import math2.py

import math
import random
import string

class HyperdimensionalEntangledBraid:
    """
    A research-level, hypothetical data structure that conceptually represents
    a hyperdimensional entangled braid (HEB). Keys are embedded into multiple
    dimensions using a fractal hash, and braided links provide shortcuts.
    """

    def __init__(self, dimensions=3, branch_factor=4):
        """
        dimensions: number of hyperdimensions used.
        branch_factor: controls the fractal hashing granularity.
        """
        self.dimensions = dimensions
        self.branch_factor = branch_factor
        # The structure could be represented by nested dictionaries for simplicity,
        # each dimension representing a 'coordinate layer'.
        self.root = {}

    def _fractal_hash(self, key):
        """
        Fractal hash a key into a vector of length `dimensions`.
        For simplicity, we:
        1. Convert key to a numeric hash.
        2. Decompose into `dimensions` coordinates by repeatedly modding by branch_factor.
        """
        base_hash = abs(hash(key))
        coords = []
        for _ in range(self.dimensions):
            coords.append(base_hash % self.branch_factor)
            base_hash //= self.branch_factor
        return tuple(coords)

    def insert(self, key, value):
        """
        Insert a key-value pair by navigating through the fractal coordinates
        and placing the value at the entangled node.
        """
        coords = self._fractal_hash(key)
        node = self.root
        # Navigate down the dimensions
        # We simplify: just treat coords as a path in nested dicts.
        for c in coords:
            if c not in node:
                node[c] = {}
            node = node[c]

        # Store the value at a special key
        node['__value__'] = (key, value)

    def search(self, key):
        """
        Search for a key by following the fractal coordinates.
        """
        coords = self._fractal_hash(key)
        node = self.root
        for c in coords:
            if c not in node:
                return None
            node = node[c]

        # Check if the value matches
        val = node.get('__value__', None)
        if val and val[0] == key:
            return val[1]
        return None

if __name__ == "__main__":
    # Basic demonstration
    heb = HyperdimensionalEntangledBraid(dimensions=3, branch_factor=4)
    heb.insert("hello", 42)
    heb.insert("world", 99)

    print("Search 'hello':", heb.search("hello"))
    print("Search 'world':", heb.search("world"))
    print("Search 'missing':", heb.search("missing"))