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  • hdu6198 number number number(递推公式黑科技)

    number number number

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
    Total Submission(s): 192    Accepted Submission(s): 126


    Problem Description
    We define a sequence F:

     F0=0,F1=1;
     Fn=Fn1+Fn2 (n2).

    Give you an integer k, if a positive number n can be expressed by
    n=Fa1+Fa2+...+Fak where 0a1a2ak, this positive number is mjfgood. Otherwise, this positive number is mjfbad.
    Now, give you an integer k, you task is to find the minimal positive mjfbad number.
    The answer may be too large. Please print the answer modulo 998244353.
     

    Input
    There are about 500 test cases, end up with EOF.
    Each test case includes an integer k which is described above. (1k109)
     

    Output
    For each case, output the minimal mjfbad number mod 998244353.
     

    Sample Input
    1
     

    Sample Output
    4
     

    Source
     

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    Statistic | Submit | Discuss | Note

    题意:斐波拉契数列,求不能由这些k个斐波那契数列数组成的最小整数

    思路:先手写找规律,再用黑科技代码模板

    //递推公式黑科技
    #include<bits/stdc++.h>
    using namespace std;
    #define X first
    #define Y second
    #define PB push_back
    #define MP make_pair
    #define MEM(x,y) memset(x,y,sizeof(x));
    #define bug(x) cout<<"bug"<<x<<endl;
    typedef long long ll;
    typedef pair<int,int> pii;
    using namespace std;
    const int maxn=1e3+10;
    const int mod=998244353;
    ll powmod(ll a,ll b){
        ll res=1;a%=mod;
        assert(b>=0);
        for(;b;b>>=1){
            if(b&1)res=res*a%mod;a=a*a%mod;
        }
        return res;
    }
    // head
    namespace linear_seq {
        const int N=10010;
        ll res[N],base[N],_c[N],_md[N];
        vector<int> Md;
        void mul(ll *a,ll *b,int k) {
            for(int i=0;i<k+k;i++) _c[i]=0;
            for(int i=0;i<k;i++)
                if (a[i])
                    for(int j=0;j<k;j++) _c[i+j]=(_c[i+j]+a[i]*b[j])%mod;
            for (int i=k+k-1;i>=k;i--)
                if (_c[i])
                    for(int j=0;j<Md.size();j++)
                        _c[i-k+Md[j]]=(_c[i-k+Md[j]]-_c[i]*_md[Md[j]])%mod;
            for(int i=0;i<k;i++) a[i]=_c[i];
        }
        int solve(ll n,vector<int> a,vector<int> b) {
        // a 系数 b 初值 b[n+1]=a[0]*b[n]+...
            ll ans=0,pnt=0;
            int k=a.size();
            assert(a.size()==b.size());
            for(int i=0;i<k;i++) _md[k-1-i]=-a[i];_md[k]=1;
            Md.clear();
            for(int i=0;i<k;i++) if (_md[i]!=0) Md.push_back(i);
            for(int i=0;i<k;i++) res[i]=base[i]=0;
            res[0]=1;
            while ((1ll<<pnt)<=n) pnt++;
            for (int p=pnt;p>=0;p--) {
                mul(res,res,k);
                if ((n>>p)&1) {
                    for (int i=k-1;i>=0;i--) res[i+1]=res[i];res[0]=0;
                    for(int j=0;j<Md.size();j++) res[Md[j]]=(res[Md[j]]-res[k]*_md[Md[j]])%mod;
                }
            }
            for(int i=0;i<k;i++) ans=(ans+res[i]*b[i])%mod;
            if (ans<0) ans+=mod;
            return ans;
        }
        vector<int> BM(vector<int> s) {
            vector<int> C(1,1),B(1,1);
            int L=0,m=1,b=1;
            for(int n=0;n<s.size();n++) {
                ll d=0;
                for(int i=0;i<L+1;i++) d=(d+(ll)C[i]*s[n-i])%mod;
                if (d==0) ++m;
                else if (2*L<=n) {
                    vector<int> T=C;
                    ll c=mod-d*powmod(b,mod-2)%mod;
                    while (C.size()<B.size()+m) C.PB(0);
                    for(int i=0;i<B.size();i++) C[i+m]=(C[i+m]+c*B[i])%mod;
                    L=n+1-L; B=T; b=d; m=1;
                } else {
                    ll c=mod-d*powmod(b,mod-2)%mod;
                    while (C.size()<B.size()+m) C.PB(0);
                    for(int i=0;i<B.size();i++) C[i+m]=(C[i+m]+c*B[i])%mod;
                    ++m;
                }
            }
            return C;
        }
        int gao(vector<int> a,ll n) {
            vector<int> c=BM(a);
            c.erase(c.begin());
            for(int i=0;i<c.size();i++) c[i]=(mod-c[i])%mod;
            return solve(n,c,vector<int>(a.begin(),a.begin()+c.size()));
        }
    };
    
    int main(){
        ll t,n;
    //    cin>>t;
        while(cin>>n){
            cout<<(linear_seq::gao(vector<int>{5,13,34,89},n-1)%mod-1)%mod<<endl;
        }
    }



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  • 原文地址:https://www.cnblogs.com/bryce1010/p/9387252.html
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