标签:style blog color io for div sp log on
递推,推得f(n) = f(n-1) + f(n-3) + f(n-4)。然后转换成矩阵相乘,如下
f(n-1) f(n-2) f(n-3) f(n-4) * 1 1 0 0 = f(n) f(n-1) f(n-2) f(n-3)
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0
从而转化为快速矩阵相乘。
1 #include <cstdio> 2 #include <cstring> 3 #include <cstdlib> 4 5 #define MATN 4 6 7 typedef struct mat_st { 8 int m[MATN][MATN]; 9 mat_st() { 10 memset(m, 0, sizeof(m)); 11 } 12 } mat_st; 13 14 int ans[MATN]={1,2,4,6}; 15 int mod; 16 17 mat_st mult_mat(mat_st a, mat_st b) { 18 mat_st ret; 19 int i, j, k; 20 21 for (i=0; i<MATN; ++i) { 22 for (j=0; j<MATN; ++j) { 23 for (k=0; k<MATN; ++k) 24 ret.m[i][j] += a.m[i][k]*b.m[k][j]; 25 ret.m[i][j] %= mod; 26 } 27 } 28 return ret; 29 } 30 31 mat_st pow_mat(mat_st a, int n) { 32 mat_st ret; 33 int i; 34 35 for (i=0; i<MATN; ++i) 36 ret.m[i][i] = 1; 37 38 while (n) { 39 if (n & 1) 40 ret = mult_mat(ret, a); 41 a = mult_mat(a, a); 42 n >>= 1; 43 } 44 return ret; 45 } 46 47 int main() { 48 int l; 49 int i; 50 mat_st e, a; 51 52 e.m[0][0] = e.m[0][1] = e.m[1][2] = e.m[2][0] = e.m[2][3] = e.m[3][0] = 1; 53 for (i=0; i<MATN; ++i) 54 a.m[0][i] = ans[MATN-1-i]; 55 56 while (scanf("%d %d", &l, &mod) != EOF) { 57 if (l <= 3) 58 printf("%d\n", ans[l]%mod); 59 else { 60 mat_st c = pow_mat(e, l-3); 61 mat_st r = mult_mat(a, c); 62 printf("%d\n", r.m[0][0]); 63 #ifndef ONLINE_JUDGE 64 fflush(stdout); 65 #endif 66 } 67 } 68 69 return 0; 70 }
标签:style blog color io for div sp log on
原文地址:http://www.cnblogs.com/bombe1013/p/3978272.html