Federated learning (FL) is a distributed machine learning framework that enables multiple clients to train a global model without providing the raw data. To incentivize high-quality client participation, it is crucial to design a suitable contribution evaluation algorithm, among which the Shapley value (SV) is widely used for its renowned fairness properties. However, the exact computation of SV requires exhaustive coalition enumeration, resulting in exponential complexity. In this paper, we make the novel observation that the SV computation is inherently redundant at both the client and coalition levels. To leverage this insight, we theoretically analyze the impact of client similarity and coalition size on SV computation, demonstrating that the marginal contributions of similar clients and large coalitions can be approximated without significantly affecting the valuation accuracy. Based on this theoretical foundation, we propose AP-Shapley, an adaptive pruning-based acceleration algorithm for SV computation. AP-Shapley dynamically prunes the computational space by first utilizing a similarity matrix to select subsets of dissimilar clients, and then applying the coalition pruning rule to eliminate redundant evaluations, collectively enhancing computational efficiency. Extensive experiments across various datasets demonstrate that AP-Shapley achieves a speedup of up to 40% over state-of-the-art methods while maintaining comparable evaluation accuracy. The source code is available at https://github.com/wlffffff/AP-Shapley .