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Using Complete Coverage Path Planning (CCPP), a cleaning robot could visit every accessible area in the workspace. The dynamic environment requires the higher computation of the CCPP algorithm because the path needs to be replanned when the path might become invalid. In previous CCPP methods, when the neighbours of the current position are obstacles or have been visited, it is challenging for the robot to escape from the deadlocks with the least extra time cost. In this study, a novel CCPP algorithm is proposed to deal with deadlock problems in a dynamic environment. A priority template inspired by the short memory model could reduce the number of deadlocks by giving the priority of directions. Simultaneously, a global backtracking mechanism guides the robot to move to the next unvisited area quickly, taking the use of the explored global environmental information. What's more, the authors extend their CCPP algorithm to a multi-robot system with a market-based bidding process which could deploy the coverage time. Experiments of apartment-like scenes show that the authors’ proposed algorithm can guarantee an efficient collision-free coverage in dynamic environments. The proposed method performs better than related approaches on coverage rate and overlap length.