hdu2817 A sequence of numbers

题目链接: 2817 ( A sequence of numbers )

算术序列即等差数列，几何序列即等比数列。

等差数列 \(a_k=a_1+(k-1)\cdot d\) （ \(d\) 为公差）

等比数列 \(a_k=a_1\cdot q^{k-1}\) （ \(q\) 为公比），由于 \(k\) 可能很大，需用快速幂计算。

/**
 * hdu2817 A sequence of numbers
 * We will call a sequence an arithmetic sequence if there is a common difference.
 * A Geometric Sequence is a sequence which the ratio of the common terms is equal.
 */

#include <iostream>
using namespace std;

typedef long long LL;


const int mod = 200907;

LL fastPow(LL a, LL b, LL mod = LLONG_MAX)
{
    a %= mod;
    LL t = 1;
    while (b) {
        if (b&1) t = t*a%mod;
        a = a*a%mod;
        b >>= 1;
    }
    return t%mod;
}

int main()
{
    int N;
    cin >> N;
    while (N--) {
        LL a, b, c;
        int k;
        cin >> a >> b >> c >> k;
        int ans;
        if (b-a == c-b) {
            LL d = b-a, a0 = a-d;
            ans = (a0%mod+d%mod*k) % mod;
        }
        else if (b%a == 0 && c%b == 0 && b/a == c/b) {
            LL q = c/b, a0 = a;
            ans = a0%mod*fastPow(q, k-1, mod)%mod;
        }
        printf("%d\n", ans);
    }
    return 0;
}

模板总结

// 用于快速计算 a^b%mod
// 待试炼
LL fastPow(LL a, LL b, LL mod = LLONG_MAX)
{
    a %= mod;
    LL t = 1;
    while (b) {
        if (b&1) t = t*a%mod;
        a = a*a%mod;
        b >>= 1;
    }
    return t%mod;
}