#!/usr/bin/env python3
"""
Correct implementation of enumerative entropy coding as described in Han et al. (2008).
This version is fully self-contained, embedding all necessary data into the stream.
"""

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

class ExpGolombCoder:
    """Exponential-Golomb coding for non-negative integers."""

    @staticmethod
    def encode(n: int) -> str:
        """Encodes a non-negative integer n >= 0."""
        if n < 0:
            raise ValueError("Exp-Golomb is for non-negative integers.")
        n_plus_1 = n + 1
        binary = bin(n_plus_1)[2:]
        leading_zeros = '0' * (len(binary) - 1)
        return leading_zeros + binary

    @staticmethod
    def decode(bits: str, start_pos: int = 0) -> Tuple[int, int]:
        """Decodes an exp-Golomb integer from a bit string."""
        pos = start_pos
        leading_zeros = 0
        while pos < len(bits) and bits[pos] == '0':
            leading_zeros += 1
            pos += 1

        if pos >= len(bits):
            raise ValueError("Incomplete exp-Golomb code: no '1' bit found.")

        num_bits_to_read = leading_zeros + 1
        if pos + num_bits_to_read > len(bits):
            raise ValueError("Incomplete exp-Golomb code: not enough bits for value.")

        code_bits = bits[pos:pos + num_bits_to_read]
        value = int(code_bits, 2) - 1
        return value, pos + num_bits_to_read


class OptimizedBinomialTable:
    """
    Computes and caches binomial coefficients C(n, k) using Python's arbitrary
    precision integers to prevent overflow.
    """

    def __init__(self):
        self._cache = {}

    def get(self, n: int, k: int) -> int:
        if k < 0 or k > n:
            return 0
        if k == 0 or k == n:
            return 1
        if k > n // 2:
            k = n - k

        key = (n, k)
        if key in self._cache:
            return self._cache[key]

        result = math.comb(n, k)
        self._cache[key] = result
        return result

    def __getitem__(self, n: int):
        return BinomialRow(self, n)


class BinomialRow:
    """Helper class to support table[n][k] syntax."""
    def __init__(self, table: OptimizedBinomialTable, n: int):
        self.table = table
        self.n = n

    def __getitem__(self, k: int) -> int:
        return self.table.get(self.n, k)


class EnumerativeEncoder:
    """
    An enumerative entropy coder aligned with the algorithm described in
    "Entropy Coding Using Equiprobable Partitioning" by Han et al. (2008).

    This implementation is self-contained, writing all necessary information
    (length, alphabet, counts, and positions) into the output stream.
    """

    def __init__(self):
        self.binom_table = OptimizedBinomialTable()

    def _rank(self, n: int, k: int, positions: List[int]) -> int:
        """Calculates the standard lexicographical rank of a combination."""
        index = 0
        for i, pos in enumerate(positions):
            index += self.binom_table.get(pos, i + 1)
        return index

    def _unrank(self, n: int, k: int, index: int) -> List[int]:
        """Converts a standard lexicographical rank back to a combination."""
        positions = []
        v_high = n - 1
        for i in range(k - 1, -1, -1):
            v_low = i
            # Binary search for the largest position p_i
            while v_low < v_high:
                mid = (v_low + v_high + 1) // 2
                if self.binom_table.get(mid, i + 1) <= index:
                    v_low = mid
                else:
                    v_high = mid - 1

            p_i = v_low
            positions.append(p_i)
            index -= self.binom_table.get(p_i, i + 1)
            v_high = p_i - 1

        positions.reverse() # Stored descending, so reverse to ascending
        return positions

    def encode(self, data: List[int]) -> bytes:
        if not data:
            return bytes()

        n = len(data)
        symbol_counts = Counter(data)

        # Optimization: encode symbols from least frequent to most frequent
        sorted_symbols = sorted(symbol_counts.keys(), key=lambda s: symbol_counts[s])
        K = len(sorted_symbols)

        bits = ""
        # Step 1: Encode sequence length n
        bits += ExpGolombCoder.encode(n)

        # Step 2: Encode header - alphabet size (K) and the alphabet itself
        bits += ExpGolombCoder.encode(K)
        for symbol in sorted_symbols:
            bits += ExpGolombCoder.encode(symbol)

        # Step 3: Encode K-1 symbol frequencies
        for i in range(K - 1):
            bits += ExpGolombCoder.encode(symbol_counts[sorted_symbols[i]])

        # Step 4: Encode symbol locations sequentially
        available_indices = list(range(n))

        for i in range(K - 1):
            symbol = sorted_symbols[i]
            k = symbol_counts[symbol]
            if k == 0:
                continue

            current_n = len(available_indices)

            # Find the positions of the current symbol within the available slots
            symbol_positions_in_available = [
                j for j, original_idx in enumerate(available_indices) if data[original_idx] == symbol
            ]

            # Optimization: Use complement method for frequent symbols
            use_complement = k > current_n / 2
            bits += '1' if use_complement else '0'

            if use_complement:
                complement_k = current_n - k
                complement_positions = [j for j in range(current_n) if j not in symbol_positions_in_available]
                index = self._rank(current_n, complement_k, complement_positions)
            else:
                index = self._rank(current_n, k, symbol_positions_in_available)

            bits += ExpGolombCoder.encode(index)

            # Update available indices for the next symbol
            used_indices = {available_indices[j] for j in symbol_positions_in_available}
            available_indices = [idx for idx in available_indices if idx not in used_indices]

        # Convert bit string to bytes with padding
        padding = (8 - len(bits) % 8) % 8
        bits += '0' * padding
        encoded_bytes = bytes(int(bits[i:i+8], 2) for i in range(0, len(bits), 8))

        return encoded_bytes

    def decode(self, encoded_bytes: bytes) -> List[int]:
        if not encoded_bytes:
            return []

        # Convert bytes to bit string
        bits = ''.join(format(byte, '08b') for byte in encoded_bytes)
        pos = 0

        # Step 1: Decode sequence length n
        n, pos = ExpGolombCoder.decode(bits, pos)

        # Step 2: Decode header - alphabet size (K) and the alphabet itself
        K, pos = ExpGolombCoder.decode(bits, pos)
        sorted_symbols = []
        for _ in range(K):
            symbol, pos = ExpGolombCoder.decode(bits, pos)
            sorted_symbols.append(symbol)

        # Step 3: Decode K-1 symbol frequencies
        counts = {}
        decoded_count_sum = 0
        for i in range(K - 1):
            symbol = sorted_symbols[i]
            count, pos = ExpGolombCoder.decode(bits, pos)
            counts[symbol] = count
            decoded_count_sum += count

        # The last symbol's count is implied
        last_symbol = sorted_symbols[-1]
        counts[last_symbol] = n - decoded_count_sum

        # Step 4: Decode symbol locations sequentially
        result = [None] * n
        available_indices = list(range(n))

        for i in range(K - 1):
            symbol = sorted_symbols[i]
            k = counts[symbol]
            if k == 0:
                continue

            current_n = len(available_indices)

            # Read complement flag
            use_complement = (bits[pos] == '1')
            pos += 1

            index, pos = ExpGolombCoder.decode(bits, pos)

            if use_complement:
                complement_k = current_n - k
                complement_positions = self._unrank(current_n, complement_k, index)
                positions_in_available = [j for j in range(current_n) if j not in complement_positions]
            else:
                positions_in_available = self._unrank(current_n, k, index)

            # Map positions from available list back to original sequence
            used_indices = set()
            for rel_pos in positions_in_available:
                abs_pos = available_indices[rel_pos]
                result[abs_pos] = symbol
                used_indices.add(abs_pos)

            # Update available indices
            available_indices = [idx for idx in available_indices if idx not in used_indices]

        # Last symbol fills all remaining positions
        for i in range(n):
            if result[i] is None:
                result[i] = last_symbol

        return result