PDDL-For-Light-Up-Problem

Setting of the game: In this exercise, your task it to model the Light Up puzzle12 in PDDL. This game is based on a 2D grid consisting of black and white cells. White cells can be lit up by placing light bulbs on the grid. Placing a light bulb at some coordinate hx, yi lights up all white cells of the same column (x), and all white cells of the same row (y), such that no black cell lies in between hx, yi and the cell, i.e., light propagation is stopped by black cells. A light bulb may only be placed in a cell that is not lighted up by another light bulb yet. Some black cells are associated with numbers. This number gives the number of light bulbs that must be placed directly (horizontally or vertically) adjacent to the black cell. For example, if the number is 0, no light bulb may be placed in a cell adjacent to the black cell. If 1, exactly one light bulb may (and must) be placed to a cell adjacent to the black cell. The goal is to light up all white cells while adhering to the aforementioned constraints.