Gain insights into competitive programming, explore C++ skills with theory, code samples, practice problems, and master faster implementation for contests like ACM ICPC, Google CodeJam, and HackerCup.

Competitive programming can be a great way to build out your programming skills, get on any major company’s radar, and earn a little extra cash along the way.

In this course, you will learn to prepare for competitive programming contests like ACM ICPC, Google CodeJam, Facebook HackerCup, and many more.

Each topic is broken down with a healthy mix of theory, code samples, step-by-step solved sample problems, illustrations, useful practice problems, and tips and tricks for faster implementation.

You will need some solid C++ foundations coming into this course, but by the end it, you will be confident enough in your C++ skills to take home the win.

Competitive Programming in C++: The Keys to Success

## Natural numbers
All positive integers starting from $1$
$1, 2, 3, 4, 5, 6, 7, 8, ...$

---

### Sum
Sum of first $n$ natural numbers is $\frac{n*(n+1)}{2}$

---
## Factorial
Denoted by the exclamation mark symbol. 

`n!` is called `n` factorial and its value is defined as:

$n! = 1 \times 2 \times 3 \times ... \times n$

i.e., `n!` is the product of the first `n` natural numbers.

---

## Factors and multiples
**Factors**: A factor of a number is a smaller or equal number such that it divides the number exactly and gives the remainder zero. For example:


Factors of $12 \to 1, 2,3,4,6,12$
**Multiples**: A multiple of a number, $n$, is a larger number such that the $n$ is a factor of that number. For example:

Multiples of $4 \to 4, 8, 12, 16, ...$

---
## Prime numbers
Prime numbers are natural numbers greater than 1 that cannot be expressed as a product of two smaller natural numbers.

They are natural numbers greater than 1 with only two factors, 1 and the number itself.

$2, 3, 5, 7, 11, ...$

**Note**: A good estimation of the number of primes $<N$  is $logN$. This is useful for complexity analysis.

---

## Modulus operator
The modulus operation between two integers, `a % b`, returns the remainder when `a` is divided by `b`. For example:

$5 \% 2 = 1$

$100 \% 89 = 11$

$2 \% 5 = 2$

$9 \% 3 = 0$

$21 \% 21 = 0$

The result of the modulus operator is $0$ if `a` is a multiple of `b`.

> We can easily check if a number is even with if `if (x % 2 == 0)`.


---
In the next lesson, we’ll go over set theory, definitions and basic operations. 



# Natural numbers
All positive integers starting from $1$
$1, 2, 3, 4, 5, 6, 7, 8, ...$

---

## Sum
Sum of first $n$ natural numbers is $\frac{n*(n+1)}{2}$

---
# Factorial
Denoted by the exclamation mark symbol. 

`n!` is called `n` factorial and its value is defined as:

$n! = 1 \times 2 \times 3 \times ... \times n$

i.e., `n!` is the product of the first `n` natural numbers.

---

# Factors and multiples
**Factors**: A factor of a number is a smaller or equal number such that it divides the number exactly and gives the remainder zero. For example:


Factors of $12 \to 1, 2,3,4,6,12$
**Multiples**: A multiple of a number, $n$, is a larger number such that the $n$ is a factor of that number. For example:

Multiples of $4 \to 4, 8, 12, 16, ...$

---
# Prime numbers
Prime numbers are natural numbers greater than 1 that cannot be expressed as a product of two smaller natural numbers.

They are natural numbers greater than 1 with only two factors, 1 and the number itself.

$2, 3, 5, 7, 11, ...$

**Note**: A good estimation of the number of primes $<N$  is $logN$. This is useful for complexity analysis.

---

# Modulus operator
The modulus operation between two integers, `a % b`, returns the remainder when `a` is divided by `b`. For example:

$5 \% 2 = 1$

$100 \% 89 = 11$

$2 \% 5 = 2$

$9 \% 3 = 0$

$21 \% 21 = 0$

The result of the modulus operator is $0$ if `a` is a multiple of `b`.

> We can easily check if a number is even with if `if (x % 2 == 0)`.


---
In the next lesson, we’ll go over set theory, definitions and basic operations. 



I am going to assume that you are already aware of the topics in this lesson. However, I will go over them briefly to brush up and as a reference if and when you need them.

Introduction

Complexity Analysis

Number Theory

Arrays and Vectors

Sieve of Eratosthenes

Strings

Sorting

Linked List

Stack

Queue

Binary Tree

2 Pointers

Heap

Binary Search Tree

Balanced Binary Search Tree

Course Conclusion

Algebra

Natural numbers

Sum