• The 2019 Asia Nanchang First Round Online Programming Contest The Nth Item


    The Nth Item
    思路:
    先用特征根法求出通向公式,然后通向公式中出现了(sqrt{17}),这个可以用二次剩余求出来,然后可以O((log(n)))求出。
    但是还不够,我们先对(n)欧拉降幂,然后求base为(sqrt{1e9})的快速幂,预处理一些东西,就可以类似O(1)求出了。
    代码:

    #pragma GCC optimize(2)
    #pragma GCC optimize(3)
    #pragma GCC optimize(4)
    #include<bits/stdc++.h>
    using namespace std;
    #define y1 y11
    #define fi first
    #define se second
    #define pi acos(-1.0)
    #define LL long long
    //#define mp make_pair
    #define pb push_back
    #define ls rt<<1, l, m
    #define rs rt<<1|1, m+1, r
    #define ULL unsigned LL
    #define pll pair<LL, LL>
    #define pli pair<LL, int>
    #define pii pair<int, int>
    #define piii pair<pii, int>
    #define pdd pair<double, double>
    #define mem(a, b) memset(a, b, sizeof(a))
    #define debug(x) cerr << #x << " = " << x << "
    ";
    #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    //head
    
    const int MOD = 998244353;
    const LL fsqrt17 = 473844410;
    const LL sqrt17 = MOD-fsqrt17;
    const LL inv2 = (MOD+1)/2;
    const LL invsqrt17 = 438914993;
    const int N = 4e4 + 5;
    LL p[N], pp[N], P[N], PP[N], q, n;
    LL f(LL n) {
        return (p[n%(N-1)]*P[n/(N-1)])%MOD;
    }
    LL F(LL n) {
        return (pp[n%(N-1)]*PP[n/(N-1)])%MOD;
    }
    int main() {
        p[0] = pp[0] = 1;
        for (int i = 1; i < N; ++i) p[i] = p[i-1]*(3+sqrt17)%MOD*inv2%MOD, pp[i] = pp[i-1]*(3+fsqrt17)%MOD*inv2%MOD;
        P[0] = PP[0] = 1;
        for (int i = 1; i < N; ++i) {
            P[i] = P[i-1]*p[N-1]%MOD;
            PP[i] = PP[i-1]*pp[N-1]%MOD;
        }
        scanf("%lld %lld", &q, &n);
        LL res = 0;
        for (int i = 1; i <= q; ++i) {
            LL ans = -(f(n%(MOD-1))-F(n%(MOD-1)))*invsqrt17%MOD;
            ans = (ans + MOD) % MOD;
            res ^= ans;
            n ^= ans*ans;
        }
        printf("%lld
    ", res);
        return 0;
    }
    
    
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  • 原文地址:https://www.cnblogs.com/widsom/p/11520233.html
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