"""
logos/network.py - The Prime Topology Network
"""

import numpy as np
import sympy
from collections import Counter
from typing import Dict, List, Tuple

class PrimeNetwork:
    """
    Represents the Radial Prime Topology as an instantiated graph object.
    Used for both visualization and signal routing validation.
    """
    
    def __init__(self, max_integer: int = 1000):
        self.max_integer = max_integer
        self.positions: Dict[int, Tuple[float, float]] = {}
        self.gpf_map: Dict[int, int] = {}
        self.prime_counts = Counter()
        self.primes: List[int] = []
        self.composites: List[int] = []
        
        # Build the network immediately
        self._build()

    def _get_gpf(self, n: int) -> int:
        """Returns the Greatest Prime Factor."""
        if n <= 1: return 1
        i = 2
        while i * i <= n:
            if n % i:
                i += 1
            else:
                n //= i
        return n

    def _build(self):
        """Constructs the network nodes and edges."""
        for n in range(1, self.max_integer + 1):
            # Radial position based on Mod 10
            # 1, 3, 7, 9 are the Prime Dissolution Vectors
            angle = np.pi/2 - (2 * np.pi * (n % 10)) / 10 # Clockwise from Top
            radius = n 
            self.positions[n] = (radius * np.cos(angle), radius * np.sin(angle))

            if n > 1:
                if sympy.isprime(n):
                    self.primes.append(n)
                else:
                    self.composites.append(n)
                    # Establish Gravity Link (Composite -> GPF)
                    gpf = self._get_gpf(n)
                    self.gpf_map[n] = gpf
                    self.prime_counts[gpf] += 1
            elif n == 1:
                self.primes.append(1) # Treat 1 as special unitary root

    def get_route(self, value: int) -> List[int]:
        """
        Trace the dissolution path of a value back to its Prime Root.
        Visualization of 'Heat Dissolution'.
        Returns list: [value, factor, ..., gpf, ..., prime]
        """
        path = [value]
        curr = value
        
        # Simple dissolution: jump to GPF repeatedly until prime
        while curr not in self.primes and curr > 1:
            if curr in self.gpf_map:
                next_hop = self.gpf_map[curr]
                if next_hop == curr: break # Should not happen if logic is correct
                path.append(next_hop)
                curr = next_hop
            else:
                # Fallback calculation if outside pre-calc range
                gpf = self._get_gpf(curr)
                path.append(gpf)
                curr = gpf
                
        return path

    def validate_wave(self, heat_code: int) -> bool:
        """
        Check if a subset of the wave aligns with valid network topology.
        (Placeholder for advanced routing logic)
        """
        # Example: Valid if heat_code modulo maps to a prime vector
        residue = heat_code % 10
        return residue in [1, 3, 7, 9]

# ==========================================
# SINGLETON INSTANCE (Self-Contained Network)
# ==========================================
# Pre-calc network to avoid re-instantiation overhead per request
SHARED_NETWORK = PrimeNetwork(max_integer=2000)