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This paper investigates reconfigurable intelligent surface (RIS)-assisted full-duplex multiple-input single-output wireless system, where the beamforming and RIS phase shifts are optimized to maximize the sum-rate for both single and distributed RIS deployment schemes. The preference of using the single or distributed RIS deployment scheme is investigated through three practical scenarios based on the links' quality. The closed-form solution is derived to optimize the beamforming vectors and a novel deep reinforcement learning (DRL) algorithm is proposed to optimize the RIS phase shifts. Simulation results illustrate that the choice of the deployment scheme depends on the scenario and the links' quality. It is further shown that the proposed algorithm significantly improves the sum-rate compared to the non-optimized scenario in both single and distributed RIS deployment schemes. Besides, the proposed beamforming derivation achieves a remarkable improvement compared to the approximated derivation in previous works. Finally, the complexity analysis confirms that the proposed DRL algorithm reduces the computation complexity compared to the DRL algorithm in the literature.