import logging
logging.basicConfig(
    level=logging.INFO,
    format='%(asctime)s - %(levelname)s - %(message)s',
    handlers=[
        logging.FileHandler('arithmetic_coding.log'),
        logging.StreamHandler()
    ]
)
dict={
    "A":[0,0.1],
    "R":[0.1,0.2],
    "I":[0.2,0.4],
    "T":[0.4,0.6],
    "H":[0.6,0.7],
    "M":[0.7,0.8],
    "E":[0.8,0.9],
    "C":[0.9,1],
}

def count(word):
    low = 0.0
    high = 1.0

    for char in word:
        if char not in dict:
            raise ValueError(f"Character '{char}' not in probability dictionary")

        # Calculate new range
        range_ = high - low
        new_low = low + dict[char][0] * range_
        new_high = low + dict[char][1] * range_

        # Update range
        low, high = new_low, new_high
        print(f'({low:.15f}, {high:.15f})')
        logging.info(f"  Range updated to: [{new_low:.15f}, {new_high:.15f}] (width: {new_high-new_low:.15f})")
    # Return the final range
    return (low + high) / 2

if __name__ == "__main__":
    count("ARITHMETIC")