HDU1021Fibonacci Again
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Fibonacci Again
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 49607 Accepted Submission(s): 23534
Problem Description
There are another kind of Fibonacci numbers: F(0) = 7, F(1) = 11, F(n) = F(n-1) + F(n-2) (n>=2).
Input
Input consists of a sequence of lines, each containing an integer n. (n < 1,000,000).
Output
Print the word "yes" if 3 divide evenly into F(n).
Print the word "no" if not.
Print the word "no" if not.
Sample Input
012345
Sample Output
nonoyesnonono
题目大意:
它新定义了一个斐波那契数列为F(0) = 7, F(1) = 11, F(n) = F(n-1) + F(n-2) (n>=2);
输入有多行,每一行有一个正整数 n(n<1000000);
输出:
Print the word "yes" if 3 divide evenly into F(n).
就是说F[n]能够被3整除,也就是F[n]对3去余为0;
思路:
如果有正整数 a, b, c, d, x; 假如: c=a+b, x=c%d ,那么可以知道 x=(a+b)%d; 易推知,x=(a%d+b%d)%d;
ps:参考同余定理
给出AC代码:
#include<iostream>using namespace std;int F[1000005];int main(){F[0] = 7 % 3, F[1] = 11 % 3;for (int i = 2; i < 1000005; i++)F[i] = (F[i - 1] + F[i - 2]) % 3;int n;while (cin >> n){if (F[n] == 0)cout << "yes" << endl;else cout << "no" << endl;}return 0;}
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