The ultimate guide to coding interviews. Developed by FAANG engineers. Boost problem-solving skills with number theory, dynamic programming, and graph theory. Get interview-ready in just a few hours.

Competitive Programming - Crack Your Coding Interview.png

Whether you’re gearing up for online coding challenges, code-a-thons, or interviews, then this course is for you. With this course, you will solidify your problem-solving skills ensuring a swift sail through any problem. 


You will be tasked with solving some of the most frequently asked questions that are brought up in FAANG interviews. You will start with the concepts of Number Theory and Divide and Conquer, and gradually move towards more complex problems like dynamic programming and graph theory.


With each problem you solve, there will be insightful explanations and full implementation details to really hammer home the concepts. By the time you finish this course, you will have the confidence to solve any problem, no matter the difficulty.

Competitive Programming - Crack Your Coding Interview, C++

## Introduction
*Graph traversal* means visiting every vertex and edge exactly once in a well-defined order. While using
certain graph algorithms, you must ensure that each vertex of the graph is visited exactly once. The order in which the vertices are visited is important and may depend upon the algorithm or question that you are solving.
During a traversal, it is important that you track which vertices have been visited. The most common way of tracking vertices is to mark them.

## Breadth-first search approach

There are many ways to traverse graphs. Breadth-First Search (BFS) is the most commonly used approach.
Breadth-First Search (BFS) is a traversing algorithm where you should start traversing from a selected node (source or starting
node) and traverse the graph layer-wise thus exploring the neighbor nodes (nodes that are directly connected to source node). You must then move towards the next-level neighbor nodes. As the name Breadth-First Search (BFS) suggests, you are required to traverse the graph breadth-wise as follows:
* First, move horizontally and visit all the nodes of the current layer
* Then, move to the next layer 

Let's look at the visualization below. Breadth-First Search (BFS) colors each vertex white, gray, or black. All vertices start out white and may later become gray and then black. A vertex is discovered the first time it is encountered during the search, at which time it becomes nonwhite. Gray and black vertices, therefore, have been discovered, but Breadth-First Search distinguishes between them to ensure that the search proceeds in a breadth-first manner. If **(u, v)** is a node pair that is connected by an edge and vertex **u** is black, then vertex **v** is either gray or black, i.e., all vertices adjacent to
black vertices have been discovered. Gray vertices may have some adjacent white vertices. They represent the frontier between discovered and undiscovered vertices.

Breadth-First Search constructs a breadth-first tree, initially containing only its root, which is the source vertex. Whenever a white vertex **v** is discovered in the course of scanning the adjacency list of an already discovered vertex **u**, the vertex **v** and the edge **(u, v)** are added to the tree. We say that **u** is the
predecessor or parent of **v** in the breadth-first tree.

Look at the illustration below for a better understanding.

# Introduction
*Graph traversal* means visiting every vertex and edge exactly once in a well-defined order. While using
certain graph algorithms, you must ensure that each vertex of the graph is visited exactly once. The order in which the vertices are visited is important and may depend upon the algorithm or question that you are solving.
During a traversal, it is important that you track which vertices have been visited. The most common way of tracking vertices is to mark them.

# Breadth-first search approach

There are many ways to traverse graphs. Breadth-First Search (BFS) is the most commonly used approach.
Breadth-First Search (BFS) is a traversing algorithm where you should start traversing from a selected node (source or starting
node) and traverse the graph layer-wise thus exploring the neighbor nodes (nodes that are directly connected to source node). You must then move towards the next-level neighbor nodes. As the name Breadth-First Search (BFS) suggests, you are required to traverse the graph breadth-wise as follows:
* First, move horizontally and visit all the nodes of the current layer
* Then, move to the next layer 

Let's look at the visualization below. Breadth-First Search (BFS) colors each vertex white, gray, or black. All vertices start out white and may later become gray and then black. A vertex is discovered the first time it is encountered during the search, at which time it becomes nonwhite. Gray and black vertices, therefore, have been discovered, but Breadth-First Search distinguishes between them to ensure that the search proceeds in a breadth-first manner. If **(u, v)** is a node pair that is connected by an edge and vertex **u** is black, then vertex **v** is either gray or black, i.e., all vertices adjacent to
black vertices have been discovered. Gray vertices may have some adjacent white vertices. They represent the frontier between discovered and undiscovered vertices.

Breadth-First Search constructs a breadth-first tree, initially containing only its root, which is the source vertex. Whenever a white vertex **v** is discovered in the course of scanning the adjacency list of an already discovered vertex **u**, the vertex **v** and the edge **(u, v)** are added to the tree. We say that **u** is the
predecessor or parent of **v** in the breadth-first tree.

Look at the illustration below for a better understanding.

Learn the breadth-first traversal technique to traverse graphs

Overview

Number Theory

Number Theory

Divide and Conquer

Greedy Algorithms

Greedy Algorithms

Recursion and Backtracking

Recursion and Backtracking

Dynamic Programming

Graphs

Bonus Lessons

Graph Traversal - Breadth-First Search

Introduction

Breadth-first search approach