"""
Base62 encoding for short URL generation.

- Uses 0-9, A-Z, a-z (62 characters)
- URL-safe (no special characters)
- More compact than hex (base16) or base64

Length vs Capacity:
- 6 chars: 62^6 = 56.8 billion unique URLs
- 7 chars: 62^7 = 3.5 trillion unique URLs
"""

CHARSET = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
BASE = len(CHARSET)  # 62


def base62_encode(num: int) -> str:
    """
    Encode an integer to a base62 string.
    """
    if num < 0:
        raise ValueError("Cannot encode negative numbers")
    if num == 0:
        return CHARSET[0]

    result = []
    while num:
        result.append(CHARSET[num % BASE])
        num //= BASE

    return "".join(reversed(result))


def base62_decode(encoded: str) -> int:
    """
    Decode a base62 string back to an integer.
    """
    if not encoded:
        raise ValueError("Cannot decode empty string")

    num = 0
    for char in encoded:
        if char not in CHARSET:
            raise ValueError(f"Invalid character: {char}")
        num = num * BASE + CHARSET.index(char)

    return num


def pad_to_length(encoded: str, length: int = 7) -> str:
    """Pad encoded string to minimum length with leading zeros."""
    return encoded.zfill(length)[-length:] if len(encoded) < length else encoded