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oct() Function Complexity

The oct() function returns the octal (base 8) representation of an integer.

Complexity Analysis

Case Time Space Notes
Convert integer O(log n) O(log n) n = integer value
Negative integer O(log n) O(log n) Adds '-0o' prefix
Large integer O(log n) O(log n) Works with arbitrary precision

Basic Usage

Decimal to Octal

# O(log n) - where n = integer value
oct(0)      # '0o0'
oct(8)      # '0o10'
oct(64)     # '0o100'
oct(512)    # '0o1000'
oct(4095)   # '0o7777'

Negative Numbers

# O(log n) - shows magnitude with minus
oct(-1)     # '-0o1'
oct(-8)     # '-0o10'
oct(-64)    # '-0o100'

Large Integers

# O(log n) - octal digits
oct(2**9)    # '0o1000'
oct(2**12)   # '0o10000'
oct(2**100)  # Very large octal number

Complexity Details

Logarithmic Time

Conversion time grows with the number of octal digits:

# Small number - few digits
oct(8)      # '0o10' - 2 digits, O(log 8) = O(3)

# Large number - more digits
oct(2**24 - 1)  # 8 octal digits
                # O(log(2**24)) = O(24)

# Relationship: octal digits = log₈(n) ≈ log₂(n) / 3

Common Patterns

File Permissions (Unix/Linux)

# O(log n) - display file permissions in octal
import os

# File mode as integer
file_mode = 0o755  # Standard permissions

# Check permission components
user = (file_mode >> 6) & 0o7      # User permissions
group = (file_mode >> 3) & 0o7     # Group permissions
other = file_mode & 0o7             # Other permissions

print(f"User: {user}, Group: {group}, Other: {other}")
# User: 7, Group: 5, Other: 5

# Display in octal
print(oct(file_mode))  # '0o755'

# Convert back from octal
permissions = int('0o755', 8)  # 493 (decimal)
assert oct(permissions) == '0o755'

Octal Escapes in Strings

# Octal digits represent characters
# Not directly needed, but useful to understand

# '\101' is character with octal code 101
char = '\101'  # Same as chr(65) = 'A'
assert char == 'A'

# View the octal code
code = ord('A')
octal_code = oct(code)  # '0o101'

Comparison with Alternatives

oct() vs format()

# oct() - returns string with '0o' prefix
oct(255)           # '0o377'

# format() - more flexible
format(255, 'o')   # '377' (no prefix)
format(255, '#o')  # '0o377' (with prefix)

# Performance - both O(log n), similar speed

oct() vs hex() vs bin()

# All O(log n) but different bases
value = 64

hex(value)    # '0x40'     (base 16) - most compact
oct(value)    # '0o100'    (base 8)  - medium
bin(value)    # '0b1000000' (base 2) - longest

# Use case:
# hex - colors, memory addresses
# oct - file permissions, historical/legacy
# bin - bit manipulation

Bidirectional Conversion

# oct() and int() are inverses
# O(log n) each way

x = 64
octal_str = oct(x)       # O(log 64)
restored = int(octal_str, 8)  # O(log 64)
assert restored == x

# Useful for configuration
mode = 0o755
octal_form = oct(mode)   # '0o755'
restored = int(octal_form, 8)  # 493 (decimal)

Performance Patterns

Batch Conversion

# O(n * log m) - n numbers, each ~m value
numbers = [0o100, 0o200, 0o400]
octal_strings = [oct(n) for n in numbers]
# O(n * log m)

# vs direct format
octal_strings = [f"{n:o}" for n in numbers]
# Similar complexity

Building Octal Values

# O(log n) - combine octal digits
def build_permissions(user, group, other):
    # Each component is 0-7
    return (user << 6) | (group << 3) | other

perms = build_permissions(7, 5, 5)  # 0o755
print(oct(perms))  # '0o755'

Practical Examples

File Operations

import os
import stat

# O(log n) - file mode operations
def get_permissions(path):
    mode = os.stat(path).st_mode
    perms = stat.S_IMODE(mode)
    return oct(perms)  # Returns octal string

# Create file with specific permissions
# os.chmod('/path/to/file', 0o644)  # Read/write owner, read others

System Calls

# O(log n) - convert to octal for system operations
# Historically common, less so now

permissions = 0o755
print(f"Setting permissions to {oct(permissions)}")
# '0o755' - rwxr-xr-x

permissions = 0o644
print(f"Setting permissions to {oct(permissions)}")
# '0o644' - rw-r--r--

Legacy Code

# Octal literals still used in modern Python
# O(log n) - conversion for display

# Python 2 required octal literals like 0755
# Python 3 uses 0o755

legacy_octal = 0o755
modern_octal = 0o755

assert legacy_octal == modern_octal

# Display
print(oct(legacy_octal))  # '0o755'

Special Cases

Zero

# O(1)
oct(0)  # '0o0'

Powers of Eight

# O(log n) - shows pattern with single digit
oct(1)      # '0o1'
oct(8)      # '0o10'
oct(64)     # '0o100'
oct(512)    # '0o1000'
oct(8**4)   # '0o10000'

Common Permission Values

# O(1) - common patterns
oct(0o755)  # '0o755' - rwxr-xr-x (normal)
oct(0o644)  # '0o644' - rw-r--r-- (file)
oct(0o600)  # '0o600' - rw------- (private)
oct(0o700)  # '0o700' - rwx------ (directory)

Octal vs Decimal Performance

import timeit

# Performance is similar, O(log n) for both
value = 262144  # 2**18

# Decimal
t1 = timeit.timeit(lambda: str(value), number=100000)

# Octal
t2 = timeit.timeit(lambda: oct(value), number=100000)

# Similar time, decimal slightly faster due to base 10

Best Practices

✅ Do:

  • Use octal for file permissions and modes
  • Use format(value, 'o') if you don't need '0o' prefix
  • Use octal literals in permission codes: 0o755
  • Use int(octal_str, 8) to parse octal

❌ Avoid:

  • Using octal without clear purpose (confusing)
  • Forgetting the '0o' prefix (Python 3 requires it)
  • Assuming octal arithmetic (it's still base 10)
  • Using octal for new code (hex or binary clearer)
  • hex() - Hexadecimal representation
  • bin() - Binary representation
  • int() - Convert to integer (can parse octal)
  • format() - Format with specifications

Version Notes

  • Python 2.x: Octal literals: 0755 (could omit 'o')
  • Python 3.x: Octal literals: 0o755 (requires 'o')
  • All versions: Works with arbitrary precision integers
  • Note: Octal rarely used in modern code, prefer hex or binary