Discover data structures and algorithms using Python. Gain insights into solving real-world problems and typical interview questions with detailed reviews, explanations, and hands-on coding exercises.

Data structures and algorithms are among the most fundamental concepts of Computer Science. Whether it’s real-world problems you’re trying to solve or the typical coding question asked in an interview, almost every problem requires you to demonstrate a deep understanding of data structures and algorithms. 

This course is a detailed review of some of the most common data structures and algorithms that you’ll see in interviews and your everyday work. With implementation details, thorough explanations, and hands-on coding exercises, you’ll quickly gain the confidence you need to solve any problem, no matter the situation.

Data Structures and Algorithms in Python

In this lesson, we will be solving the following problem:

Given an array of $n$ distinct integers sorted in ascending order, write a function that returns a **fixed point** in the array. If there is not a fixed point, return `None`.

>A fixed point in an array `A` is an index `i` such that `A[i]` is equal to `i`.

The naive approach to solving this problem is pretty simple. You iterate through the list and check if each element matches its index. If you find a match, you return that element. Otherwise, you return `None` if you don't find a match by the end of the `for` loop. Have a look at the code below: 

# Time Complexity: O(n)
# Space Complexity: O(1)
def find_fixed_point_linear(A):
    for i in range(len(A)):
        if A[i] == i:
            return A[i]
    return None

As the entire list is traversed once to find the fixed point, spending constant time on each element, the time complexity for the linear implementation above is $O(n)$. As we haven't used any additional space in the implementation above, the space complexity is $O(1)$. Now we need to think about how we can improve the solution above. We can use the following two facts to our advantage:
* The list is sorted. 
* The list contains *distinct* elements. 

Let's look at the slides below to get a rough idea of how we have taken advantage of the above facts. 

In this lesson, you will learn how to find a fixed number in a list using a binary search in Python. 

Introduction

Stack

Singly Linked Lists

Circular Linked Lists

Doubly Linked Lists

Arrays

Binary Trees

Binary Search Trees

Binary Search

Recursion

String Processing

Find Fixed Number