Valley Hall topological photonic crystals, inspired by topological insulators in condensed matter physics, have provided a promising solution to control the flow of light. Recently, the dynamic manipulation property of topological photonic crystals has been widely studied. Here, we propose a novel solution for programmable valley photonic crystals, called field programmable topological edge array (FPTEA), based on the field reorientation property of nematic liquid crystals and robust valley-protected edge modes. FPTEA is composed of an array of graphene-like lattices with C3 symmetry, in which the birefringence of liquid crystal is larger than 0.5105. Due to the dielectric anisotropy of liquid crystals being sensitive to external fields such as light, heat, electric, and magnetic fields, each lattice is tunable, and the topological propagation routes and even the lattice parameters can be dynamically changed while changing the distribution of external fields. We numerically demonstrate three methods of composing an FPTEA device to design arbitrary passive optical devices by electric driving, thermal inducing, or UV writing. These results show the great application potential of liquid crystals in topological photonic crystals, and enrich the design of programmable integrated topological devices with broad working bandwidth ranging from microwave to visible light.