Introduction | Data Structure and Algorithms | Quick Notes | Back to Old days

Variable: A variable is nothing but a box with a label(its name) and a predefined type promise that you cannot be broken later. Have a look at mathematical equation below. 

X + 2Y = 45

Here, the names X and Y are placeholders for some data that can justify the equation if put in their places. Similarly, in computer science programming we need something to hold data and variables are nothing but that.

Data Types: In the above example, X and Y can hold any type of value such as an Integer value(5, 10) or real value(2.0, 5.8). But to solve this equation, we have to relate them to a particular kind of value they can take and Data Type is that name used for this purpose in computer science.  Or “A data type is a set of data with predefined values used to declare variables/objects. Example: integer, float, double, character, string etc.”

In computer memory, everything is either 0 or 1. A data type is a thing that tells the compiler about what kind of values a particular set of bytes are of and depending on that the compiler takes further decisions on them.

A data type can be a predefined one or can be customized according to the need. Based on this definition criteria they fall into two categories.

    1. System-defined data types(Primitive data types): As their name specifies, they are defined by the system. The primitive data type provided by many programming languages are int, float, double, char, bool etc. The number of bits allocated for each primitive data type depends on the programming language using, the compiler, and the operating system. For the same primitive type, different programming languages may use different sizes and thus their domain(total available values) will also get change. For example, int may take 2 or 4 bytes. If it is of 2 bytes then it’s domain will be -215 to 215-1 and if 4 bytes then the domain will be -232 to 232-1.
  1. User-defined data types: If primitive data types are not enough, we can define our own data type fulfilling all our requirements. Classes are the best example of user-defined data types that most of the programming languages provide. Swift provides class, struct, enum and protocol, four kinds of user-defined data types.

Data Structure: Data Structure is an arrangement of data in such a way that they can be efficiently stored and retrieved. Or we can say that it is a special kind of format for organizing data. The general data structure includes Stack, Queue, Linked List, Tree, Graphs and so on.

Depending upon the organization of data elements Data Structures are classified into two types

  1. Linear Data Structure: Linked List, Stack, and Queue are linear data structures as elements are arranged in a linear manner in them.
  2. Non-Linear Data Structure: Tree and Graph are non-linear data structure as elements are stored in a non-linear manner in them.

We talk about Data Structures as an Abstract Model and their Concrete Implementation.

An Abstract Data Type is a logical and mathematical model defining some set of rules that have to be followed and some list of operations that have to be implemented by the concrete implementation of that model. We can think of ADT as a black box which hides the inner structure and design of a data type.

For example, an Abstract model of a Car can be… an object having four wheels, a steering, brake, accelerator, motor, some number of seats etc. etc. with on/off, run and some other operations.

A concrete implementation of an abstract model is called Concrete Data Type. For example, Duster is a concrete implementation of abstract model Car.

A list, Stack, Queue, Tree, Graphs etc. are abstract data types having some logical set of rules and operations that have to be defined by their concrete implementation regardlessly of which programming language is getting used. In Java, inside java.util package there is a “List” interface which is nothing but an abstract model of List Data Structure whereas, ArrayList and LinkedList are two concrete implementations of List ADT.

Algorithm: An algorithm is a step by step unambiguous instructions to solve a given problem. There are two main criteria for judging the merits of an algorithm.

  1. Correctness: Is it solving the problem in a finite number of steps. Correction can be measured by comparing the expected and resulted output.
  2. Efficiency: How much resources does it take to solve the complete problem?

Algorithm Analysis: Algorithm analysis is nothing but finding the complexity(time and space usage) of an algorithm in terms of input size, being machine independent and considering just basic computer steps. It is the only way to find out the efficiency of an algorithm so that it can be compared with others to choose the best. Complexity is considered in terms of processing time(Rate of growth), memory usage, developer efforts etc.

The rate of growth is a function which defines at what rate the running time increases as the input size increases. Let’s take an example, Suppose in a party, one guest consumes 2 bottles of water. The number of water bottles needed will be, twice the number of guests will come. Here the rate of growth of water bottle consumption is 2n, where n is the number of guests. Rate of growth function f(n) can be defined as  f(n) = 2n.

Why  Algorithm Analysis: There may so many ways to solve a particular problem. But we need the most efficient solution out of all and to get which solution is most efficient, the analysis is needed.

Types of analysis: From algorithm analysis, we basically want to know that with which input the one algorithm takes the least time and with which it takes the longest time. Based on algorithm’s measurement is divided into following 3 types.

  • Worst case: Defines the input for which the algorithm takes a long time.
  • Best case: Defines the input for which the algorithm takes a least time.
  • Average case: Defines the input for which the algorithm takes less than longer time but more than the last time.

Let’s say there are two packets of goodies.
One packet has between 10 and 20 goodies in it (we’ll call this Packet A).
One packet has between 30 and 40 goodies in it (we’ll call this Packet B).
You can pick only one of them but you don’t know which packet is Packet A or which packet is Packet B.

Here, for you, the worst case will be, if you choose Packet A and the best case will be if you choose Packet B.

Asymptotic Notation: Asymptotic notation is kind of syntax or units that are used to express the best, worst and average cases of an algorithm.

  1. Big-O Notation(Upper Bound Function): This notation represents the upper bound of an algorithm which means in any case running time will not be more than this.

In General, Big-O is used to represent the worst-case efficiency of an algorithm where lower bound is not considered. It is represented as f(n) = O(g(n)) where, g(n) is the function which represents the upper bound of f(n).

   General Rule of Big-O notation:

  • Ignore Constants: Example, the upper bound of 4n is n.
  • Ignore lower order terms: Example, g(n)  of function f(n) = n2 + 2n will be n2 (or any value bigger than this), as n2 will be contributing more than 2n for reaching the worst case.

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In simple words, we have a complex function f(n) and a simple function g(n) and we want to find a constant c such as, when multiplied with g(n), the resultant value will always be greater than f(n) from some point n0 for all n>n0.

Question: Find Big-O of  f(n) = n2 + 5.

Note: n2 is the upper bound(contributing the most in rate of growth) of this equation. Let’s take g(n) = n2, but to prove f(n) = O(n2) we need to have some positive integer c and n0 which can satisfy  f(n) <= c*g(n). we can substitute any value of c that satisfy the condition. So, let’s put c = 2(or more than 2 will also be fine).

n2+5 <= c*n2

n2+5 <= 2n2

5 <= n²

Hence found, g(n) = n2 and Big-O of f(n) with c = 2 and n0 = 3.

Note: there can be any number of combination of c and n0. And if n2 is upper bounding f(n) then any value greater than n2 such as n3, n4  will also upper bound f(n) thus, they can also be big O of f(n) but we should always consider the tighter upper bound.

  1. Omega-𝛀 Notation(Lower Bound Function): This notation represents the lower bound of an algorithm which means, in any case, the running time can never be less than this. Generally, it is represented as f(n) = 𝛀(g(n)) where, g(n) is lower bound of f(n).

Here, we have a complex function f(n) and a simple function g(n) and we want to find a constant c such as, when multiplied with g(n), will lower bound the function f(n) from some point n0 for all n>n0. we can say f(n) ∈ 𝛀(g(n)) if there exists c>0 and n0 >0 such that f(n) = n0.

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Question: Find Big-𝛀 of  f(n) = n + 5.

Let’s assume g(n) = n and prove f(n) = 𝛀(g(n)) by satisfying, f(n) >= c*g(n) for some c > 0, n0>0 and n>=n0 .

n + 5 >= c*n

Here, we can substitute any value of c that satisfy the condition. But looks like 1 is the only value which can satisfy this.

n + 5 >= n

Hence found, g(n) = n and Big- 𝛀 of f(n) with c = 1 and n0 = 1 for all n > 1.

Notice: there can be any combination of c and n0. And if n is lower bounding f(n) then any value less than n such as logn, log(logn)  will also lower bound f(n) thus, they can also be big 𝛀 of f(n).

  1. Big-𝚹 Notation(Average Function): This notation represents the average time that can be taken by an algorithm. Generally, it is represented as f(n) = 𝚹(g(n)) where, O(g(n)) >= f(n) >= 𝛀(g(n)).

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Big-𝚹 notation defined as 𝚹(g(n)) = { f(n): there exist positive numbers c1, c2 and n0 such that  c1*g(n) >= f(n) >= c2*g(n) for all n>= n0}. Or in simple words, we have a complex function f(n) and a simple function g(n) and we want to find a constant c1 and c2 such as, when multiplied with g(n), will middle bound the function f(n) for all value for n >= n0.

Question: Find Big-𝚹 of  f(n) = n2 + 5.

Let’s assume g(n) = n2 and prove f(n) = 𝚹(g(n)) by satisfying, c1*g(n) >= f(n) >= c2*g(n) for some c1,c2 and n0 > 0 for all n>= n0

c1n2 >= n2 + 5 >= c2n2

Here, we can substitute any value of c1 and c2 which satisfies the equation. C1 = 5, c2= 1 and n0= 1 satisfying the equation.

Hence found, g(n) = n2 and Big-𝚹  of f(n) with C1 = 5, c2= 1 and n0 = 1 for all n>1.
In General, worst case is considered to tell the efficiency of an algorithm and Big-O is one used to represent that. Big-𝚹 is considered only when the Big-O and Big-𝛀 of an algorithm are same.


That’s all about the introduction of Data Structure and Algorithm but stay connected for next chapter “Linked List”. Happy Learning!! 🙂 

WWDC 2018 | Keynote |Quick Notes | 2 mins

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“Today is all about Software,” Apple CEO Tim said as he took the stage at WWDC 2018.

It all started with statistics.

  • 20 million iOS developers
  • 500 million weekly app store visits
  • 81% using iOS 11 where only 8% using latest Android
  • Developers earned 100 million through App Store


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  • New iOS 12 will be released as a free update, every model back to the 5S will get a performance boost.
  • ARKit, second generation, which included a lot of cool updates, most interesting is the ability for multiple users to observe and interact with the same environment from different angles.
  • Apple Screen time, now iOS 12 will tell you how much time you’re spending with your iPhone and which are the apps.
  • Do not disturb a lot of improvements, while you are sleeping will hide the notification, one step one time notifications.
  • Photos, with iOS 12 they have revamped it. Allowing more search options driven by AI, share the photos through iMessage.
  • Siri, it’s handling 10 billion requests per month and now Apple is allowing you to interact with it more, create shortcuts to trigger app features.
  • Animojis, more personal now. It’s super accurate, face-tracking and tongue tracking capabilities. Surely it will feel you very familiar.
  • Group FaceTime, now chat with 32 people at once with emoji, sticker, and other effects support.

iOS Apps updates

  • Stocks, new UI with better performance
  • Apple News app.
  • Apple iBooks getting a redesign and a new name.
  • Voice Memos, iPad getting it for the first time and recording will be now synced to iCloud.


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So far biggest functions of the Apple iWatch is fitness, now Apple adding more components which let you challenge your friends.

  • Automatic workout detection using your heart-beats(once you stop working out your heart rate decreases, so it will automatically stop).
  • Walkie-Talkie, Texting/phone are tough using watch screen so Apple added an instant audio messaging app called walkie-talkie (uses the wifi or cellular to interact with other devices).
  • Siri on Watch, allow third-party apps to show you more information. Now just lift your wrist and start talking it means no more “Hey Siri”.
  • Podcasts app is coming on your wrist.


4 Ways to Solve The Problem | Quick-Notes

Problem-solving requires two types of mental skills, analytical and creative. I know this sounds very high level So let’s talk about the basic fundamentals what generally I try to follow in day to day professional and personal activities.

  1. Listen carefully You need to pay very close attention to any information in the problem description. The optimal solution for a sorted vs unsorted array will be totally different so don’t miss anything.
  2. Brute Force Yes correct, Get the brute force solution as soon as possible, don’t think about the optimal solution. I always catch the first thought that comes to my mind. Don’t think about code, the algorithm just rough idea.
  3. Optimize Now it’s time to work on your Brute Force with some BUD (Bottlenecks, Unnecessary work and last Duplicated work) techniques.
    1. Remove the unused information.
    2. Solve it manually on paper with an example.
    3. Reverse engineer your thought process. HOW DID YOU DO?
    4. Make a Time VS Space trade-off.  CAN YOU REDUCE-IT MORE?
  4. Implement Congratulations now you have an optimal solution on paper. The last goal is to write beautiful, modularize code.

If you are trying to solve the problem in interview KEEP TALKING because your interviewer wants to hear how you’re going to approach the problem and it will make the interview more interactive.

Thanks a lot for reading the quick-notes!

Quick Notes | Swift classes into Objective-C Code when you have multiple targets.

How to use Swift classes into Objective Code when you have multiple targets.

For using Swift classes in Objective-C Code when you have one target in your app. We generally need to andimport TargetName-Swift.h next to add support in your Swift file you need to inherit if from NSObject or use @objc flag.

What if you have multiple targets in your codebase? As you cannot import, TargetNameA-Swift.h TargetNameB-Swift.h etc. In that case, you can tell the compiler that not to create Swift module specific to target change it to project name because the project will be same and unique.

For achieving this select your every target, Build Settings and change the build configuration.

Objective-C Generated Interface Header Name —> replace  $(SWIFT_MODULE_NAME)-Swift.h that is specific to the each target, with ​​​​$(PROJECT_NAME)-Swift.h

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Later import PROJECT_NAME-Swift.h in your Objective C code to make use of your Swift code.

iOS Wireless Install, Debug Builds using WiFi | Quick Notes

Yes, correct you heard it right. It was the most awaited feature because nobody wants to spend a lot on Apple connectors, haha. But unfortunately, I don’t see people are utilizing this features. So here we go with one to kick start.


  1. iOS device with later or iOS 11 OS version.
  2. MacBook with macOS 10.12.4 or later.
  3. Xcode IDE with 9 or later
  4. Developer Macbook and iOS device should be on same WiFi network.

I hope after reading prerequisites you are clear about what is gonna happen. Let’s move on further steps.

Step: 1 Here you need your connector cable for first and yes last time. Connect your iOS device and open Xcode.

Step 2: Switch to,Window,Devices and Simulators options, below is the screen for reference.

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Step 3: Just enable the optionConnect via network.

Step 4: Sometimes it will ask you to provide your iOS device IP to enter but in my case, it didn’t ask.

Thanks for reading!

Benefits of Storyboards | iOS

Lots of developers consulted with me regarding on how to use storyboard with too many team members like when you have 20 developers on your team? So I have collected my thoughts on that today. I have used Storyboard as well as XIB so here are my thoughts on both.

  • Storyboards are the really nice way to see complete application flow without running into Simulator, you can see the screen flow and the navigation between them, it’s one of key thing that makes your application architecture better.
  • For a larger team of multiple developers it’s really difficult to use the same storyboard because at the end it’s XML file so really very hard to merge and you will end up with a lot of conflicts, So I have noted, a lot of developers suggest XIB here but I don’t see any reason why they choose XIB and I think the best idea is the divide the complete application in different storyboard according to their use-case, that is the first activity I always do, divide complete app into as much as possible storyboard you can (but it’s not like 1 storyboard for 1 ViewController) and use storyboard reference to connect them.
  • I worked in rapid prototype development (deliver the complete application in 15-20 days, developed POC in 7 days) so the biggest benefit that I earned from storyboard is Mock-up, I can create complete app mock-up without writing a single line of code and really easy to manage the transition between views.
  • Few issues that I feel with the storyboard is, it fails at runtime means if you made a mistake with segue name, the class doesn’t exist etc. Yes, it gives issue at compile as well only if you didn’t merge it properly (merge conflicts with XML tags).
  • Using Storyboard, no need to run your app on the different simulator to verify the UI, it gives you fantastic feature called preview (Click on the Assistant editor, select your storyboard, choose automation to preview).
  • Developers say it’s harder to reuse the code in storyboard but my opinion is, first think and implement, try to use mix approach with the storyboard, XIB (wherever requires use XIB to make it reusable on different storyboards).
  • Yes, storyboard creates an issue when you create one in Xcode 8 and try to open it in Xcode 7 but lots of developers already raised this concern with Apple so hopefully, we will hear something from Apple soon.

Thank you for reading! Please do share your thoughts if any.

Creating and Distributing iOS Frameworks | Swift | Tips & Tricks

Why do we need to create frameworks? because it has three major purposes mentioned below and also you can share your code with your team, other developer or iOS community.

  • Code encapsulation
  • Code modularity
  • Code reuse

Let’s create the iOS framework.

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Now just give some meta-data about your framework like name, organization, identifier etc (I hope you’re already aware of it).

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We’re good to go till now. Just add the files that you want to keep within your framework.


Build the framework project to make sure that you get build succeeded with no build warnings or errors.

Things that you need to take care.

  • Make sure to check Copy items if needed, so that the files actually copy into the new project instead of just adding a reference. Frameworks need their own code, not references, to be independent.
  • Double-check that each of the files has Target Membership in ThreeRingControl to make sure they appear in the final framework. You can see this in the File Inspector for each file.
  • Double-check the access modifiers, while creating framework access modifiers plays very important roles.
  • if you’re creating Swift framework make sure you’re extending classes from NSObject otherwise it won’t reflect once you will import the framework.

Thanks for reading.