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array Module Complexity

The array module provides one mutable sequence type, array.array, that stores its items as packed C values of a single type chosen by a type code. The buffer is contiguous and over-allocated the way a list's is, so indexing, appending and shifting cost what they cost on a list. What changes is storage: each item takes itemsize bytes instead of a pointer plus a separate Python object, and each read converts the stored value to a Python object.

n is the items in the array, k is the items in the other operand - the initializer, the iterable or array being added, the slice, the bytes or string being converted - and i is an index. Bounds count items; an item is a fixed itemsize bytes, so bytes and items differ only by a constant. Comparing one stored value with another object is priced O(1). Every call that adds items is amortized the way append() is: the call that reallocates can also move the n items already there.

Complexity Reference

array

Operation	Time	Space	Notes
array.array(typecode[, initializer])	O(k)	O(k)	Any iterable of values; bytes is taken as machine values
array.ArrayType	O(1)	O(1)	Another name for array.array
array.typecodes	O(1)	O(1)	A string of the type codes this build supports
array.typecode, array.itemsize	O(1)	O(1)	Fixed for the array's lifetime
array.buffer_info()	O(1)	O(1)	(address, length) of the buffer
len(a)	O(1)	O(1)

Access and search

Operation	Time	Space	Notes
a[i]	O(1)	O(1)	Converts the stored value to a Python object
a[i] = x	O(1)	O(1)	For an integer type code, a value outside its range raises OverflowError
a[start:stop:step]	O(k)	O(k)	k = items in the slice; a new array, not a view
Iterating an array	O(1) per item	O(1)	Each step converts one stored value to a Python object
x in a, array.index(x[, start[, stop]])	O(n)	O(1)	Stops at the first match
array.count(x)	O(n)	O(1)	Always compares every item
a == b, a < b	O(n)	O(1)	== between arrays of different lengths is O(1)

Adding and removing

Operation	Time	Space	Notes
array.append(x)	O(1) amortized	O(1)	O(n) on the append that reallocates
array.extend(iterable)	O(k)	O(k)	An array argument must have the same type code; a bad item stops it with earlier items kept
a += b	O(k)	O(k)	b must be an array of the same type code
array.insert(i, x)	O(n)	O(1)	Shifts the items after i
array.pop([i])	O(n)	O(1)	O(1) for the last item
array.remove(x)	O(n)	O(1)	Scans for the first match, then shifts the items after it
del a[i], del a[start:stop]	O(n)	O(1)	Shifts the items after the deleted range
a[start:stop] = b	O(n + k)	O(k)	b must be an array of the same type code
array.clear()	O(1)	O(1)	Python 3.13+
array.reverse()	O(n)	O(1)	In place
array.byteswap()	O(n)	O(1)	In place
a + b	O(n + k)	O(n + k)	A new array
a * m, a *= m	O(n·m)	O(n·m)	m = repeat count
copy.copy(a), copy.deepcopy(a)	O(n)	O(n)	The items are plain values, so a deep copy is the same buffer copy

Conversions and files

Operation	Time	Space	Notes
array.tolist()	O(n)	O(n)	One Python object per item
array.fromlist(list)	O(k)	O(k)	Accepts only a list; a bad item leaves the array unchanged
array.tobytes()	O(n)	O(n)	A copy of the buffer
array.frombytes(buffer)	O(k)	O(k)	The length must be a multiple of itemsize
array.tofile(f)	O(n)	O(1)	Writes in fixed-size blocks, so the extra memory is one block, not the array
array.fromfile(f, k)	O(k)	O(k)	One read() of k·itemsize bytes
array.tounicode()	O(n)	O(n)	'u' and 'w' arrays only
array.fromunicode(s)	O(k)	O(k)	'u' and 'w' arrays only
memoryview(a)	O(1)	O(1)	Shares the buffer; while a view exists, anything that resizes the array raises BufferError

Type Codes

The type code fixes the bytes per item. The integer codes map to C types, whose sizes are fixed only as minimums, so 'i' and 'l' in particular vary by platform. array.typecodes lists what this build has.

import array

assert array.array('b').itemsize == 1  # signed char
assert array.array('B').itemsize == 1  # unsigned char
assert array.array('h').itemsize >= 2  # signed short
assert array.array('q').itemsize >= 8  # signed long long
assert array.array('f').itemsize == 4  # float
assert array.array('d').itemsize == 8  # double
assert array.array('i').itemsize >= 2  # C int: 4 on common platforms

# Values are checked against the type code on the way in
values = array.array('b', [-128, 0, 127])  # O(k)
try:
    values[0] = 128  # O(1)
except OverflowError as error:
    assert 'maximum' in str(error)
else:
    raise AssertionError('128 fit in a signed char')

assert set('bBhHiIlLqQfd') <= set(array.typecodes)  # O(1)

Memory Compared with a List

Both are O(n). A list's sys.getsizeof() counts one pointer per item and none of the objects the pointers reach, while an array's counts its whole buffer at itemsize bytes per item. So getsizeof() alone flatters the list: the per-item objects only the list has are left out.

import array
import sys

values = list(range(2_000, 12_000))  # above the small-int cache: distinct objects
packed = array.array('i', values)    # O(k)

assert sys.getsizeof(packed) < sys.getsizeof(values)  # 4-byte items against 8-byte pointers

# getsizeof() of the list leaves out the ints themselves
reachable = sys.getsizeof(values) + sum(sys.getsizeof(v) for v in values)  # O(n)
assert reachable > 2 * sys.getsizeof(values)

# The array's storage is its items times itemsize, plus the header
payload = sys.getsizeof(packed) - sys.getsizeof(array.array('i'))
assert payload >= len(packed) * packed.itemsize

Reading Items

An array holds raw values, not objects. Indexing, iteration, in, index(), count() and tolist() each build a Python object from the stored value, so the saving is in storage, not in element access. in and index() stop at the first match; count() always walks every item.

import array

readings = array.array('q', [10**12, 2 * 10**12, 3 * 10**12])

first = readings[0]  # O(1)
assert first == 10**12
assert readings[0] is not first  # a new object on every read

assert 2 * 10**12 in readings              # O(n), stops at the match
assert readings.index(3 * 10**12) == 2     # O(n)
assert readings.count(10**12) == 1         # O(n), every item
assert readings.tolist() == [10**12, 2 * 10**12, 3 * 10**12]  # O(n)

# A slice is a new array
window = readings[1:]  # O(k)
window[0] = 0
assert readings[1] == 2 * 10**12

Adding and Removing Items

Growth and Shrinking

The buffer grows in steps, so most appends only fill a spare slot and the occasional one reallocates. Removing items one at a time never gives memory back: the buffer shrinks only when a single call removes a run of items at once, such as a slice deletion or clear().

import array
import sys

values = array.array('i')
for n in range(1_000):
    values.append(n)  # O(1) amortized
assert len(values) == 1_000

full = sys.getsizeof(values)
for _ in range(900):
    values.pop()  # O(1) at the end
assert sys.getsizeof(values) == full  # the buffer was kept

del values[10:]  # O(n) - one call removes the run
assert sys.getsizeof(values) < full

Inserting in the Middle

insert(), pop(i), remove() and slice deletion shift every item after the position, as on a list. Only the end of the array is cheap.

import array

values = array.array('i', [1, 2, 3, 4, 5])

values.insert(0, 0)  # O(n) - shifts five items
assert values[0] == 0

assert values.pop() == 5   # O(1)
assert values.pop(0) == 0  # O(n) - shifts the rest back

values.remove(3)  # O(n) - scan, then shift
assert values.tolist() == [1, 2, 4]

Extending

extend() takes any iterable and converts one item at a time, so a bad item stops it with the earlier ones already appended. fromlist() accepts only a list and leaves the array unchanged on a bad item. += and slice assignment accept only an array of the same type code.

import array

values = array.array('i', [1])

try:
    values.extend([2, 'x'])  # O(k)
except TypeError:
    assert values.tolist() == [1, 2]  # 2 was kept
else:
    raise AssertionError('a str was stored in an int array')

try:
    values.fromlist([3, 'x'])  # O(k)
except TypeError:
    assert values.tolist() == [1, 2]  # nothing was kept
else:
    raise AssertionError('a str was stored in an int array')

values += array.array('i', [3, 4])  # O(k)
try:
    values += [5]
except TypeError as error:
    assert 'array' in str(error)
else:
    raise AssertionError('+= accepted a list')

assert values.tolist() == [1, 2, 3, 4]

Bytes, Files and Buffers

Converting to and from Bytes

tobytes() and frombytes() copy the buffer as machine values, in native byte order. byteswap() converts in place when the other side uses the opposite order.

import array

values = array.array('h', [1, 256])
raw = values.tobytes()  # O(n) - a copy
assert len(raw) == len(values) * values.itemsize

restored = array.array('h')
restored.frombytes(raw)  # O(k)
assert restored == values

restored.byteswap()  # O(n), in place
assert restored.tolist() == [256, 1]

Files

tofile() writes the buffer in fixed-size blocks, so it needs no copy of the whole array. fromfile() asks for all k items in one read() call; when the file holds fewer whole items, it appends those and raises EOFError.

import array
import io

values = array.array('d', [0.5] * 1_000)
stream = io.BytesIO()
values.tofile(stream)  # O(n) time, one block of extra memory

stream.seek(0)
loaded = array.array('d')
loaded.fromfile(stream, 1_000)  # O(k)
assert loaded == values

# Asking for more than the file holds appends what was there, then raises
stream.seek(0)
short = array.array('d')
try:
    short.fromfile(stream, 2_000)
except EOFError:
    assert len(short) == 1_000
else:
    raise AssertionError('fromfile read past the end')

Sharing the Buffer

memoryview() exposes the array's buffer without copying it. While a view is alive the array cannot resize, so appends, removals and clear() raise BufferError until the view is released.

import array

values = array.array('i', [1, 2, 3])
view = memoryview(values)  # O(1) - no copy
values[0] = 10
assert view[0] == 10  # the same memory

try:
    values.append(4)
except BufferError as error:
    assert 'exporting buffers' in str(error)
else:
    raise AssertionError('the array resized under a live view')

view.release()
values.append(4)  # O(1) amortized again
assert len(values) == 4

Common Patterns

Accumulating Numeric Samples

import array
import io

samples = array.array('d')
for step in range(10_000):
    samples.append(step * 0.5)  # O(1) amortized, 8 bytes per item

total = sum(samples)  # O(n) - one float object per item, built as it goes
assert total == 0.5 * sum(range(10_000))

sink = io.BytesIO()
samples.tofile(sink)  # O(n)
assert len(sink.getvalue()) == len(samples) * samples.itemsize

Performance Best Practices

✅ Do:

• Use an array for large collections of one numeric type, where packed storage saves memory
• Append and pop at the end; only the end is O(1)
• Move binary data with frombytes(), tobytes(), fromfile() and tofile(), which copy machine values without building an object per item
• Use tofile() for a large array: it writes without a copy of the whole buffer
• Delete a slice, or call clear() on 3.13+, to give memory back; popping item by item keeps the buffer

❌ Avoid:

• An array for speed of element access - every read builds a Python object
• insert(0, x) or pop(0) in a loop - each is O(n); use collections.deque for a queue
• Holding a memoryview longer than needed - the array cannot resize while it exists

Version Notes

• Python 3.13+: Added clear() and the 'w' type code (a 4-byte Unicode character); the 'u' type code emits DeprecationWarning
• All Python 3: tofile() and tobytes() write native byte order; call byteswap() for the other order

Related Modules

• list - Any object per slot, at a pointer plus the object per item
• struct - Pack mixed-type records rather than runs of one type
• memoryview - Zero-copy views of an array's buffer
• collections - deque for O(1) appends and pops at both ends