题目:
题解:
struct Matrix {
int mat[2][2];
};
struct Matrix matrixMultiply(struct Matrix* a, struct Matrix* b) {
struct Matrix c;
for (int i = 0; i < 2; i++) {
for (int j = 0; j < 2; j++) {
c.mat[i][j] = (*a).mat[i][0] * (*b).mat[0][j] + (*a).mat[i][1] * (*b).mat[1][j];
}
}
return c;
}
struct Matrix matrixPow(struct Matrix a, int n) {
struct Matrix ret;
ret.mat[0][0] = ret.mat[1][1] = 1;
ret.mat[0][1] = ret.mat[1][0] = 0;
while (n > 0) {
if (n & 1) {
ret = matrixMultiply(&ret, &a);
}
n >>= 1;
a = matrixMultiply(&a, &a);
}
return ret;
}
int fib(int n) {
if (n < 2) {
return n;
}
struct Matrix q;
q.mat[0][0] = q.mat[0][1] = q.mat[1][0] = 1;
q.mat[1][1] = 0;
struct Matrix res = matrixPow(q, n - 1);
return res.mat[0][0];
}