The 2019 Aisa Nanchang First Round Online Programming Contest ——H

Posted 2022-10-08 kayiko

思路：矩阵快速幂+map

代码：

#include<cmath>
#include<algorithm>
#include<cstdio>
#include<map>
const int INF=0x3f3f3f3f;
const int maxn = 1e7+10;
const int mod=998244353;
using namespace std;
typedef long long ll;
map<ll,ll> mp;
ll n;
struct mat

    ll m[4][4];
unit;
mat operator * (const mat &a,const mat& b)

    mat q;
    q.m[1][1] = (a.m[1][1]*b.m[1][1] + a.m[1][2]*b.m[2][1])%mod;
    q.m[1][2] = (a.m[1][1]*b.m[1][2] + a.m[1][2]*b.m[2][2])%mod;
    q.m[2][1] = (a.m[2][1]*b.m[1][1] + a.m[2][2]*b.m[2][1])%mod;
    q.m[2][2] = (a.m[2][1]*b.m[1][2] + a.m[2][2]*b.m[2][2])%mod;
    return q;

mat f,ans;
ll pow_mat(mat a,ll n)

    if(mp.count(n)) return mp[n];
    ll temp = n;
    while(n)
    
        if(n&1)
        
            n--;
            f=f*a;
        
        n>>=1;
        a=a*a;
    
    return mp[temp] = f.m[1][1]%mod;

ll kk[maxn];
int main()

    ll Q,N;
    scanf("%lld%lld",&Q,&N);
    ll tmp=N;
    for(int i=0; i<Q; i++)
    
        f.m[1][1]=1;
        f.m[1][2]=0;
        ans.m[1][1]=3;
        ans.m[1][2]=1;
        ans.m[2][1]=2;
        ans.m[2][2]=0;
        ll nn= pow_mat(ans,tmp-1);
        kk[i] = nn % mod ;
        tmp^=(nn*nn);
    
    ll aa=kk[0];
    for(int i=1; i<Q; i++)
    
        aa^=kk[i];
    
    printf("%lld\n",aa%mod);
    return 0;