logN時間複雜度的斐波那契數列

引入矩陣冪次乘法

class Solution {
public:
    int fib(int n) {
        if(n < 1) return 0;
        if(n < 3) return 1;

        vector<vector<int>> begin{{1,1}};
        vector<vector<int>> base{{1,1},{1,0}};

        vector<vector<int>> res = matrix_mul(begin,base,n-3);
        return res[0][0]+res[0][1];
    }

    vector<vector<int>> matrix_mul(vector<vector<int>> res,vector<vector<int>> &base,int power){
        for(;power != 0;power = power>>1){
            if(power&1){
                res = muli_matrix(res,base);
            }
            base = muli_matrix(base,base);
        }
        return res;
    }

    vector<vector<int>> muli_matrix(vector<vector<int>> m1,vector<vector<int>> m2){
        int row = m1.size(),col = m2[0].size(),num = m1[0].size();
        vector<vector<int>> res(row,vector<int>(col,0));
        for(int i = 0;i < row;i++){
            for(int j = 0;j < col;j++){
                for(int k = 0;k < num;k++){
                    res[i][j] += m1[i][k]*m2[k][j];
                }
            }
        }
        return res;
    }
};

int main(){
    Solution *s = new Solution();
    int res = s->fib(6);
    cout << res << endl;
}