hpuvj【3070】Fibonacci(矩阵快速幂求模)
2017-08-14 18:20
295 查看
Fibonacci
Submit Status
Description
In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of
the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
An alternative formula for the Fibonacci sequence is
.
Given an integer n, your goal is to compute the last 4 digits of Fn.
Input
The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.
Output
For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).
Sample Input
Sample Output
Hint
As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by
.
Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:
.
Source
Stanford Local 2006
一道涉及到矩阵快速幂的知识的题 本来快速幂没学好 今天还专门说这个了,所以 看了半天才略懂了 一些,代码如下:
Fibonacci
Submit Status
Description
In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of
the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
An alternative formula for the Fibonacci sequence is
.
Given an integer n, your goal is to compute the last 4 digits of Fn.
Input
The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.
Output
For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).
Sample Input
Sample Output
Hint
As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by
.
Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:
.
Source
Stanford Local 2006
Time Limit: 1000MS | Memory Limit: 65536KB | 64bit IO Format: %I64d & %I64u |
Description
In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of
the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
An alternative formula for the Fibonacci sequence is
.
Given an integer n, your goal is to compute the last 4 digits of Fn.
Input
The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.
Output
For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).
Sample Input
0 9 999999999 1000000000 -1
Sample Output
0 34 626 6875
Hint
As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by
.
Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:
.
Source
Stanford Local 2006
一道涉及到矩阵快速幂的知识的题 本来快速幂没学好 今天还专门说这个了,所以 看了半天才略懂了 一些,代码如下:
#include<stdio.h> #include<string.h> #include<algorithm> using namespace std; struct Mat//定义矩阵 { int a[2][2]; void init() { memset(a,0,sizeof(a)); a[0][0]=a[1][1]=1; } }; Mat mul(Mat a,Mat b)//矩阵乘法 { Mat ans; ans.init(); for(int i=0;i<2;i++) { for(int j=0;j<2;j++) { ans.a[i][j]=0; for(int k=0;k<2;k++) { ans.a[i][j]+=a.a[i][k]*b.a[k][j]; } ans.a[i][j]%=10000; } } return ans; } Mat power(Mat a,int num)//矩阵快速幂模板 { Mat ans; ans.init(); while(num) { if(num%2==1) { ans=mul(ans,a); } num/=2; a=mul(a,a); } return ans; } int main() { int n; while(scanf("%d",&n)!=EOF&&n!=-1) { if(n==0) { printf("0\n"); continue; } Mat a,ans; a.a[0][1]=a.a[0][0]=a.a[1][0]=1; a.a[1][1]=0; ans=power(a,n); printf("%d\n",ans.a[0][1]%10000); } return 0; }
Fibonacci
Time Limit: 1000MS | Memory Limit: 65536KB | 64bit IO Format: %I64d & %I64u |
Description
In the Fibonacci integer sequence, F0 = 0, F1 = 1, and Fn = Fn − 1 + Fn − 2 for n ≥ 2. For example, the first ten terms of
the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
An alternative formula for the Fibonacci sequence is
.
Given an integer n, your goal is to compute the last 4 digits of Fn.
Input
The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.
Output
For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).
Sample Input
0 9 999999999 1000000000 -1
Sample Output
0 34 626 6875
Hint
As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by
.
Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:
.
Source
Stanford Local 2006
相关文章推荐
- POJ 3070 Fibonacci(矩阵快速幂)
- poj_3070 Fibonacci(矩阵快速幂)
- poj 3070 Fibonacci(矩阵快速幂模板题)
- 3070 Fibonacci 矩阵快速幂
- POJ 3070 Fibonacci(矩阵快速幂)
- poj 3070 Fibonacci (快速矩阵乘法)
- poj 3070 Fibonacci(矩阵快速幂)
- poj 3070 Fibonacci(矩阵快速幂)
- POJ 3070 Fibonacci (矩阵快速幂)
- POJ 3070 Fibonacci.(矩阵快速幂)
- POJ 3070 Fibonacci(矩阵快速幂)
- poj -3070 Fibonacci (矩阵快速幂)
- 【POJ】3070 - Fibonacci(矩阵快速幂)
- 3070 Fibonacci 矩阵快速幂
- Poj3070 Fibonacci (矩阵快速幂)
- POJ 3070 Fibonacci(矩阵快速幂)
- 矩阵快速幂——Fibonacci ( POJ 3070 )
- poj 3070 Fibonacci(矩阵快速幂)
- POJ3070 - Fibonacci 矩阵快速幂
- POJ 3070 Fibonacci 矩阵快速幂