So Easy!

Problem Description
　　A sequence Sn is defined as:

Where a, b, n, m are positive integers.┌x┐is the ceil of x. For example, ┌3.14┐=4. You are to calculate Sn.
　　You, a top coder, say: So easy! 
 
Input
　　There are several test cases, each test case in one line contains four positive integers: a, b, n, m. Where 0< a, m < 215, (a-1)2< b < a2, 0 < b, n < 231.The input will finish with the end of file.
Output
　　For each the case, output an integer Sn.
Sample Input
2 3 1 2013 2 3 2 2013 2 2 1 2013
Sample Output
4 14 4
Source
2013 ACM-ICPC长沙赛区全国邀请赛
 1 /*思路：若(a+√b)n == x + y·√b（x、y为整数），则(a－√b)n == x － y·√b。又因为a－1 < √b < a，
 2 所以0 < (a－√b)n < 1，即x－1 < y·√b < x，所以ceil（(a+√b)n） == 2x。接下来事情就容易多了，
 3 同时对x、y两部分进行快速幂取模即可*/
 4 #include <cstdio>
 5 typedef long long LL;
 6 LL a,b,n,m;
 7 void solve() {
 8     LL ans1(1),ans2(0),t1(a),t2(1);
 9     LL tmp;
10     while(n) {
11         if(n&1) {
12             tmp = ans1;
13             ans1 = (ans1*t1+ans2*t2*b)%m;
14             ans2 = (tmp*t2+ans2*t1)%m;
15         }
16         tmp = t1;
17         t1 = (t1*t1+t2*t2*b)%m;
18         t2 = 2*tmp*t2%m;
19         n >>= 1;
20     }
21     printf("%lld\n",ans1*2%m);
22 }
23 int main() {
24     while(~scanf("%lld%lld%lld%lld",&a,&b,&n,&m))
25         solve();
26     return 0;
27 }
View Code(转载）

 

posted @ 2013-06-03 17:49  1002liu  阅读(236)  评论(0)  编辑  收藏  举报