Autonomous exploration is crucial and highly challenging for various intelligent operations of unmanned aerial vehicles (UAVs). However, low-efficiency problems caused by low-quality trajectory or back-and-forth maneuvers (BFM) still exist. To improve the exploration efficiency in unknown environments, a fast autonomous exploration planner (FAEP) is proposed in this paper. We firstly design a novel frontiers exploration sequence generation method to significantly reduce BFM during the exploration by considering multi-level factors in asymmetric traveling salesman problem (ATSP). Then, according to the exploration sequence and the distribution of frontiers, an adaptive yaw planning method is proposed to cover more frontiers by yaw change during an exploration journey. In addition, to increase the fluency of flight, a dynamic replanning strategy is also adopted. The main technical contributions of the proposed approach are to provide a comprehensive global coverage path with less BFM, and use adaptive yaw planning to generate more reasonable yaw trajectory. We present extensive comparison and real-world experiments to validate the effectiveness and correctness of our method. Experimental results show the proposed approach has better performance compared to typical and state-of-the-art methods in these flat scenarios without lots of scattered obstacles. We release our implementation as an open-source package <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{1}$</tex-math></inline-formula> for the community.