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.