Codeforces Round #230 (Div. 1) C题 (复合矩阵连乘)
这题关键是要想到把系数矩阵复合到原来的斐波那契矩阵当中,然后矩阵连乘。
代码:
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <map>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#define ll __int64
#define lson l , m , rt << 1
#define rson m + 1 , r , rt << 1 | 1
using namespace std;
int k , K ; ll n ;
struct ret {
ll dir[88][88] ;
} e , E ;
ll c[44][44] ;
const ll mod = 1000000007 ;
void muil ( ret x , ret y , ret &z ) {
int i , j , l ;
for ( i = 0 ; i < K ; i ++ )
for ( j = 0 ; j < K ; j ++ )
for ( l = 0 ; l < K ; l ++ ) {
if ( l == 0 ) z.dir[i][j] = x.dir[i][l] * y.dir[l][j] ;
else z.dir[i][j] += x.dir[i][l] * y.dir[l][j] ;
z.dir[i][j] %= mod ;
}
}
void init ( int n ) {
memset ( e.dir , 0 , sizeof ( e.dir ) ) ;
int i , j ;
for ( i = 0 ; i <= 40 ; i ++ ) {
c[i][0] = 1 ;
for ( j = 1 ; j <= i ; j ++ )
c[i][j] = ( c[i-1][j] + c[i-1][j-1] ) % mod ;
}
for ( i = 0 ; i <= n ; i ++ )
for ( j = 0 ; j <= i ; j ++ )
e.dir[i+n+1][j] = e.dir[i][j+n+1] = e.dir[i][j] = c[i][j] ;
for ( i = 0 ; i < K ; i ++ ) E.dir[i][i] = 1 ;
e.dir[2*(n+1)][n] = e.dir[2*(n+1)][2*(n+1)] = 1 ;
}
ll gao ( ll n ) {
ret ans = E , f = e ;
while ( n ) {
if ( n & 1 ) muil ( ans , f , ans ) ;
muil ( f , f , f ) ;
n >>= 1 ;
}
ll fuck = 0 ;
for ( int i = 0 ; i < K - 1 ; i ++ )
fuck = ( fuck + ans.dir[K-1][i] ) % mod ;
return fuck ;
}
int main() {
scanf ( "%I64d%d" , &n , &k ) ;
if ( n == 1 ) {
puts ( "1" ) ;
return 0 ;
}
K = (k+1) * 2 + 1 ;
init ( k ) ;
printf ( "%I64d\n" , gao ( n ) ) ;
return 0;
}
原文:http://blog.csdn.net/a1054949000/article/details/19486037