hdu 4291 A Short problem(矩阵快速幂)
2015-09-29 00:32
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A Short problem
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 2349 Accepted Submission(s): 821
Problem Description
According to a research, VIM users tend to have shorter fingers, compared with Emacs users.
Hence they prefer problems short, too. Here is a short one:
Given n (1 <= n <= 1018), You should solve for
g(g(g(n))) mod 109 + 7
where
g(n) = 3g(n - 1) + g(n - 2)
g(1) = 1
g(0) = 0
Input
There are several test cases. For each test case there is an integer n in a single line.
Please process until EOF (End Of File).
Output
For each test case, please print a single line with a integer, the corresponding answer to this case.
Sample Input
0 1 2
Sample Output
0 1 42837
Source
2012 ACM/ICPC Asia Regional Chengdu Online
Recommend
liuyiding
题解:每层都有一个循环周期,即循环节。
#include<cstdio> #include<algorithm> #include<cstring> #include<iostream> #include<string> #include<vector> #define ll long long using namespace std; ll n; typedef vector<ll>vec; typedef vector<vec>mat; mat mul(mat &A,mat &B,ll Mod) { mat C(A.size(),vec(B[0].size())); for(int i=0; i<A.size(); i++) { for(int k=0; k<B.size(); k++) { for(int j=0; j<B[0].size(); j++) { C[i][j]=(C[i][j]+A[i][k]*B[k][j])%Mod; } } } return C; } mat pow_mod(mat A,ll x,ll Mod) { mat B(A.size(),vec(A.size())); for(int i=0; i<A.size(); i++) { B[i][i]=1; } while(x>0) { if(x&1)B=mul(B,A,Mod); A=mul(A,A,Mod); x>>=1; } return B; } int main() { //freopen("test.in","r",stdin); ll Mod[3]= {183120,222222224,1000000007}; while(~scanf("%I64d",&n)) { if(n==0||n==1) { printf("%I64d\n",n); continue; } mat A(2,vec(2)); ll ans=0; for(int i=0; i<3; i++) { A[0][0]=3; A[0][1]=1; A[1][0]=1; A[1][1]=0; if(n-1<0)continue; A=pow_mod(A,n-1,Mod[i]); n=A[0][0]%Mod[i]; } printf("%I64d\n",n); } return 0; }
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