Solve a Jigsaw Puzzle

You are given a collection of jigsaw puzzle pieces. Each piece has four edges: top, right, bottom, and left. A helper function `match(edgeA, edgeB)` is provided; it returns `true` if two edges can be connected and `false` otherwise. The puzzle is known to form one complete rectangular grid, but the number of rows and columns is not given. Pieces may need to be rotated. Implement a `solve(pieces)` function that returns a valid rectangular arrangement of all pieces, including each piece's orientation, such that every horizontally or vertically adjacent pair of edges matches according to `match`. You may assume: - Every piece must be used exactly once. - A valid solution exists. - The puzzle has no missing pieces. - Border edges do not need to match anything outside the puzzle. Discuss the algorithm, data structures, and time and space complexity.