The Hydro Unit Commitment problem (HUC) specific to hydroelectric units is part of the electricity production planning problem, called Unit Commitment Problem (UCP). More specifically, the studied case is that of the HUC with a single unit, denoted 1-HUC. The unit is located between two reservoirs. The horizon is discretized in time periods. The unit operates at a finite number of points defined as pairs of the generated power and the corresponding water flow. Several constraints are considered. Each reservoir has an initial volume, as well as window resource constraints, defined by a minimum and maximum volume per time period. At each time period, there is an additional positive, negative or zero intake of water in the reservoirs. The case of a price-taker revenue maximization problem is considered. An efficient exact A* variant, so called HA*, is proposed to solve the 1-HUC accouting for window constraints, with a reduced search space and a dedicated optimistic heuristic. This variant is compared to a classical Resource Constrained Shortest Path Problem (RCSPP) algorithm and an MILP formulation solved with CPLEX. Results show that the proposed algorithm outperforms both concurrent alternatives in terms of computational time in average on a set of realistic instances, meaning that HA* exhibits a more stable behavior with more instances solved.