279 1511
9111 5309 6000 1234
1079 2136 9999 1237
0 0 0 0

 

Sample Output

 

Case 1: 6
Case 2: 546
Case 3: 500
Case 4: 220

#include<iostream>
#include<cmath>
#include<cstdio>
#include<sstream>
#include<cstdlib>
#include<string>
#include<string.h>
#include<cstring>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<ctime>
#include<bitset>
#include<cmath>
#define eps 1e-6
#define INF 0x3f3f3f3f
#define PI acos(-1.0)
#define ll __int64
#define LL long long
#define lson l,m,(rt<<1)
#define rson m+1,r,(rt<<1)|1
//#define M 1000000007
using namespace std;
//以上内容直接无视~

int is_used[11000];
int main()
{int T=0,Z,I,M,L,ans,l;
   //freopen("in.txt","r",stdin);
   //freopen("out.txt","w",stdout);
while(cin>>Z>>I>>M>>L,Z||I||M||L)
{
memset(is_used,0,sizeof(is_used));
 L=(Z*L+I)%M;
 ans=0;
while(is_used[L]==0)
{is_used[L]=1;
L=(Z*L+I)%M;
ans++;
}
cout<<"Case "<<++T<<": "<<ans<<endl;
}
return 0;
}

 

 

模拟1下第一位可能不能循环所以。。。从第二位计算起就可以了~memset(a,0,sizeof(a)) 中间是0。。。这么次犯了这个错。。。下次就记住了。。。