Sorting, Minimum and Maximum

Sorting, Minimum and Maximum in Python min, max, and sorted all need the objects to be orderable. Learn More about it here.

Section 72.1: Make custom classes orderable

min, max, and sorted all need the objects to be orderable. To be properly orderable, the class needs to define all of the 6 methods lt, gt, ge, le, ne and eq:

class IntegerContainer(object):
def init(self, value):
self.value = value
def repr(self):
return "{}({})".format(, self.value)
def lt(self, other):
print('{!r} - Test less than {!r}'.format(self, other))
return self.value < other.value def le(self, other): print('{!r} - Test less than or equal to {!r}'.format(self, other)) return self.value <= other.value def gt(self, other): print('{!r} - Test greater than {!r}'.format(self, other)) return self.value > other.value
def ge(self, other):
print('{!r} - Test greater than or equal to {!r}'.format(self, other))
return self.value >= other.value
def eq(self, other):
print('{!r} - Test equal to {!r}'.format(self, other))
return self.value == other.value
def ne(self, other):
print('{!r} - Test not equal to {!r}'.format(self, other))
return self.value != other.value

Though implementing all these methods would seem unnecessary, omitting some of them will make your code prone to bugs.

alist = [IntegerContainer(5), IntegerContainer(3), IntegerContainer(10), IntegerContainer(7)
res = max(alist)
Out: IntegerContainer(3) - Test greater than IntegerContainer(5)
IntegerContainer(10) - Test greater than IntegerContainer(5)
IntegerContainer(7) - Test greater than IntegerContainer(10) print(res)
Out: IntegerContainer(10)
res = min(alist)
Out: IntegerContainer(3) - Test less than IntegerContainer(5)
IntegerContainer(10) - Test less than IntegerContainer(3) – Python® Notes for Professionals 362

IntegerContainer(7) - Test less than IntegerContainer(3) print(res)
Out: IntegerContainer(3)
res = sorted(alist)
Out: IntegerContainer(3) - Test less than IntegerContainer(5)
IntegerContainer(10) - Test less than IntegerContainer(3)
IntegerContainer(10) - Test less than IntegerContainer(5)
IntegerContainer(7) - Test less than IntegerContainer(5)
IntegerContainer(7) - Test less than IntegerContainer(10) print(res)
Out: [IntegerContainer(3), IntegerContainer(5), IntegerContainer(7), IntegerContainer(10)]

sorted with reverse=True also uses lt:

res = sorted(alist, reverse=True)
Out: IntegerContainer(10) - Test less than IntegerContainer(7)
IntegerContainer(3) - Test less than IntegerContainer(10)
IntegerContainer(3) - Test less than IntegerContainer(10)
IntegerContainer(3) - Test less than IntegerContainer(7)
IntegerContainer(5) - Test less than IntegerContainer(7)
IntegerContainer(5) - Test less than IntegerContainer(3) print(res)
Out: [IntegerContainer(10), IntegerContainer(7), IntegerContainer(5), IntegerContainer(3)]

But sorted can use gt instead if the default is not implemented:

del # The IntegerContainer no longer implements "less than"
res = min(alist)
Out: IntegerContainer(5) - Test greater than IntegerContainer(3)
IntegerContainer(3) - Test greater than IntegerContainer(10)
IntegerContainer(3) - Test greater than IntegerContainer(7) print(res)
Out: IntegerContainer(3)

Sorting methods will raise a TypeError if neither lt nor gt are implemented:

del # The IntegerContainer no longer implements "greater then"
res = min(alist)
TypeError: unorderable types: IntegerContainer() < IntegerContainer()

functools.total_ordering decorator can be used simplifying the effort of writing these rich comparison methods. If you decorate your class with total_ordering, you need to implement eq, ne and only one of the lt, le, ge or gt, and the decorator will fill in the rest:

import functools
class IntegerContainer(object):
def init(self, value):
self.value = value
def repr(self):
return "{}({})".format(, self.value) – Python® Notes for Professionals 363

def lt(self, other):
print('{!r} - Test less than {!r}'.format(self, other))
return self.value < other.value def eq(self, other): print('{!r} - Test equal to {!r}'.format(self, other)) return self.value == other.value def ne(self, other): print('{!r} - Test not equal to {!r}'.format(self, other)) return self.value != other.value IntegerContainer(5) > IntegerContainer(6)
Output: IntegerContainer(5) - Test less than IntegerContainer(6)
Returns: False
IntegerContainer(6) > IntegerContainer(5)
Output: IntegerContainer(6) - Test less than IntegerContainer(5)
Output: IntegerContainer(6) - Test equal to IntegerContainer(5)
Returns True

Notice how the > (greater than) now ends up calling the less than method, and in some cases even the eq method. This also means that if speed is of great importance, you should implement each rich comparison method yourself.

Section 72.2: Special case: dictionaries

Getting the minimum or maximum or using sorted depends on iterations over the object. In the case of dict, the iteration is only over the keys:

adict = {'a': 3, 'b': 5, 'c': 1}
Output: 'a' max(adict)
Output: 'c' sorted(adict)
Output: ['a', 'b', 'c']

To keep the dictionary structure, you have to iterate over the .items():

Output: ('a', 3) max(adict.items())
Output: ('c', 1) sorted(adict.items())
Output: [('a', 3), ('b', 5), ('c', 1)]

For sorted, you could create an OrderedDict to keep the sorting while having a dict-like structure:

from collections import OrderedDict
Output: OrderedDict([('a', 3), ('b', 5), ('c', 1)]) res = OrderedDict(sorted(adict.items()))
Output: 3

By value – Python® Notes for Professionals

Again this is possible using the key argument:

min(adict.items(), key=lambda x: x[1])

Output: (‘c’, 1)

max(adict.items(), key=operator.itemgetter(1))

Output: (‘b’, 5)

sorted(adict.items(), key=operator.itemgetter(1), reverse=True)

Output: [(‘b’, 5), (‘a’, 3), (‘c’, 1)]

Section 72.3: Using the key argument

Finding the minimum/maximum of a sequence of sequences is possible:

list_of_tuples = [(0, 10), (1, 15), (2, 8)]

Output: (0, 10)

but if you want to sort by a specific element in each sequence use the key-argument:

min(list_of_tuples, key=lambda x: x[0])

Output: (0, 10)

min(list_of_tuples, key=lambda x: x[1])

Output: (2, 8)

sorted(list_of_tuples, key=lambda x: x[0])

Output: [(0, 10), (1, 15), (2, 8)]

sorted(list_of_tuples, key=lambda x: x[1])

Output: [(2, 8), (0, 10), (1, 15)]

Sorting by first element

Sorting by second element

Sorting by first element (increasing)

Sorting by first element

import operator
The operator module contains efficient alternatives to the lambda function max(list_of_tuples, key=operator.itemgetter(0)) # Sorting by first element
Output: (2, 8)
max(list_of_tuples, key=operator.itemgetter(1)) # Sorting by second element

Output: (1, 15)

sorted(list_of_tuples, key=operator.itemgetter(0), reverse=True) # Reversed (decreasing)

Output: [(2, 8), (1, 15), (0, 10)]

sorted(list_of_tuples, key=operator.itemgetter(1), reverse=True) # Reversed(decreasing)

Output: [(1, 15), (0, 10), (2, 8)]

Section 72.4: Default Argument to max, min

You can’t pass an empty sequence into max or min:


ValueError: min() arg is an empty sequence

However, with Python 3, you can pass in the keyword argument default with a value that will be returned if the sequence is empty, instead of raising an exception: – Python® Notes for Professionals 365

max([], default=42)

Output: 42

max([], default=0)

Output: 0

Section 72.5: Getting a sorted sequence

Using one sequence:

sorted((7, 2, 1, 5)) # tuple

Output: [1, 2, 5, 7]

sorted(['c', 'A', 'b']) # list

Output: [‘A’, ‘b’, ‘c’]

sorted({11, 8, 1}) # set

Output: [1, 8, 11]

sorted({'11': 5, '3': 2, '10': 15}) # dict

Output: [’10’, ’11’, ‘3’] # only iterates over the keys

sorted(‘bdca’) # string

Output: [‘a’,’b’,’c’,’d’]

The result is always a new list; the original data remains unchanged.

Section 72.6: Extracting N largest or N smallest items from an iterable

To find some number (more than one) of largest or smallest values of an iterable, you can use the nlargest and nsmallest of the heapq module:

import heapq

get 5 largest items from the range

heapq.nlargest(5, range(10))

Output: [9, 8, 7, 6, 5]

heapq.nsmallest(5, range(10))

Output: [0, 1, 2, 3, 4]

This is much more efficient than sorting the whole iterable and then slicing from the end or beginning. Internally these functions use the binary heap priority queue data structure, which is very efficient for this use case.

Like min, max and sorted, these functions accept the optional key keyword argument, which must be a function that, given an element, returns its sort key.

Here is a program that extracts 1000 longest lines from a file:

import heapq
with open(filename) as f:
longest_lines = heapq.nlargest(1000, f, key=len)

Here we open the file, and pass the file handle f to nlargest. Iterating the file yields each line of the file as a separate string; nlargest then passes each element (or line) is passed to the function len to determine its sort key. – Python® Notes for Professionals 366

len, given a string, returns the length of the line in characters.

This only needs storage for a list of 1000 largest lines so far, which can be contrasted with

longest_lines = sorted(f, key=len)[1000:]

which will have to hold the entire file in memory.

Section 72.7: Getting the minimum or maximum of several values


Output: 1


Output: 7

Section 72.8: Minimum and Maximum of a sequence

Getting the minimum of a sequence (iterable) is equivalent of accessing the first element of a sorted sequence:

min([2, 7, 5])

Output: 2

sorted([2, 7, 5])[0]

Output: 2

The maximum is a bit more complicated, because sorted keeps order and max returns the first encountered value.

In case there are no duplicates the maximum is the same as the last element of the sorted return:

max([2, 7, 5])

Output: 7

sorted([2, 7, 5])[-1]

Output: 7

But not if there are multiple elements that are evaluated as having the maximum value:

class MyClass(object):
def init(self, value, name):
self.value = value = name
def lt(self, other):
return self.value < other.value
def repr(self):
return str(
sorted([MyClass(4, 'first'), MyClass(1, 'second'), MyClass(4, 'third')])

Output: [second, first, third]

max([MyClass(4, 'first'), MyClass(1, 'second'), MyClass(4, 'third')])

Output: first

Any iterable containing elements that support < or > operations are allowed.

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