Bright and dark soliton solutions to the partial reverse space-time nonlocal Mel'nikov equation

General bright and dark soliton solutions to the partial reverse space-time nonlocal Mel'nikov equation with parity-time symmetry are constructed by the Hirota bilinear method with KP hierarchy reduction method. These solutions of arbitrary order are given in forms of Gram-type determinants. The properties of propagation and collision of analytical solution including both bright and dark solitons are discussed in details. In the end, we provide a simple variable transformation to convert the nonlocal Mel'nikov equation to a local Mel'nikov equation.