Autonomous exploration and mapping in unknown environments is a critical capability for robots. Existing exploration techniques (e.g., heuristic-based and learning-based methods) do not consider the regional legacy issues, i.e., the great impact of smaller unexplored regions on the whole exploration process, which results in a dramatic reduction in their later exploration efficiency. To this end, this paper proposes a Local-and-Global Strategy (LAGS) algorithm that combines a local exploration strategy with a global perception strategy, which considers and solves the regional legacy issues in the autonomous exploration process to improve exploration efficiency. Additionally, we further integrate Gaussian process regression (GPR), Bayesian optimization (BO) sampling, and deep reinforcement learning (DRL) models to efficiently explore unknown environments while ensuring the robot's safety. Extensive experiments show that the proposed method could explore unknown environments with shorter paths, higher efficiencies, and stronger adaptability on different unknown maps with different layouts and sizes.