HDOJ 1005

最新推荐文章于 2020-05-04 19:23:37 发布

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最新推荐文章于 2020-05-04 19:23:37 发布

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分类专栏： algorithm 文章标签： hdoj c++ algorithm

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HDOJ 1005: Number Sequence

problem

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).

solution

At first glance, it was similar to Fibonacci sequence and I then tried to code the same as it. But I received a time litmit exceeded error for the increase value n. So I convinced that this approch doesn’t work well.

After considering this issue deeply, I find the value of f(n) is between 0 and 6, because there is a mod operator at tail. as A and B is two defined numbers, the value depends on two variables f(n-1) and f(n-2). Therefore, f(n) has at most 7*7=49 possible values. So we need to caculate the first 49 values regarded as a period.

#include <iostream>
using namespace std;

int main()
{
    int a, b, n;
    int m[49];
    m[0] = m[1] = 1;
    while (cin >> a >> b >> n, a && b && n)
    {
        for (int i = 2; i < 49; i++)
        {
            m[i] = (a * m[i - 1] + b * m[i - 2]) % 7;
        }
        cout << m[(n - 1) % 49] << endl;
    }
    return 0;
}