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

Let's discuss the solution to the challenge in the previous lesson. The problem was to find the product of two positive integers. 

## Implementation

Let's have a look at the implementation below:

def recursive_multiply(x, y):

    # This cuts down on the total number of
    # recursive calls:
    if x < y:
        return recursive_multiply(y, x)
    if y == 0:
        return 0
    return x + recursive_multiply(x, y-1)

x = 500
y = 2000

print(x * y)
print(recursive_multiply(x, y))

## Explanation

The hint indicated the following: 

```
5 * 3 = 5 + 5 + 5 = 15
```

We make use of the hint in the implementation. Let's skip the code on **lines 5-6** for a while and discuss the code afterward. On **line 7**, we check if `y` equals `0`. If it does, `0` is returned on **line 8**. Otherwise, `x` is added to the sum returned from the recursive call on **line 9**. `y-1` is passed to the next recursive call as `x` is added once in the current recursive call. So overall, `x` will be added together `y` times in all the recursive calls. This will return the product of `x` and `y` at the end of all the recursive calls. 

Now, in the implementation provided above, we make `y` recursive calls so if `x` equals `500` and `y` equals `2000`, we get the following error:

```
RecursionError: maximum recursion depth exceeded in comparison
```
if we skip the **lines 5-6** from the above implementation. Check out the code below:


Let's discuss the solution to the challenge in the previous lesson. The problem was to find the product of two positive integers. 

# Implementation

Let's have a look at the implementation below:

# Explanation

The hint indicated the following: 

```
5 * 3 = 5 + 5 + 5 = 15
```

We make use of the hint in the implementation. Let's skip the code on **lines 5-6** for a while and discuss the code afterward. On **line 7**, we check if `y` equals `0`. If it does, `0` is returned on **line 8**. Otherwise, `x` is added to the sum returned from the recursive call on **line 9**. `y-1` is passed to the next recursive call as `x` is added once in the current recursive call. So overall, `x` will be added together `y` times in all the recursive calls. This will return the product of `x` and `y` at the end of all the recursive calls. 

Now, in the implementation provided above, we make `y` recursive calls so if `x` equals `500` and `y` equals `2000`, we get the following error:

```
RecursionError: maximum recursion depth exceeded in comparison
```
if we skip the **lines 5-6** from the above implementation. Check out the code below:


This lesson contains the solution review for the challenge to find the product of two numbers. 

Introduction

Stack

Singly Linked Lists

Circular Linked Lists

Doubly Linked Lists

Arrays

Binary Trees

Binary Search Trees

Binary Search

Recursion

String Processing

Solution Review: Product of Two Positive Integers

Implementation

Explanation