\( \newcommand{\NOT}{\neg} \newcommand{\AND}{\wedge} \newcommand{\OR}{\vee} \newcommand{\XOR}{\oplus} \newcommand{\IMP}{\Rightarrow} \newcommand{\IFF}{\Leftrightarrow} \newcommand{\TRUE}{\text{True}\xspace} \newcommand{\FALSE}{\text{False}\xspace} \newcommand{\IN}{\,{\in}\,} \newcommand{\NOTIN}{\,{\notin}\,} \newcommand{\TO}{\rightarrow} \newcommand{\DIV}{\mid} \newcommand{\NDIV}{\nmid} \newcommand{\MOD}[1]{\pmod{#1}} \newcommand{\MODS}[1]{\ (\text{mod}\ #1)} \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\cA}{\mathcal A} \newcommand{\cB}{\mathcal B} \newcommand{\cC}{\mathcal C} \newcommand{\cD}{\mathcal D} \newcommand{\cE}{\mathcal E} \newcommand{\cF}{\mathcal F} \newcommand{\cG}{\mathcal G} \newcommand{\cH}{\mathcal H} \newcommand{\cI}{\mathcal I} \newcommand{\cJ}{\mathcal J} \newcommand{\cL}{\mathcal L} \newcommand{\cK}{\mathcal K} \newcommand{\cN}{\mathcal N} \newcommand{\cO}{\mathcal O} \newcommand{\cP}{\mathcal P} \newcommand{\cQ}{\mathcal Q} \newcommand{\cS}{\mathcal S} \newcommand{\cT}{\mathcal T} \newcommand{\cV}{\mathcal V} \newcommand{\cW}{\mathcal W} \newcommand{\cZ}{\mathcal Z} \newcommand{\emp}{\emptyset} \newcommand{\bs}{\backslash} \newcommand{\floor}[1]{\left \lfloor #1 \right \rfloor} \newcommand{\ceil}[1]{\left \lceil #1 \right \rceil} \newcommand{\abs}[1]{\left | #1 \right |} \newcommand{\xspace}{} \newcommand{\proofheader}[1]{\underline{\textbf{#1}}} \)
NOTE: This is the archived 2022-23 version of these notes, and may be out of date. Current CSC110/111 students should visit the current notes page, https://www.teach.cs.toronto.edu/~csc110y/fall/notes/.

A.1 Python Built-In Function Reference

Adapted from https://docs.python.org/3/library/functions.html. Note that not all built-in functions are shown.

Built-in Function Description
abs(x) Return the absolute value of a number. The argument may be an integer or a floating point number.
all(iterable) Return True if all elements of the iterable are true (or if the iterable is empty).
any(iterable) Return True if any element of the iterable is true. If the iterable is empty, return False.
chr(i)

Return the string representing a character whose Unicode code point is the integer i. For example, chr(97) returns the string 'a', while chr(8364) returns the string '€'. This is the inverse of ord().

The valid range for the argument is from 0 through 1,114,111. ValueError will be raised if i is outside that range.
divmod(a, b) Take two (non complex) numbers as arguments and return a pair of numbers consisting of their quotient and remainder when using integer division. For integers, the result is the same as (a // b, a % b). 
filter(
  function,
  iterable
)
 Construct an iterator from those elements of iterable for which function returns True. iterable may be either a sequence, a container which supports iteration, or an iterator.
id(object) Return the “identity” of an object. This is an integer which is guaranteed to be unique and constant for this object during its lifetime.
input([prompt])

If the prompt argument is present, it is written to standard output without a trailing newline. The function then reads a line from input, converts it to a string (stripping a trailing newline), and returns that. Example:

>>> s = input('Type in a word: ')
Type in a word: Python  # "Python" is user input
>>> s
'Python'
 
isinstance(
  object,
  classinfo
)
 Return True if the object argument is an instance of the classinfo argument, or of a subclass thereof. If object is not an object of the given type, the function always returns False.
len(s) Return the length (the number of items) of an object. 
# Form 1

max(
  iterable,
 *
  [, key,
  default]
)


# Form 2

max(
  arg1,
  arg2,
  *args,
  [key]
)

Return the largest item in an iterable or the largest of two or more arguments.

If one positional argument is provided, it should be an iterable. The largest item in the iterable is returned. If two or more positional arguments are provided, the largest of the positional arguments is returned.

There are two optional keyword-only arguments. The key argument specifies a one-argument ordering function like that used for list.sort().

The default argument specifies an object to return if the provided iterable is empty. If the iterable is empty and default is not provided, a ValueError is raised. If multiple items are maximal, the function returns the first one encountered.

 
# Form 1

min(
  iterable, *
  [, key,
  default]
)

# Form 2

min(
  arg1,
  arg2,
  *args,
  [key]
)

Return the smallest item in an iterable or the smallest of two or more arguments.

If one positional argument is provided, it should be an iterable. The smallest item in the iterable is returned. If two or more positional arguments are provided, the smallest of the positional arguments is returned.

There are two optional keyword-only arguments. The key argument specifies a one-argument ordering function like that used for list.sort().

The default argument specifies an object to return if the provided iterable is empty. If the iterable is empty and default is not provided, a ValueError is raised. If multiple items are minimal, the function returns the first one encountered.

 
open(
  file,
  mode='r'
)

Open file and return a corresponding file object. If the file cannot be opened, an OSError is raised.

file is a path-like object giving the pathname (absolute or relative to the current working directory) of the file to be opened.

mode is an optional string that specifies the mode in which the file is opened. It defaults to ‘r’ which means open for reading in text mode. Other common values are ‘w’ for writing (truncating the file if it already exists), ‘x’ for exclusive creation and ‘a’ for appending.
ord(c) Given a string representing one Unicode character, return an integer representing the Unicode code point of that character. For example, ord('a') returns the integer 97 and ord('€') (Euro sign) returns 8364. This is the inverse of chr(). 
pow(
  base, exp
  [, mod]
)
 Return base to the power exp; if mod is present, return base to the power exp, modulo mod (computed more efficiently than pow(base, exp) % mod). The two-argument form pow(base, exp) is equivalent to using the power operator: base ** exp. 
print(
  *objects,
  sep=' ',
  end='\'
)

Print objects to standard output, separated by sep and followed by end. sep and end, if present, must be given as keyword arguments.

Both sep and end must be strings; they can also be None, which means to use the default values.
reversed(seq) Return a reverse iterator. 
round(
  number
  [, ndigits]
)

Return number rounded to ndigits precision after the decimal point. If ndigits is omitted or is None, it returns the nearest integer to its input.

For the built-in types supporting round(), values are rounded to the closest multiple of 10 to the power minus ndigits; if two multiples are equally close, rounding is done toward the even choice (so, for example, both round(0.5) and round(-0.5) are 0, and round(1.5) is 2).

Any integer value is valid for ndigits (positive, zero, or negative). The return value is an integer if ndigits is omitted or None. Otherwise the return value has the same type as number. Note: The behavior of round() for floats can be surprising: for example, round(2.675, 2) gives 2.67 instead of the expected 2.68. This is not a bug: it’s a result of the fact that most decimal fractions can’t be represented exactly as a float. See Floating Point Arithmetic: Issues and Limitations for more information.

 
sorted(
  iterable, *,
  key=None,
  reverse=False
)

Return a new sorted list from the items in iterable.

Has two optional arguments which must be specified as keyword arguments.

key specifies a function of one argument that is used to extract a comparison key from each element in iterable(for example,key=str.lower). The default value isNone(compare the elements directly).reverseis a boolean value. If set toTrue`, then the list elements are sorted as if each comparison were reversed.

 
sum(
  iterable,
  /,
  start=0
)
 Sums start and the items of an iterable from left to right and returns the total.
type(object)

Return the type of an object.

The isinstance() built-in function is recommended for testing the type of an object, because it takes subclasses into account.