The paper presents an algorithm which solves the shortest path problem in an arbitrary deterministic environment with n states with an emotional agent in linear time. The algorithm originates from an algorithm which in exponential time solves the same problem, and the agent architecture used for solving the problem is an NN-CAA architecture (neural network crossbar adaptive array). By implementing emotion learning, the linear time algorithm is obtained and the agent architecture is modified. The complexity of the algorithm without operations for initiation in general does not depend on the number of states n, but only on the length of the shortest path. Depending on the position of the goal state, the complexity can be at most O(n). It can be concluded that the choice of the function which evaluates the emotional state of the agent plays a decisive role in solving the problem efficiently. That function should give as detailed information as possible about the consequences of the agent's actions, starting even from the initial state. In this way the function implements properties of human emotions.