This is a very comprehensive 94-part course on competitive programming. It gets you from knowing basic programming to being a yellow-red rated coder on Codeforces / CodeChef / TopCoder / etc.

The primary objectives of this course are to learn about 30 different algorithms and data structures. The algorithm tutori...

Defining Greedy Algorithm

An algorithm is called greedy if it follows the problem-solving heuristic of making the locally optimal choice at each stage with the aim of finding a global optimum.

In most situations, a greedy strategy does not lead to the optimal solution. Hence, it is extremely important to reason about the correctness of the greedy strategy before using it to solve a problem.

Problem 1: Too much to do!

Let's say you have to maximise the number of tasks that you complete in a 10-hour duration. You are given an array T = [2, 4, 1, 6] where T_i denotes the time required to complete the i^th task.

The answer to this question would be 3 as you would choose to do tasks T₂, T₀ and T₁ — which take 1, 2 and 4 hours respect...

We want to sort an array with n elements. Quick-sort does this by breaking up the array into non-overlapping segments, sorting them separately and then combining the results.

For instance, suppose we have a box with slips of paper with numbers between 100 and 300 to be sorted. We could first separate the slips into two bunches: those with values below 200 and those with values above 200. We can sort these bunches separately. Since all the values in the second bunch are larger than those in the first bunch, we can combine them easily into a single sorted bunch. (See Sorting | Online Study Material - IARCS for a great resource on this.)

Algorithm with Example

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...