【难】【数学】斐波那契数列的O(logn)解法

题目：《编程之美》 P163

class Matrix{public:unsigned int a11, a12, a21, a22;Matrix(int a, int b, int c, int d) :a11(a), a12(b), a21(c), a22(d){}//重载矩阵的乘法Matrix operator*(const Matrix &other){Matrix r(0,0,0,0);r.a11 = a11*other.a11 + a12*other.a21;r.a12 = a11*other.a12 + a12*other.a22;r.a21 = a21*other.a11 + a22*other.a21;r.a22 = a21*other.a12 + a22*other.a22;return r;}};//计算矩阵A的m次方Matrix MatrixPow(const Matrix &A,unsigned int m){Matrix res(1, 0, 0, 1);//单位矩阵Matrix cur = A;while (m){if (m & 1)res = res*cur;cur = cur*cur;m = m >> 1;}return res;}unsigned int Fibonacci(int n){if (n < 0)throw new exception;if (n == 0 || n == 1)return n;Matrix A(1, 1, 1, 0);Matrix r = MatrixPow(A, n - 1);return r.a11;}