HDU——1005Number Sequence(模版題 二維矩陣快速冪+操作符過載)
阿新 • • 發佈:2019-01-29
Number Sequence
f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.
Given A, B, and n, you are to calculate the value of f(n). Input The input consists of multiple test cases. Each test case contains 3 integers A, B and n on a single line (1 <= A, B <= 1000, 1 <= n <= 100,000,000). Three zeros signal the end of input and this test case is not to be processed. Output For each test case, print the value of f(n) on a single line. Sample Input 1 1 3 1 2 10 0 0 0 Sample Output 2 5
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 148003 Accepted Submission(s): 35976
f(1) = 1, f(2) = 1, f(n) = (A * f(n - 1) + B * f(n - 2)) mod 7.
Given A, B, and n, you are to calculate the value of f(n). Input The input consists of multiple test cases. Each test case contains 3 integers A, B and n on a single line (1 <= A, B <= 1000, 1 <= n <= 100,000,000). Three zeros signal the end of input and this test case is not to be processed. Output For each test case, print the value of f(n) on a single line. Sample Input 1 1 3 1 2 10 0 0 0 Sample Output 2 5
最近學了簡單一點的二維的矩陣快速冪,發現十分好用。於是又找以前做過的遞推式的題目。大部分人做法應該是暴力打表發現迴圈節規律取前49項即可,但是這題也很適合用矩陣來加速求需要的某一項。只要會矩陣或者行列式的乘法就可以。另外為了寫起來自然美觀把函式改成了操作符過載。
(矩陣寫法可以有很多種,F1,F2位置互換、橫著寫或者更離譜也行,只要能得出正確結果即可)
若求出遞推式後只要注意一下指數到底應該是n還是n-1還是n-2,然後稍微特判一下,其他應該沒啥問題。
#include<iostream> #include<algorithm> #include<cstdlib> #include<sstream> #include<cstring> #include<cstdio> #include<string> #include<deque> #include<stack> #include<cmath> #include<queue> #include<set> #include<map> using namespace std; typedef long long LL; #define INF 0x3f3f3f3f struct mat { int pos[2][2]; mat(){memset(pos,0,sizeof(pos));} }; inline mat operator*(const mat &a,const mat &b) { mat c; for (int i=0; i<2; i++) { for (int j=0; j<2; j++) { for (int k=0; k<2; k++) { c.pos[i][j]+=(a.pos[i][k]*b.pos[k][j])%7; } } } return c; } inline mat operator^(mat a,LL b) { mat r;r.pos[0][0]=r.pos[1][1]=1; mat bas=a; while (b!=0) { if(b&1) r=r*bas; bas=bas*bas; b>>=1; } return r; } int main(void) { ios::sync_with_stdio(false); int n,a,b; while (cin>>a>>b>>n&&(a||b||n)) { if(n==1) { cout<<1<<endl; continue; } mat one,t; one.pos[0][0]=one.pos[1][0]=1; t.pos[0][0]=a,t.pos[0][1]=b;t.pos[1][0]=1; t=t^(n-2); one=t*one; cout<<one.pos[0][0]%7<<endl; } return 0; }