To enhance path planning efficiency in unmanned aerial vehicle (UAV) search missions in complex environments, this paper proposes a coverage path planning (CPP) algorithm for a UAV that integrates the deep Q-network (DQN) with the A* algorithm (DQN-A*). In the proposed DQN-A* algorithm, a dual-driven reward mechanism is established, comprising a probability-weighted reward and a step-dependent reward, steering the UAV toward high-probability regions. Furthermore, to handle previously unknown obstacles in real time, the algorithm employs a multi-stage obstacle-identification strategy, enabling the UAV to improve coverage of traversable cells by dynamically adjusting its local path when newly detected obstacles are encountered. A theoretical analysis derives a principled recommended range for the UAV positional identifier based on statistical feature analysis; this range is then validated through extensive simulations. Additionally, Hamiltonian path pre-training is introduced to accelerate convergence. Comparative simulations demonstrate that the proposed DQN-A* algorithm achieves higher area-coverage and target-detection probabilities than benchmark algorithms in environments with unknown obstacles, offering valuable insights for positional encoding in deep reinforcement learning (DRL)-based robotic coverage problems.