Problem Description
A numbersequence 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 inputconsists of multiple test cases. Each test case contains 3 integers A, B and non a single line (1 <= A, B <= 1000, 1 <= n <= 100,000,000). Threezeros signal the end of input and this test case is not to be processed.
Output
For each testcase, 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
#include <iostream>
#include <memory.h>
using namespace std;
int f[101];
int main()
{
int A,B,n;
while(cin>>A>>B>>n)
{
if(A==0&&B==0&&n==0)
break;
memset(f,0,sizeof(f));
f[1]=1;f[2]=1;
int i,j,start,end,xxx,flag=0;
for(i=3;i<=n&&!flag;i++)
{
f[i]=(A*f[i-1]%7+B*f[i-2]%7)%7;
for(j=2;j<=i-1;j++)
if(f[i-1]==f[j-1]&&f[i]==f[j])
{ start=j;
end=i;
flag=1;
break;
}
}
xxx=end-start;
if(flag)
cout<<f[start+(n-start)%xxx]<<endl;
else
cout<<f[n]<<endl;
}
return 0;
}
