I recommend watching the following videos for learning about graphs. These are really well made videos and he covers a lot in these short videos, so if you feel overwhelmed, use the rewind and pause buttons.

Introduction to Graphs

What are graphs? What are different types of graphs (directed and undirected, trees and DAGs, etc)? And examples of using them to model web links, flights between cities, and other things.

Video for concept and walkthrough

First, let's watch a slow-paced easy-to-follow walkthrough of the breadth-first search and depth-first search algorithms.

This discussion is for expanding your array of maneuvers needed to code quickly and efficiently.

STL:

The first and most important thing that I'd like to discuss about is the C++ STL. Learning it would enable you to code up an assortment of algorithms and complicated data structures in a matter of seconds.

You can learn to use the C++ STL from the following amazing sites:

Studytonight : Contains syntax and examples for most of the STL containers and algorithms.

Sanfoundry : Shows how to implement what you've learnt in complete programs

Topcoder(Highly recommended) : This place teaches yo...

Number Theory is a topic which you will come across frequently in programming contests. I feel this is a topic which has a lot of resources but these resources are scattered. Therefore, I write this tutorial trying to bring in all the best resources together. There are many people who feel I am not good at Math, can I be a good competitive programmer?. This tutorial is for you guys. Don't hesitate to read it as the material here is presented in extremely lucid form and anyone can understand it. Feel free to ask in case you have any doubts.

In many problems especially in problems where the answer can become very very large, you must have found that they ask you to report the answer modulo 10^9+7. Let us learn more about this modulo operator and it's properties.

Introduction

I will strongly encourage you to read all the topics in this section : What is modular arithmetic? (article), starting wit...

Prerequisites: Segment Trees and Merge-Sort.

Motivation: Given an array of N integers. You have to answer some queries in form (l, r, k). To answer this query you have to print the number of integers less than k in the sub-array array[l .... r].

You should be able to solve the problem in O(log^2 n) per query at least. How? You can use Merge Sort Trees.

Now what is a Merge Sort Tree? Merge Sort Tree is actually a Segment Tree but each node contains a vector. If the range of the node is [l,r] then the vector will contain the elements of array[l...r] but in sorted order.

To solve the above problem we can make a Merge Sort Tree first and go into relevant segments and binary search on the vector that was stored in those nodes to count how many numbers are less than k. This will give O(log^2 n).

Building the Merge Sor...