Python’s built-in `sorted()`

function enables programmers to sort a list efficiently and easily. On the other hand, the `list.sort()`

method provides an in-place sorting mechanism. Additionally, Python allows for custom sorting using the `key`

parameter in these functions, enabling more advanced sorting scenarios.

In this article, I’ll show you **how to find an element in a Python data structure (e.g., list, set, dict, tuple) that is already sorted.**

Binary search is a powerful technique to search through sorted lists at lightning speed. Python’s standard library provides the `bisect`

module, which offers utilities that facilitate binary search operations on sorted lists, making it an attractive option for working with sorted data.

## Finding Elements in Sorted Lists

Searching for elements in a sorted list can be much more efficient compared to an unsorted list. In this section, we’ll discuss three methods for finding elements in sorted lists: Binary Search, `Bisect_left`

, and `Bisect_right`

. π

### Binary Search

π **Binary search** is a classic algorithm to search for an element in a sorted list. It works by repeatedly dividing the list in half and checking the middle element.

π If the middle element matches the target, we’re done.

π If the middle element is greater than the target, the target must lie in the left half.

π If the middle element is less than the target, the target must lie in the right half.

This process continues until the target is found or the list is exhausted.

Here is a simple implementation:

def binary_search(lst, target): left, right = 0, len(lst) - 1 while left <= right: mid = left + (right - left) // 2 if lst[mid] == target: return mid elif lst[mid] < target: left = mid + 1 else: right = mid - 1 return -1

π More efficient than a linear search, the binary search algorithm operates in *O(log n)* time complexity.

### Bisect_left

The `bisect_left()`

function from Python’s built-in `bisect`

module is an alternative to the binary search algorithm. It finds the index of where the target element should be inserted to maintain the sorted order. If the target is already present in the input list, it returns the index of the leftmost occurrence of the target.

Here’s an example of using `bisect_left`

:

from bisect import bisect_left lst = [1, 3, 4, 4, 6, 8] target = 4 index = bisect_left(lst, target) # Check if the index contains the target in the list if index != len(lst) and lst[index] == target: print(f"Element found at index {index}") else: print("Element not found.")

π‘ This function can be handy for maintaining sorted lists, updating them as new elements are inserted.

### Bisect_right

Similar to `bisect_left()`

, the `bisect_right()`

function from the `bisect`

module returns the index where the target element should be inserted while preserving the order of the input sorted list. However, it returns the index of the rightmost occurrence of the target in the case that the target already exists in the list.

Here’s an example with `bisect_right`

:

from bisect import bisect_right lst = [1, 3, 4, 4, 6, 8] target = 4 index = bisect_right(lst, target) # Check if the index-1 contains the target in the list if index > 0 and lst[index - 1] == target: print(f"Element found at index {index - 1}") else: print("Element not found.")

π Both `bisect_left`

and `bisect_right`

offer a clear and concise way to find elements in sorted lists, while maintaining the order efficiently.

By understanding and applying these three methods, searching for elements in sorted lists becomes a breeze. Happy coding! π

## Built-in Python Functions and Methods

### Sorted Function

The `sorted()`

function is a built-in Python function that takes an iterable and returns a new sorted list. It’s not limited to lists, accepting various iterable data types. This function is particularly useful when you need a sorted version of the original iterable without modifying it. π§

Here’s an example:

numbers = [4, 1, 3, 2] sorted_numbers = sorted(numbers) print(sorted_numbers) # Output: [1, 2, 3, 4]

You can also customize the sorting using arguments like `key`

and `reverse`

. For example, using `lambda`

function with `sorted()`

:

students = [('Alice', 18), ('Bob', 20), ('Charlie', 17)] sorted_students = sorted(students, key=lambda x: x[1], reverse=True) print(sorted_students) # Output: [('Bob', 20), ('Alice', 18), ('Charlie', 17)]

### Sort Method

Python lists have a built-in `sort()`

method that modifies the list in-place. It returns `None`

, emphasizing that the original list is changed, and no new list is created. π

Example of using `sort()`

method:

numbers = [4, 1, 3, 2] numbers.sort() print(numbers) # Output: [1, 2, 3, 4]

Similar to `sorted()`

function, the `sort()`

method also accepts `key`

and `reverse`

arguments:

students = [('Alice', 18), ('Bob', 20), ('Charlie', 17)] students.sort(key=lambda x: x[1], reverse=True) print(students) # Output: [('Bob', 20), ('Alice', 18), ('Charlie', 17)]

### Other List Methods

Several other list methods are useful in handling sorted lists. For example, `index()`

, `count()`

, `len()`

, and `pop()`

can provide valuable insights or modify the list when needed. π

`index()`

: Returns the first index of a given value.`count()`

: Returns the number of occurrences of a given value.`len()`

: Returns the length of the list.`pop()`

: Removes an item at a specified index and returns it.

Here’s an example:

numbers = [1, 2, 3, 4, 4, 4, 5] index_4 = numbers.index(4) num_4 = numbers.count(4) length_numbers = len(numbers) last_item = numbers.pop() print(index_4) # Output: 3 print(num_4) # Output: 3 print(length_numbers) # Output: 7 print(last_item) # Output: 5

You can download my Python list methods cheat sheet by clicking on the image here:

## Sorting Techniques

### Sorting Lists

In Python, you can easily sort a list in ascending order using the `sorted()`

function or the `list.sort()`

method. The `sorted()`

function returns a new sorted list, while `list.sort()`

modifies the original list in-place.

numbers = [5, 2, 3, 1, 4] sorted_numbers = sorted(numbers) # returns [1, 2, 3, 4, 5] numbers.sort() # modifies numbers to [1, 2, 3, 4, 5]

For descending order, add the `reverse=True`

parameter:

descending_numbers = sorted(numbers, reverse=True) # returns [5, 4, 3, 2, 1]

### Sorting Tuples

Tuples are immutable, so you can only use the `sorted()`

function to get a sorted list of its elements. You can then convert the list back to a tuple if needed.

tuple_example = (5, 2, 3, 1, 4) sorted_tuple = tuple(sorted(tuple_example)) # returns (1, 2, 3, 4, 5)

### Sorting Strings

Strings can also be sorted using the `sorted()`

function, which returns a list of characters in alphabetical order. To convert the result back to a string, use `''.join()`

.

string_example = "hello" sorted_string = ''.join(sorted(string_example)) # returns "ehllo"

### Sorting Sets

Sets are unordered, but you can still sort their elements using the `sorted()`

function, which then returns a sorted list.

set_example = {5, 2, 3, 1, 4} sorted_set = sorted(set_example) # returns [1, 2, 3, 4, 5]

We have actually created a video on sorting sets here:

π **Recommended**: How To Sort A Set Of Values?

### Sorting Dictionaries

Dictionaries can be sorted by keys or values. Use the `sorted()`

function along with a lambda function as a `key`

parameter to specify the sorting criteria.

dict_example = {"a": 3, "b": 1, "c": 2} sorted_by_key = dict(sorted(dict_example.items())) # returns {"a": 3, "b": 1, "c": 2} sorted_by_value = dict(sorted(dict_example.items(), key=lambda item: item[1])) # returns {"b": 1, "c": 2, "a": 3}

Remember to keep the sorting techniques simple and appropriate for the data types you’re working with! ππ‘

## Custom Sorting

### Using Key Argument

The `key`

argument allows you to provide a custom sorting criterion for your lists. It takes a function as a value, which is applied to each element of the list before performing the actual sort. π

For instance, the following code sorts a list of numbers by their absolute values:

numbers = [-5, 3, -2, 1, 4] sorted_numbers = sorted(numbers, key=abs)

Here, the `abs()`

function gets the absolute value of each number, and the list is sorted accordingly. You can also use lambda functions for more complex sorting criteria:

data = [("apple", 3), ("banana", 1), ("orange", 2)] sorted_data = sorted(data, key=lambda x: x[1])

In this example, the `key`

argument specifies that the second element of each tuple should be used as the sorting criterion.

### Using Reverse Parameter

The `reverse`

parameter is a simple **boolean** flag that allows you to change the sort order from ascending (default) to descending. π To use it, just set it to `True`

:

numbers = [1, 2, 3, 4, 5] sorted_numbers = sorted(numbers, reverse=True)

This will yield a sorted list `[5, 4, 3, 2, 1]`

, which is sorted in descending order.

### Using Cmp Parameter

β οΈ The `cmp`

parameter was used in Python 2 for providing a **custom comparison** function to the `sorted`

and `list.sort()`

functions. However, it’s been removed in Python 3, but you can achieve the same functionality using the `key`

parameter or functools module.

Here’s how to use the `key`

parameter to implement custom comparison logic:

def custom_compare(x): # Your custom comparison logic here return x data = [1, 2, 3, 4, 5] sorted_data = sorted(data, key=custom_compare)

Replace the comment with your own logic for sorting your data.

For more advanced use cases, you can leverage the `functools`

module and its `cmp_to_key`

function:

import functools def custom_compare(x, y): # Your custom comparison logic here return x - y data = [1, 2, 3, 4, 5] sorted_data = sorted(data, key=functools.cmp_to_key(custom_compare))

Again, replace the comment with your own comparison logic for better control over the sorting process. π οΈ Remember, though, that using the `key`

argument is usually more efficient and easier to understand.

## Advanced Sorting Concepts

### Sorting in NumPy

NumPy, a popular library in Python, offers powerful tools for sorting arrays efficiently. The `sort`

function in NumPy can be applied to one-dimensional arrays and allows sorting in both ascending and descending order. To sort a NumPy array, you can simply use the following syntax:

import numpy as np arr = np.array([9, 3, 5, 1]) sorted_arr = np.sort(arr)

In cases where you need to sort a two-dimensional array along a specific axis (e.g., **left** to **right** or **side** to **side**), you can use the `axis`

parameter:

arr_2d = np.array([[3, 2, 1], [6, 5, 4]]) sorted_arr_2d = np.sort(arr_2d, axis=1)

Moreover, NumPy also provides the `argsort`

function, which returns the indices of the sorted elements instead of the actual values.

### Sorting Complex Numbers

Python has built-in support for **complex numbers**, and sorting them can be a bit tricky. Since complex numbers have both real and imaginary parts, comparisons are not directly possible using traditional sorting **methods**.

To sort a **list** of complex numbers, you can create a **comparison** function that returns a specific value based on the properties of the complex numbers. For instance, you can sort based on the real part, the imaginary part, or the magnitude:

complex_list = [1 + 2j, 2 + 1j, 3 + 4j] sorted_by_real = sorted(complex_list, key=lambda x: x.real) sorted_by_imag = sorted(complex_list, key=lambda x: x.imag) sorted_by_magnitude = sorted(complex_list, key=lambda x: abs(x))

Keep in mind that the above examples use the `sorted`

function, which creates a new sorted list without altering the original one. If you want to sort the list in-place, you may use the `.sort()`

**method** instead, with the same `key`

parameter.

By using NumPy and custom sorting functions, you can confidently sort a wide range of **iterables** in Python, including complex numbers and even more advanced data types. Just remember the importance of choosing the right sorting strategy and the specific properties to use as comparison metrics. π

## Operations on Sorted Lists

In this section, we will discuss various operations on sorted lists in Python. These operations include inserting elements, removing elements, and performing copy and in-place operations.

### Inserting Elements

When working with sorted lists, you may want to insert elements while maintaining the sorted order. In Python, you can use the `bisect.insort()`

function from the `bisect`

module to accomplish this.

The syntax for using `insort()`

is:

import bisect bisect.insort(array, element)

where `array`

is the sorted list, and `element`

is the item you wish to insert in the correct position to maintain the sorted order. For example:

import bisect numbers = [1, 3, 4, 6, 8] bisect.insort(numbers, 5) print(numbers)

This code would output `[1, 3, 4, 5, 6, 8]`

, as the new element `5`

is inserted in the appropriate position to maintain the ascending order. π

### Removing Elements

To remove an element from a sorted list, you can use the `remove()`

method. The syntax for using `remove()`

is:

array.remove(element)

where `array`

is the sorted list, and `element`

is the item you wish to remove from the list. Please note that this method will remove the first occurrence of the specified item. For example:

numbers = [1, 3, 4, 6, 8] numbers.remove(3) print(numbers)

This code would output `[1, 4, 6, 8]`

, as the element `3`

is removed from the list.

### Copy and In-place Operations

When working with sorted lists, you might want to create a **copy** of a list or perform **in-place** operations. To create a copy of the list, you can use the `copy()`

method:

new_list = array.copy()

For in-place operations, you have a few options. To sort a list in-place, you can use the `sort()`

method:

array.sort()

This method sorts the elements in the list in ascending order by default. However, you can also specify optional parameters such as `key`

for a custom sorting function and `reverse`

to sort the list in descending order. For example:

array.sort(reverse=True)

Another in-place operation is `append()`

, which adds an element to the end of the list:

array.append(element)

Please note that when using `append()`

, the new element may not be inserted in the correct position to maintain the sorted order. This operation is best used when adding elements to the list before sorting it. In such cases, don’t forget to call the `sort()`

method afterwards to maintain the sorted order. π

## Frequently Asked Questions

### How to perform binary search in Python?

Binary search is an efficient algorithm for finding an element in a sorted list. Python’s `bisect`

library provides an easy way to perform binary search. You can use `bisect_left`

or `bisect_right`

from the `bisect`

module to find the position where an element can be inserted while maintaining the sorted order. π

from bisect import bisect_left sorted_list = [1, 3, 4, 4, 6, 8] x = 4 # Find the position using binary search index = bisect_left(sorted_list, x) print(f"Element {x} should be inserted at: {index}")

### What is the purpose of bisect in Python?

The purpose of `bisect`

module in Python is to provide functions for searching and inserting elements into sorted lists while maintaining their sorted order. It is useful when working with large datasets where sorting elements is computationally expensive or maintaining a sorted list at all times is crucial. π

### How to search for an element in a sorted array using Python?

To search for an element in a sorted array using Python, you can use binary search algorithm which can be implemented with the help of `bisect_left`

function from the `bisect`

module. When searching for an element, the `bisect_left`

function returns the index of the element if it is present in the list or the index where the element should be inserted while maintaining the sorted order. π

### What is the time complexity of searching in a sorted list in Python?

Searching for an element in a sorted list using the binary search algorithm has time complexity of O(log n), where n is the number of elements in the list. This time complexity makes binary search an efficient method for searching elements in large sorted lists. β±οΈ

### How to find the index of an element in a sorted list in Python?

You can find the index of an element in a sorted list in Python by using the `bisect_left`

function from the `bisect`

module. The `bisect_left`

function will return the index of the element if it is present in the list. Otherwise, it will return the index where the element should be inserted while maintaining the sorted order. β¨

from bisect import bisect_left sorted_list = [1, 3, 4, 4, 6, 8] x = 4 # Find the index using binary search index = bisect_left(sorted_list, x) print(f"Element {x} found at index: {index}" if sorted_list[index] == x else f"Element {x} not found")

### What is the difference between bisect_left and bisect_right in Python?

`bisect_left`

and `bisect_right`

are two functions from the `bisect`

module that work with sorted lists. The difference between the two lies in how they handle duplicate elements:

`bisect_left`

: Returns the leftmost index where an element can be inserted into the sorted list while maintaining the sorted order. If the element already exists in the list, it returns the index of the first occurrence.`bisect_right`

: Returns the rightmost index where the element can be inserted into the sorted list while maintaining the sorted order. If the element already exists in the list, it returns the index just after the last occurrence. π

While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.

To help students reach higher levels of Python success, he founded the programming education website Finxter.com that has taught exponential skills to millions of coders worldwide. He’s the author of the best-selling programming books Python One-Liners (NoStarch 2020), The Art of Clean Code (NoStarch 2022), and The Book of Dash (NoStarch 2022). Chris also coauthored the Coffee Break Python series of self-published books. He’s a computer science enthusiast, freelancer, and owner of one of the top 10 largest Python blogs worldwide.

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