Data Structures and Algorithmic Trading: Machine Learning

As a developer, I remember back when I started taking computer science classes at Texas Tech. Now you have to know that I taught myself programming so essentially I took a backwards approach to learning computer science, which means that I learned how to build real-world applications first and then I got my bachelor's in computer science and later on, have gone into grad school. 

In the last lesson, we talked about importance of sorting.

Today we will discuss how to write a function: “rotate” that rotates and array of size n by d elements..

Let us look at an example.. We have an array with elements 1,2,3,4,5,6 and 7.. We want to rotate this by a factor of 2, i.e. by 2 places. On rotation of the original array by 2. 

We'll be talking about specific sorting algorithms today. I want to start by motivating why we're interested in sorting, which should be fairly easy. Then I want to discuss a particular sorting algorithm that's called insertion sort. That's probably the simplest sorting algorithm you can write, its five lines of code.

So merge sort is also something that you've probably seen. But there probably will be a couple of subtleties that come out as I describe this algorithm that, hopefully, will be interesting to those of you who already know merge sort. And for those of you who don't, it's a very pretty algorithm. It's a standard recursion algorithm-- recursive algorithm-- similar to a binary search. What we do, here, is we have an array, A. 

One of the cutest little data structures that was ever invented is called the heap. And we're going to use the heap as an example implementation of a priority queue. And we'll also use heaps to build a sorting algorithm, called heap sort, that is very, very different from either insertion sort or merge sort. And it has some nice properties that neither insertions sort nor merge sort have. 

Any time you see an array, and you say we're going to be looking at the heap representation of the array, the picture on the right tells you what the heap looks like. And so that I'm not going to fill in all of these. You can, but I'll do a couple. So you have 10 here, and 8, 7, et cetera. So that's a heap structure. 

Now he has a friend who needs some money. He ask for 35$ and that too in minimum number of coins. Now if he was to just give money he could have given it in quite a number of ways. He could give seven coins of 5$, a 10$ coin and five 5$ coins and so on. But since he is supposed to pay minimum number of coins, he has to come up with a greedy idea. 

In this lesson we are going to understand topological sorting. Let’s begin this with a brief introduction of what topological sort is. Given a directed acyclic graph, topological sort is a linear ordering of its vertices, such that for every directed edge from vertex 'u' to vertex 'v' 'u' comes before 'v' in the ordering. 

Hello friends! In this lecture we are going to see breadth first traversal technique in graphs. The idea behind breadth first is to traverse the graph in layers. Let's see what we mean by layers here. Consider a graph as shown. If we have our starting vertex as 1, our breadth first traversal will cover the graph as follows. 

We learned about BFS technique in the last lesson. In this lesson we are going to see depth first traversal technique in graphs. The idea in depth first search is pretty simple. Given a graph we have to go forward depth wise while there is any such possibility, if not then we have to backtrack. 

The kind of records that we want have a setting where each row is uniquely identified through the telephone number of the employees. Now, for this we define three operations. We will be adding new employee records. 

This lesson will help you to understand Dijkstra's shortest path algorithm, a shortest path algorithm is run on a weighted graph. It starts with an initial node and a goal node, and it finds the least cost path from the initial node to the goal node.

In this lesson we are going to cover Open Addressing, which is one of a collision resolving technique in hashing. Before we begin with this tutorial we would strongly advise you to be aware of the terms that we have covered in our previous lesson on hashing.

So if we have to delete key 18, its slot should be marked as deleted and not empty. So here we make a note that, we can insert a key at a slot with deleted state but our search operation should not stop on this slot. Next we move on to Quadratic Probing. The basic difference is that here the increment is quadratic, instead of i we have i^2. Notice the increment is 0, 1, 4, 9 and so on. Let’s again see it with the same example. 

In this lesson we are going to cover Cycle Detection in an undirected graph. An undirected graph is any graph in which the flow has not been indicated or directions are not given.

So the problem statement is that we are given an Undirected graph and we have to check whether it contains a cycle or not. I.e. print true if there are one or more cycle or a false if there are none. 

Continuing in the theme of sorting in general, but in particular, binary search trees, which are a kind of way of doing dynamic sorting, if you will, where the elements are coming and going. And at all times, you want to know the sorted order of your elements by storing them in a nice binary search tree. 

Remember, in general, a binary search tree is a tree. It's binary, and it has the search property. Those three things. This is a rooted binary tree. It has a root. It's binary, so there's a left child and a right child. Some nodes lack a right or left child. Some nodes lack both. 

We talked about AVL trees in the previous two lectures. And out last two lectures will be about computational complexity and it’s relation to machine learning. I’ll talk briefly about the combination of these two.

There are very mature and refined theories and algorithms for or balancing the goodness-of-fit you can get on a data set with how well you'll do out-of-sample on new data drawn from the same distribution process.