Java Code to check if two binary trees are identical or not

Java Code to check if two binary trees are identical or not

The idea is to traverse both trees and compare value at their root node. If the value matches, we recursively check if left subtree of first tree is identical to left subtree of second tree and right subtree of first tree is identical to right subtree of second tree. If the value at their root node differs, the trees violates data property. If at any point in the recursion, the first tree is empty & second tree is non-empty or second tree is empty & first tree is non-empty, the trees violates structural property and they cannot be identical.

// Java program to see if two trees are identical

  // A binary tree node

class Node 
{
    int data;
    Node left, right;  

    Node(int item) 
    {
        data = item;
        left = right = null;
    }
}

  
class BinaryTree 
{
    Node root1, root2;
    /* Given two trees, return true if they are structurally identical */
boolean identicalTrees(Node a, Node b) 
    {
      /*1. both empty */
        if (a == null && b == null)
            return true;

        /* 2. both non-empty -> compare them */
        if (a != null && b != null) 
            return (a.data == b.data
           identicalTrees(a.left, b.left)
identicalTrees(a.right, b.right)); 

        /* 3. one empty, one not -> false */
        return false;
    }

    /* Driver program to test identicalTrees() function */

    public static void main(String[] args) 
    {
        BinaryTree tree = new BinaryTree();
        tree.root1 = new Node(1);
        tree.root1.left = new Node(2);
        tree.root1.right = new Node(3);
        tree.root1.left.left = new Node(4);
        tree.root1.left.right = new Node(5);

        tree.root2 = new Node(1);
        tree.root2.left = new Node(2);
        tree.root2.right = new Node(3);
        tree.root2.left.left = new Node(4);
        tree.root2.left.right = new Node(5);
        if (tree.identicalTrees(tree.root1, tree.root2))
            System.out.println("Both trees are identical");
        else
            System.out.println("Trees are not identical");  
    }
}

What are Microservices?

The idea behind microservices is that some types of applications become easier to build and maintain when they are broken down into smaller, composable pieces which work together. Each component is developed separately, and the application is then simply the sum of its constituent components. This is in contrast to a traditional, "monolithic" application which is all developed all in one piece.

There are many reasons why this approach is considered an easier way to develop large applications, particular enterprise applications, and various types of software as a service delivered over the Internet.

One of the reasons is from a project engineering perspective. When the different components of an application are separated, they can be developed concurrently. Another is resilience. Rather than relying upon a single virtual or physical machine, components can be spread around multiple severs or even multiple data centers. If a component dies, you spin up another, and the rest of the application can continue to function. It allows more efficient scaling, as rather than scaling up with bigger and more powerful machines, or just more copies of the entire application, you can scale out with duplicate copies of the heaviest-used parts..

Is this a new concept?

The idea of separating applications into smaller parts is nothing new; there are other programming paradigms which address this same concept, such as Service Oriented Architecture (SOA). What may be new are some of the tools and techniques used to deliver on the promise of microservices.

The common definition of microservices generally relies upon each microservice providing an API endpoint, often but not always a stateless REST API which can be accessed over HTTP(S) just like a standard webpage. This method for accessing microservices make them easy for developers to consume as they only require tools and methods many developers are already familiar with.

Microservices depend not just on the technology being set up to support this concept, but on an organization having the culture, know-how, and structures in place for development teams to be able to adopt this model. Microservices are a part of a larger shift in IT departments towards a DevOps culture, in which development and operations teams work closely together to support an application over its lifecycle, and go through a rapid or even continuous release cycle rather than a more traditional long cycle.

Why is open source important for microservices?

When you design your applications from the ground up to be modular and composable, it allows you to use drop-in components in many places where in the past you may have required proprietary solutions, either because the licensing of the components, or specialized requirements. Many application components can be off-the-shelf open source tools.

A focus on microservices may also make it easier for application developers to offer alternative interfaces to your applications. When everything is an API, communications between application components become standardized. All a component has to do to make use of your application and data is to be able to authenticate and communicate across those standard APIs. This allows both those inside and, when appropriate, outside your organization to easily develop new ways to utilize your application's data and services.

Where do Docker and container technologies come in?

Many people see Docker or other container technologies as enablers of a microservice architecture.

Unlike virtual machines, containers are designed to be pared down to the minimal viable pieces needed to run whatever the one thing the container is designed to do, rather than packing multiple functions into the same virtual or physical machine. The ease of development that Docker and similar tools provide help make possible rapid development and testing of services.

Of course, containers are just a tool, and microservice architecture is just a concept. So it is entirely possible to build an application which could be described as following a microservices approach without using containers, just as it would be possible to build a much more traditional application inside of a container (although this may not be a good idea).

How do you orchestrate microservices?

In order to actually run an application based on microservices, you need to be able monitor, manage, and scale the different constituent parts. There are a number of different tools that might allow you to accomplish this. For containers, open source tools like Kubernetes, Docker Swarm, or Apache projects like Mesos or ZooKeeper might be a part of your solution. Alternatively, for non-container pieces of an application, other tools may be used for orchestrating components: for example, in an OpenStack cloud you might use Heat for managing application components. Another option is to use a Platform as a Service (PaaS) tool, which lets developers focus on writing code by abstracting some of the underlying orchestration technology and allowing them to easily select off-the-shelf open source components for certain parts of an application, like a database storage engine, a logging service, a continuous integration server, web server, or other pieces of the puzzle. Some PaaS systems like OpenShift directly use upstream projects like Docker and Kubernetes for managing application components, while others try to re-implement management tools themselves.

What about existing applications?

While utilizing microservices may be an important component of an organization's IT strategy going forward, there are certainly many applications which don't meet this model, nor is it likely that those applications will be rearchitected overnight to meet this new paradigm. Microservices and traditional applications can work together in the same environments, provided the organization has a solid bi-modal IT strategy.

Data Structures - Asymptotic Analysis( Big O, Theta θ, Omega Ω Notation)

Asymptotic analysis of an algorithm refers to defining the mathematical boundation/framing of its run-time performance. Using asymptotic analysis, we can very well conclude the best case, average case, and worst case scenario of an algorithm.

Asymptotic analysis is input bound i.e., if there's no input to the algorithm, it is concluded to work in a constant time. Other than the "input" all other factors are considered constant.The main idea of asymptotic analysis is to have a measure of efficiency of algorithms that doesn’t depend on machine specific constants, and doesn’t require algorithms to be implemented and time taken by programs to be compared. Asymptotic notations are mathematical tools to represent time complexity of algorithms for asymptotic analysis. 

Asymptotic analysis refers to computing the running time of any operation in mathematical units of computation. For example, the running time of one operation is computed as f(n) and may be for another operation it is computed as g(n2). This means the first operation running time will increase linearly with the increase in n and the running time of the second operation will increase exponentially when n increases. Similarly, the running time of both operations will be nearly the same if n is significantly small.

Usually, the time required by an algorithm falls under three types −

Best Case − Minimum time required for program execution.

Average Case − Average time required for program execution.

Worst Case − Maximum time required for program execution.

Asymptotic Notations

Following are the commonly used asymptotic notations to calculate the running time complexity of an algorithm.

Ο Notation

Ω Notation

θ Notation

Big Oh Notation, Ο

The notation Ο(n) is the formal way to express the upper bound of an algorithm's running time. It measures the worst case time complexity or the longest amount of time an algorithm can possibly take to complete. The Big O notation defines an upper bound of an algorithm, it bounds a function only from above. For example, consider the case of Insertion Sort. It takes linear time in best case and quadratic time in worst case. We can safely say that the time complexity of Insertion sort is O(n^2). Note that O(n^2) also covers linear time.

If we use Θ notation to represent time complexity of Insertion sort, we have to use two statements for best and worst cases:

1. The worst case time complexity of Insertion Sort is Θ(n^2).

2. The best case time complexity of Insertion Sort is Θ(n).

Omega Notation, Ω

The notation Ω(n) is the formal way to express the lower bound of an algorithm's running time. It measures the best case time complexity or the best amount of time an algorithm can possibly take to complete. Just as Big O notation provides an asymptotic upper bound on a function, Ω notation provides an asymptotic lower bound.Ω Notation can be useful when we have lower bound on time complexity of an algorithm.

Theta Notation, θ

The notation θ(n) is the formal way to express both the lower bound and the upper bound of an algorithm's running time.The theta notation bounds a functions from above and below, so it defines exact asymptotic behavior.

A simple way to get Theta notation of an expression is to drop low order terms and ignore leading constants. For example, consider the following expression.

3n3 + 6n2 + 6000 = Θ(n3)

Dropping lower order terms is always fine because there will always be a n0 after which Θ(n3) has higher values than Θn2) irrespective of the constants involved.

Volatile vs Atomic in Java

Volatile and Atomic are two different concepts. Volatile ensures, that a certain, expected (memory) state is true across different threads, while Atomics ensure that operation on variables are performed atomically.

Take the following example of two threads in Java:

Thread A:

value = 1;
done = true;
Thread B:

if (done)
  System.out.println(value);
Starting with value = 0 and done = false the rule of threading tells us, that it is undefined whether or not Thread B will print value. Furthermore value is undefined at that point as well! To explain this you need to know a bit about Java memory management (which can be complex), in short: Threads may create local copies of variables, and the JVM can reorder code to optimize it, therefore there is no guarantee that the above code is run in exactly that order. Setting done to true and then setting value to 1 would be a possible outcome of the JIT.

volatile only ensures, that at the moment of access of such a variable, the new value will be immediately visible to all other threads and the order of execution ensures, that the code is at the state you would expect it to be. So in case of the code above, defining done as volatile will ensure that whenever Thread B checks the variable, it is either false, or true, and if it is true, then value has been set to 1 as well.

As a side-effect of volatile, the value of such a variable is set thread-wide atomically (at a very minor cost of execution speed). This is however only important on 32-bit systems that i.E. use long (64-bit) variables (or similar), in most other cases setting/reading a variable is atomic anyways. But there is an important difference between an atomic access and an atomic operation. Volatile only ensures that the access is atomically, while Atomics ensure that the operation is atomically.

Take the following example:

i = i + 1;
No matter how you define i, a different Thread reading the value just when the above line is executed might get i, or i + 1, because the operation is not atomically. If the other thread sets i to a different value, in worst case i could be set back to whatever it was before by thread A, because it was just in the middle of calculating i + 1 based on the old value, and then set i again to that old value + 1. Explanation:

Assume i = 0
Thread A reads i, calculates i+1, which is 1
Thread B sets i to 1000 and returns
Thread A now sets i to the result of the operation, which is i = 1
Atomics like AtomicInteger ensure, that such operations happen atomically. So the above issue cannot happen, i would either be 1000 or 1001 once both threads are finished.

Does making all fields Final makes the class Immutable in Java?

One of the common misconceptions among many Java Programmer is that a class with all final fields automatically becomes Immutable. This is not correct, you can easily break immutability of certain class if the final field it contains is a mutable one, as we'll see in this article. One of the most common examples of this is a java.util.Date. You have to be extra cautious to keep your class' immutability intact with mutable fields. When you return a reference to a mutable object, you are sharing ownership of that reference with whoever receives it. This can break invariant, such as immutability.

Another example of this kind of pattern which can break immutability is returning collection or array from the getters method .

So, even though, the field which is pointing to Date or Collection or array object is final, you can still break the immutability of the class by breaking Encapsulation by returning a reference to the original mutable object.


There are two ways to avoid this problem, first, don't provide getters to mutable objects if you can avoid it. If you must, then consider returning a copy or clone of the mutable object. If you are returning a collection, you could wrap it as an unmodifiable collection. Since we cannot make an array final or unmodifiable in Java