Pro.ID21179 TitlePsuedo-Random Numbers Title链接http://10.20.2.8/oj/exercise/problem?problem_id=21179 AC0 Submit0 Ratio- 时间&空间限制描述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 (Z x L + I) mod M, 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: Last Random Number, L | (Z×L+I) | Next Random Number, (Z×L+I) mod M ----------------------|---------|---------------------------------- 4 | 33 | 9 9 | 68 | 8 8 | 61 | 1 1 | 12 | 0 0 | 5 | 5 5 | 40 | 4 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! 输入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. 输出Description 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 (Z x L + I) mod M, 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: Last Random Number, L | (Z×L+I) | Next Random Number, (Z×L+I) mod M ----------------------|---------|---------------------------------- 4 | 33 | 9 9 | 68 | 8 8 | 61 | 1 1 | 12 | 0 0 | 5 | 5 5 | 40 | 4 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 Source 样例输入7 5 12 4
5173 3849 3279 1511
9111 5309 6000 1234
1079 2136 9999 1237
0 0 0 0 样例输出Case 1: 6
Case 2: 546
Case 3: 500
Case 4: 220 作者 |
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