hdu-1005 Number Sequence

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题目链接:

http://acm.hdu.edu.cn/showproblem.php?pid=1005

题目:

Number Sequence

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 170367    Accepted Submission(s): 42027


Problem Description
A number sequence is defined as follows:

f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.

Given A, B, and n, you are to calculate the value of f(n).
 

 

Input
The input consists of multiple test cases. Each test case contains 3 integers A, B and n on a single line (1 <= A, B <= 1000, 1 <= n <= 100,000,000). Three zeros signal the end of input and this test case is not to be processed.
 

 

Output
For each test case, print the value of f(n) on a single line.
 

 

Sample Input
1 1 3
1 2 10
0 0 0
 

 

Sample Output
2
5

题意概括:输入三个数A B n,根据题目给出的公式f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.计算f(n)。

解题思路:我们从公式得出一个结论:无论n有多大,f(n)总为一个不大于7的数,而且,f(n)是根据f(n-1)和f(n-2)得到的,所以f(n)必成一个循环数组,所以这个数组最坏的可能的循环节为7*7=49,并且49一定是这个数组的循环节,所以可以根据打表前49个数据,并对49取余得到相应的答案。这就是抽屉原理,详情请自行百度。

AC代码:

# include <stdio.h>

int a,b;

int f(int x,int y)
{
    int sum;
    sum=(a*x+b*y)%7;
    return sum;
}

int main ()
{
    int i,n,ret,l,m[1010];
    m[1]=1; m[2]=1;
    while(scanf("%d%d%d",&a,&b,&n)!=EOF)
    {
        if(!a&&!b&&!n)
            break;
        for(i=3;i<100;i++)//根据抽屉原理,循环节必在前五十个中 
            m[i]=f(m[i-1],m[i-2]);
            
        printf("%d\n",m[n%49]);
    }
    return 0;
}

 

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