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Temporal networks can describe multiple types of complex systems with temporal information in the real world. As an effective method for analyzing such network, temporal graph pattern (TGP) counting has received extensive attention and has been applied in diverse domains. In this paper, we study the problem of counting the TGP in the temporal network. Then, an exact algorithm is proposed based on the time first search (TFS) algorithm. This algorithm can reduce the intermediate results generated in the graph isomorphism and has high computational efficiency. To further improve the algorithm performance, we design an estimation algorithm by applying the edge sampling strategy to the exact algorithm. Finally, we evaluate the performances of the two algorithms by counting both the symmetric and asymmetric TGP. Extensive experiments on real datasets demonstrated that the exact algorithm is faster than the existing algorithm and the estimation algorithm can greatly reduce the running time while guaranteeing the accuracy.