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

Geometric progression is a sequence of numbers such that each term after the first is obtained by multiplying the previous one by a fixed non-zero number, called the **common ratio**. For example:

$3, 6, 12, 24, ...$

Here the first term, $a$, is $3$, $a=3$, and the common ratio, $r$, is $2$, $r=2$.

In general, 

$a, ar, ar^2, ar^3, ... , ar^{n-1}$

Where the $nth$ term $= ar^{n-1}$

# Sum
The sum of GP with $n$ terms is

$a + ar + ar^2 + ... + ar^{n-1}$

$= \frac{(1-r)(a + ar + ar^2 + ... + ar^{n-1})}{1-r}$

$= \frac{(a + ar + ar^2 + ... + ar^{n-1}) - (ar + ar^2 + ar^3 + ... + ar^{n})}{1-r}$

$= \frac{a-ar^{n}}{1-r}$

$= \frac{a(1-r^n)}{1-r}$

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# Infinite geometric progression

This is a special and very useful case of GP   when the common ratio is $r < 1$. 

It is easy to see that this is only where terms become smaller and smaller and hence the sum converge to a value when the number of terms $n \to \infty$

## Sum
The sum is easy to calculate using the formula for the sum of GP terms.


We have

$sum =\frac{a(1-r^n)}{1-r}$

As $n \to\infty, r^n \to 0$

$sum = \frac{a}{1-r}$

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In the next lesson, we'll start learning PnC (Permutations and Combinations), starting with permutation.

In the lesson, we'll learn about geometric progression.

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

Geometric Progression (GP)