【HDOJ】3221 Brute-force Algorithm

归来吧很好推导。T(n) = a^f(n-1)*b^f(n)%p。
主要难点在于求mod和fibo。引用如下公式
A^B%C = A^(B%phi(C) + phi(C))%C, 满足B>=phi(C)。

 /*  */
 #include <iostream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 using namespace std;

 #define rep(i,a,n)     for (int i=a;i<n;i++)
 #define per(i,a,n)     for (int i=n-1;i>=a;i--)
 #define pb             push_back
 #define mp             make_pair
 #define all(x)         (x).begin(),(x).end()
 #define SZ(x)         ((int)(x).size())
 #define lson        l, mid, rt<<1
 #define rson        mid+1, r, rt<<1|1

 const int maxn = ;
 __int64 a, b, p, n;
 __int64 fibo[maxn];
 __int64 phi;

 typedef struct {
     __int64 m[][];
 } mat_t;

 mat_t res;

 mat_t matMult(mat_t a, mat_t &b) {
     mat_t c;

     memset(c.m, , sizeof(c.m));
     rep(i, , ) {
         rep(j, , ) {
             rep(k, , ) {
                 c.m[i][j] += a.m[i][k] * b.m[k][j];
                 if (c.m[i][j] > phi) {
                     c.m[i][j] = c.m[i][j]%phi+phi;
                 }
             }
         }
     }
     return c;
 }

 __int64 euler(__int64 x) {
     __int64 ret = x, i;

     for (i=; i*i<=x; ++i) {
         if (x%i == ) {
             ret = ret / i * (i-);
             while (x%i == )
                 x /= i;
         }
     }
     if (x > )
         ret = ret / x * (x-);
     return ret;
 }

 __int64 myPow(__int64 base, __int64 n) {
     __int64 ret = ;

     while (n) {
         if (n & )
             ret = ret * base %p;
         base = base * base %p;
         n >>= ;
     }
     return ret;
 }

 void matFibo(__int64 n) {
     mat_t base;

     res.m[][] = base.m[][] = ;
     res.m[][] = res.m[][] = res.m[][] =\
     base.m[][] = base.m[][] = base.m[][] = ;

     while (n) {
         if (n & )
             res = matMult(base, res);
         base = matMult(base, base);
         n >>= ;
     }
 }

 void getFibo(__int64 &an, __int64 &bn) {
     int i;

     fibo[] = ;
     fibo[] = ;
     for (i=; i<=n; ++i) {
         fibo[i] = fibo[i-] + fibo[i-];
         if (fibo[i] > phi)
             break;
     }
     if (i > n) {
         an = fibo[n-];
         bn = fibo[n];
         return ;
     }
     matFibo(n-);
     an = res.m[][];
     bn = res.m[][];
 }

 int main() {
     int i, j, k;
     int t;
     __int64 an, bn, ans;

     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     scanf("%d", &t);
     rep(tt, , t+) {
         scanf("%I64d %I64d %I64d %I64d", &a, &b, &p, &n);
         printf("Case #%d: ", tt);
         if (a== || b== || p==) {
             printf("0\n");
         } else if (n == ) {
             printf("%I64d\n", a%p);
         } else if (n == ) {
             printf("%I64d\n", b%p);
         } else {
             phi = euler(p);
             getFibo(an, bn);
             ans = myPow(a, an)*myPow(b, bn)%p;
             printf("%I64d\n", ans);
         }
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }