# SPDX-License-Identifier: AGPL-3.0-or-later
from dataclasses import dataclass
from typing import List, Tuple


@dataclass
class WolframHypergraph:
    """
    Simulates the Wolfram Physics Project Hypergraph.
    Universe is a set of relations (Hyperedges).
    """

    edges: List[Tuple[int, ...]]
    max_node_id: int

    def evolve(self, steps: int = 1):  # type: ignore
        """
        Applies a rewrite rule.
        Rule: {{x, y}, {y, z}} -> {{x, z}, {x, w}, {y, w}}
        (Triangle completion with new node w)
        """
        for _ in range(steps):
            new_edges = []
            matched_indices = set()

            # Naive pattern matching O(E^2)
            # Find (x, y) and (y, z)
            for i, e1 in enumerate(self.edges):
                if i in matched_indices:
                    continue
                if len(e1) != 2:
                    continue

                x, y = e1

                for j, e2 in enumerate(self.edges):
                    if i == j or j in matched_indices:
                        continue
                    if len(e2) != 2:
                        continue

                    if e2[0] == y:  # Found chain x->y->z
                        z = e2[1]

                        # Apply Rule
                        w = self.max_node_id + 1
                        self.max_node_id += 1

                        # New edges: {x,z}, {x,w}, {y,w}
                        new_edges.append((x, z))
                        new_edges.append((x, w))
                        new_edges.append((y, w))

                        matched_indices.add(i)
                        matched_indices.add(j)
                        break

            # Keep unmatched edges
            for k, e in enumerate(self.edges):
                if k not in matched_indices:
                    new_edges.append(e)  # type: ignore

            self.edges = new_edges  # type: ignore

    def dimension_estimate(self) -> float:
        """
        Estimates the effective dimension of the space graph.
        Growth rate of neighborhood ball B(r).
        V(r) ~ r^d  => d ~ log(V) / log(r)
        """
        # Very simplified: just return node count growth log?
        # Or just return current edge count as proxy for complexity
        return len(self.edges)
