【D - ECJTU_ACM 11级队员2012年暑假训练赛(2)】
2012-07-10 15:45
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D - D
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u
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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 Fnmod 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:
.
Time Limit:1000MS Memory Limit:65536KB 64bit IO Format:%I64d & %I64u
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 Fnmod 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:
.
// Project name : D ( Fibonacci ) // File name : main.cpp // Author : Izumu // Date & Time : Tue Jul 10 14:02:23 2012 #include <iostream> #include <stdio.h> using namespace std; int p[30][4]={1,1,1,0}; void mm(int * ret,int * a,int * b) { int x[4],y[4],i; for(i=0;i<4;i++) { x[i]=a[i]; y[i]=b[i]; } ret[0] = (x[0]*y[0] + x[1]*y[2]) % 10000; ret[1] = (x[0]*y[1] + x[1]*y[3]) % 10000; ret[2] = (x[2]*y[0] + x[3]*y[2]) % 10000; ret[3] = (x[2]*y[1] + x[3]*y[3]) % 10000; } int main() { int i,n; int a[4]={0,1,1,0}; for(i=1;i<30;i++) { mm(p[i],p[i-1],p[i-1]); } while(1) { scanf("%d",&n); if(n==-1) break; a[0]=1;a[1]=0;a[2]=0;a[3]=1; for(i=0;i<30;i++) { if(n&(1<<i)) { mm(a,a,p[i]); } } cout << a[1] << endl; } return 0; } // end // ism
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