The motivation for binary indexed trees is similar to that of segment trees. However, note that segment trees are much more flexible than binary indexed trees, and usually its true that any problem that can be solved with BIT can be solved with segment trees but not the other way around.

Video tutorial: This is a superb tutorial, giving the motivation, walking through example, and going step-by-step through the pseudocode.

In this post I will introduce the concept of persistent data structures. We shall deal with a couple of problems: COT, MKTHNUM

Consider the following question:

Given a linked list, you need to support 2 operations.

1. Update the first x values.
2. Print the linked list after k’th update (k <= number of update operations made till now)

Simple solution is to create a new linked list after each update operation. print it when needed. Let us optimize it for memory.

We are only updating first x elements of the linked list. That means the new linked list will be almost same as previous linked list if x is small. We shall take advantage of this and avoid allocating memory for some elements. We can allocate memory for x elements, store new values in them, then point the next pointer of x’th node...

Prerequisites: Matrix in algebra, Matrix multiplication

Introduction: Matrix Exponentiation (also known as matrix power, repeated squaring) is a technique used to solve linear recurrences. This technique is very useful in competitive programming when dealing with linear recurrences (appears along Dynamic Programming). This technique also solves a lot of problems in graph theory. Only solving recurrences is covered here, applications on graph theory will be discussed later.

Video tutorial: This video shows how you can use matrices to calculate the n-th fibonacci number (where n is very large ~10^18). You should be able to understand the technique after watching this video. Exercises will be added soon.

Given an undirected weighted graph, a minimum spanning tree (MST) is a subset of the edges of the graph which form a tree and have the minimum total edge weight. For a MST to exist, the graph must be connected (that is, every pair of nodes must be reachable from each other).

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...