Determine Whether P's Position Is Unique

You are given an `R x C` rectangular grid and a set of named entities. Each entity must be placed in exactly one distinct cell. You are also given a collection of relational clues describing how the entities may be positioned relative to one another. Examples of such clues include constraints like being in the same row, same column, left/right of another entity, or above/below another entity. Implement a function that determines whether the location of a particular target person `P` is uniquely determined by all valid placements that satisfy every clue. Return the unique coordinate `(row, column)` of `P` if exactly one valid assignment places `P` in a single location. Otherwise, report that no unique solution exists. Assume rows and columns are 1-indexed.