Uva-350 Pseudo-Random Numbers
2014-07-26 07:42
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Pseudo-Random Numbers |
applications, including simulation.
A common pseudo-random number generation technique is called the linearcongruential method. If the last pseudo-random number generated was
L,then the next number is generatedby evaluating (
, where
Z is a constantmultiplier, 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 firstrandom number (usually called the
seed) is 4, then we can determine thenext few pseudo-random numbers are follows:
As you can see, the sequence of pseudo-random numbers generated by thistechnique repeats after six numbers. It should be clear that the longestsequence that can be generated usingthis technique is limited by the modulus,
M.
In this problem you will be given sets of values for Z, I,
M, and theseed, L. Each of these will have no more than four digits. For each suchset of values you are to determine the lengthof the cycle of pseudo-random numbers that will be generated. But becareful: 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 theinput 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 numbersbefore 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
题意:
给 L
= (Z * L[n-1] + I) mod M,求L
的循环周期。L不一定从初值处开始循环。Z,I,M,L都是不大于四位的整数。
解析:
直接模拟当相同的数字出现两次,跳出循环。
#include <stdio.h> #include <string.h> const int N = 10010; int flag ; int main() { int Z,L,I,M; int cas = 1; while(scanf("%d%d%d%d",&Z,&I,&M,&L) != EOF) { if(Z==0 && L==0 && I==0 && M==0) break; memset(flag,0,sizeof(flag)); int cut = 0; int tmp = L; while( ++cut ) { tmp = (Z * tmp + I) % M; flag[tmp]++; if(flag[tmp]==2) break; } printf("Case %d: %d\n",cas++,cut-1); } return 0; }
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