uva 350 Pseudo-Random Numbers

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mb64c0dbd1b47b5 2023-07-26 17:18:37 ©著作权

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uva 350 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!

解题思路：只要注意形成的循环第一个元素不一定是原先的l，没什么难度，但是因为格式WA了两次 orz。再一次证明了格式的重要性。

#include<stdio.h>
#include<string.h>
int main(){
	int cnt2 = 1;
	int num[100000];
	int Z, L, I, M;
	int cnt, l, flag = 0;
	while (scanf("%d %d %d %d\n", &Z, &I, &M, &L) != EOF) {
		if (Z == 0 && M == 0 && I == 0 && L == 0) {break;}
		flag = 0;
		cnt = 0;
		memset(num, 0, sizeof(num));
		num[cnt++] = L;
		for( ; ; ) {
			L = (Z * L + I) % M;
			for (int i = 0; i < cnt; i++) {
				if (L == num[i]) {
					flag = i;
					break;
				}
			}
			if (flag != 0) {
				break;
			}
			num[cnt++] = L;
		}
		printf("Case %d: %d\n", cnt2++, cnt - flag);
	}
	return 0;
}