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Introduction to Merge Sort in Data Structure

It is a recursive procedure based on the divide and conquers technique to solve a problem. This means it divides the main problem into smaller problems and later merges them to get the solution to the bigger one. In Merge Sort, we divide the list of elements into smaller lists until and unless the single element is left in the list and then these are merged in correct order to get the sorted list of elements. This is also a comparison-based sorting algorithm with O(nlogn) of complexity. Here we will discuss merge sort in a data structure along with its algorithm and applications.

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Algorithm for Merge Sort in Data Structure

Merge Sort works similar to quick Sort where one uses a divide and conquer algorithm to sort the array of elements. It uses a key process Merge(myarr, left,m, right) to combine the sub-arrays divided using m position element. This process works on one assumption that the two sub-arrays contain the elements in a sorted manner. Below is pseudo-code to implement Merge Sort for a given array myarr which has its last index as right.

Algorithm:

LArray[ i ] = A [ left + i -1] RArray[ j ]= A[ q + j ] if LArray[ i ] < R [ j ] A[ k ] = LArray[ i ] else A[ k ] = RArray[ j ] j = j + 1

Explanation: First, we have algorithm MERGE-SORT that takes an array as an argument and sees if the last index is greater than the left index to see if the array contains some elements to be sorted. Then a middle point m is calculated to divide the array into 2 sub-arrays, and the same algorithm is called for those sub-arrays. When recursive calls end and we end up having single elements in each sub-array, the MERGE algorithm is called.

This algorithm declares 2 arrays LArray and RArray to hold the elements in 2 sub-arrays. Then, elements in the 2 sub-arrays are compared simultaneously, and Array A is populated with elements in the sorted arrays. This algorithm is preferred over quick sort while working with the linked list as in quicksort, and there was a need to access the elements a lot which is of O(n) complexity in case of the linked list.

In the above picture, elements of the array are sorted using Merge sort. Also, we can see the sequence or the order in which the elements are processed.

Example to Implement Merge Sort in Data Structure

Here are some examples of implementing merge sort:

RArray = myarr[mid:] myarr[k] = LArray[i] myarr[k] = RArray[j] myarr[k] = LArray[i] myarr[k] = RArray[j] myarr = [45,12,86,3,24,36,9] printList(myarr)

Output:

Time Complexity

As it is a recursive algorithm, its time complexity can be expressed as a recurrence relation. Here are the 3 types of time complexity which are explained below:

T(n) = 2T(n/2) + Θ(n)

2. Average Case: This is the case when the elements are partially sorted. The complexity of merge sort, in this case, is Θ(nlogn).

3. Best Case: This is when all the elements are already sorted, but still recursive calls are made thus, complexity is Θ(nlogn).

And Complexity of Merge algorithm is O(n) in all cases. Thus Merge sort is a stable algorithm that uses O(n) of auxiliary space and Divides and Conquer paradigm to sort the list of elements.

Applications of Merge Sort

Here are some of the applications of merge sort which are explained below:

Sorting linked lists: Since random access of elements takes much time in case of the linked list, Merge Sort provides a quick solution to sort the linked list elements. This also stores the elements in self-made arrays and does not need random access in the linked list thus, and it provides a good solution to sort elements in O(nlogn).

Inversion Count Problem: This is a problem where the degree of sorting of elements is calculated in a list of array. N case array is sorted degree is 0, and in case of reverse sorted list degree becomes maximum.

Used internal Sorting: The type of sorting required to be done on data resides in secondary memory. This is required in case when the amount of data is too large to fit into the main memory. Since the memory location of data need not be contiguous in secondary memory thus merge sort is preferred.

Conclusion

Merge Sort is a divide and conquer algorithm that uses a merge process to merge the two sub-arrays into one by sorting its elements incorrect order. It works on one assumption that the elements in these sub-arrays are already sorted. This is a stable algorithm often used to sort the LinkedList or inversion count problems or external Sorting.

Data Structure And Algorithms Insertion Sort

Data Structure and Algorithms Insertion Sort

This is an in-place comparison-based sorting algorithm. Here, a sub-list is maintained which is always sorted. For example, the lower part of an array is maintained to be sorted. An element which is to be ‘insert’ed in this sorted sub-list, has to find its appropriate place and then it has to be inserted there. Hence the name, insertion sort.

The array is searched sequentially and unsorted items are moved and inserted into the sorted sub-list (in the same array). This algorithm is not suitable for large data sets as its average and worst case complexity are of Ο(n2), where n is the number of items.

How Insertion Sort Works?

We take an unsorted array for our example.

Insertion sort compares the first two elements.

It finds that both 14 and 33 are already in ascending order. For now, 14 is in sorted sub-list.

Insertion sort moves ahead and compares 33 with 27.

And finds that 33 is not in the correct position.

It swaps 33 with 27. It also checks with all the elements of sorted sub-list. Here we see that the sorted sub-list has only one element 14, and 27 is greater than 14. Hence, the sorted sub-list remains sorted after swapping.

By now we have 14 and 27 in the sorted sub-list. Next, it compares 33 with 10.

These values are not in a sorted order.

So we swap them.

However, swapping makes 27 and 10 unsorted.

Hence, we swap them too.

Again we find 14 and 10 in an unsorted order.

We swap them again. By the end of third iteration, we have a sorted sub-list of 4 items.

This process goes on until all the unsorted values are covered in a sorted sub-list. Now we shall see some programming aspects of insertion sort.

Algorithm

Now we have a bigger picture of how this sorting technique works, so we can derive simple steps by which we can achieve insertion sort.

Step 1 − If it is the first element, it is already sorted. return 1; Step 2 − Pick next element Step 3 − Compare with all elements in the sorted sub-list Step 4 − Shift all the elements in the sorted sub-list that is greater than the value to be sorted Step 5 − Insert the value Step 6 − Repeat until list is sorted Pseudocode procedure insertionSort( A : array of items ) int holePosition int valueToInsert for i = 1 to length(A) inclusive do: /* select value to be inserted */ valueToInsert = A[i] holePosition = i /*locate hole position for the element to be inserted */ A[holePosition] = A[holePosition-1] holePosition = holePosition -1 end while /* insert the number at hole position */ A[holePosition] = valueToInsert end for end procedure

Java Program To Implement The Graph Data Structure

In this article, we will understand how to implement the graph data structure. we implement the graph data structure we implement graphs in Java using HashMap collection. HashMap elements are in the form of key-value pairs. We can represent the graph adjacency list in a HashMap.

Below is a demonstration of the same −

Suppose our input is −

Number of Vertices: 5 Number of edges: 5

The desired output would be −

The connections between the nodes of the Graph are: 1 - 2 1 - 3 1 - 4 2 - 4 2 - 5 3 - 4 3 - 5 4 - 5 Algorithm Step 1 - START Step 2 - Declare an object of a Graph class namely graph_object, two integers in class ‘Edge’ namely source and destination, and two integers in ‘main’ function namely vertices_count, edges_count. Step 3 - Define the values. Step 4 - Initialize values for the vertices and count. Step 5 - Create a new instance of the previously defined class. Step 6 - Initialize the instance with relevant values. Step 7 - Iterate over the instance using a ‘for’ loop, and display the output on the console. Step 8 - Display the result Step 9 - Stop Example 1

Here, we bind all the operations together under the ‘main’ function.

public class Graph { class Edge { int source, destination; } int vertices, edges; Edge[] edge; Graph(int vertices, int edges) { this.vertices = vertices; this.edges = edges; edge = new Edge[edges]; for(int i = 0; i < edges; i++) { edge[i] = new Edge(); } } public static void main(String[] args) { int vertices_count = 5; int edges_count = 8; Graph graph_object = new Graph(vertices_count, edges_count); System.out.println("A graph object is defined."); graph_object.edge[0].source = 1; graph_object.edge[0].destination = 2; graph_object.edge[1].source = 1; graph_object.edge[1].destination = 3; graph_object.edge[2].source = 1; graph_object.edge[2].destination = 4; graph_object.edge[3].source = 2; graph_object.edge[3].destination = 4; graph_object.edge[4].source = 2; graph_object.edge[4].destination = 5; graph_object.edge[5].source = 3; graph_object.edge[5].destination = 4; graph_object.edge[6].source = 3; graph_object.edge[6].destination = 5; graph_object.edge[7].source = 4; graph_object.edge[7].destination = 5; System.out.println("The connections between the edges of the Graph are: "); for(int i = 0; i < edges_count; i++) { System.out.println(graph_object.edge[i].source + " - " + graph_object.edge[i].destination); } } } Output A graph object is defined. The connections between the edges of the Graph are: 1 - 2 1 - 3 1 - 4 2 - 4 2 - 5 3 - 4 3 - 5 4 - 5 Example 2

Here, we encapsulate the operations into functions exhibiting object-oriented programming.

public class Graph { class Edge { int source, destination; } int vertices, edges; Edge[] edge; Graph(int vertices, int edges) { this.vertices = vertices; this.edges = edges; edge = new Edge[edges]; for(int i = 0; i < edges; i++) { edge[i] = new Edge(); } } static void print(Graph graph_object,int edges_count){ System.out.println("The connections between the edges of the Graph are: "); for(int i = 0; i < edges_count; i++) { System.out.println(graph_object.edge[i].source + " - " + graph_object.edge[i].destination); } } static void connect_edges(Graph graph_object){ graph_object.edge[0].source = 1; graph_object.edge[0].destination = 2; graph_object.edge[1].source = 1; graph_object.edge[1].destination = 3; graph_object.edge[2].source = 1; graph_object.edge[2].destination = 4; graph_object.edge[3].source = 2; graph_object.edge[3].destination = 4; graph_object.edge[4].source = 2; graph_object.edge[4].destination = 5; graph_object.edge[5].source = 3; graph_object.edge[5].destination = 4; graph_object.edge[6].source = 3; graph_object.edge[6].destination = 5; graph_object.edge[7].source = 4; graph_object.edge[7].destination = 5; } public static void main(String[] args) { int vertices_count = 5; int edges_count = 8; Graph graph_object = new Graph(vertices_count, edges_count); System.out.println("A graph object is defined."); connect_edges(graph_object); print(graph_object, edges_count); } } Output A graph object is defined. The connections between the edges of the Graph are: 1 - 2 1 - 3 1 - 4 2 - 4 2 - 5 3 - 4 3 - 5 4 - 5

How To Merge Videos In Windows 10

It’s fairly easy to merge multiple video clips in Windows 10 and create a single video file.

In Windows 10 you can either use a built-in app called Photos or a third-party app to merge videos. Besides being a great photo organizer, the Photos app lets you edit videos, add text to your videos and add background music among other things.

Table of Contents

Use the Built-in Photos App to Merge Videos in Windows 10

Follow the steps below to merge videos in Windows 10 in an easy way:

Open the Start menu, search for Photos, and select Photos from the search results.

Select New video at the top and choose New video project. This starts a new project to merge your videos.

When prompted, enter a title for the project or use the default name. Select OK.

Select Add and choose From this PC to upload a video from your computer.

Select the videos you want to merge in the File Explorer window that opens. Press and hold down Ctrl to select multiple items.

Your imported videos are now available in Photos. Select the first video and choose Place in the storyboard to add the video to the timeline.

You can also just drag the video from the Project library and drop it in the bottom Storyboard section.

Repeat Step 6 for all videos.

Once all the videos have been added to the storyboard, you can drag and drop your videos in the Storyboard section to change their order.

Select Finish video at the top-right of the Photos window.

Select High from the Video Quality dropdown menu, and then select Export.

Choose a folder to save the merged video and select Export at the bottom.

Note: You can only export your videos in MP4 in the Photos app. This might change in the future but currently, there’s no support for other video formats. You can use a program like Handbrake to convert between different video formats.

Use Kdenlive to Merge Videos in Windows 10

Download and install the free Kdenlive video editor on your PC.

Open the video editor when it’s installed.

Select the Project menu at the top and choose Add Clip or Folder. This lets you import the videos you want to merge into one file.

Select the videos that you’d like to merge. Hold down the Ctrl key to select multiple videos and import them in Kdenlive.

Drag the first video and drop it onto the timeline.

Drag the second video and place it next to the first video.

Repeat Step 7 until you place all the videos in the timeline.

Select the Render option at the top of the Kdenlive interface.

Select the folder icon next to the Output file and choose a folder to save your merged video in.

Choose a format for your video file from the Format menu.

Select Render to File at the bottom to start making a merged video file.

The live merge process on your screen tells you how long till the final video is ready.

When merging has finished, close Kdenlive.

Use Olive Video Editor to Combine Videos

Olive Video Editor is another free and open-source program to merge and edit videos on Windows 10. Follow the steps below to use this program:

Install and open Olive Video Editor on your PC.

Select the File menu at the top and choose Import. This lets you add the videos that you want to combine.

Select the videos you want to merge. You can select multiple videos by holding down the Ctrl key while making a selection.

Back to the editor screen, drag your first video from the list to the timeline.

Drag the other videos so that all your videos are placed on the timeline, sequentially.

Select the File menu at the top and choose Export.

Select a format, range, and the other options for your output video file. It’s optional to configure these options. Select Export at the bottom.

Choose a folder to save your merged video in and select Save at the bottom.

When Olive Video Editor has merged your videos, the resulting file will be available in your specified folder.

Conclusion

How To Sort The Objects In A List In Python?

In Python, a list is an ordered sequence that can hold several object types such as integer, character, or float. In other programming languages, a list is equivalent to an array. Square brackets are used to denote it, and a comma (,) is used to divide two items in the list.

In this article, we will show you how to sort the objects and elements in a list using python. Below are the different methods to accomplish this task −

Using sort() method

Using sorted() method

Assume we have taken a list containing some elements. We will return the list elements after sorting either in ascending or descending order.

NOTE − If the object/element of the list is a string the elements are sorted in alphabetical order.

Method 1: Using sort() method

The sort() method sorts the original list in place. It signifies that the sort() method changes the order of the list’s elements

By default, the sort() method uses the less-than operator (<) to sort the entries of a list i.e, in ascending order. In other words, it prioritizes lesser elements above higher ones.

To sort elements from highest to lowest(descending order), use the reverse=True parameter in the sort() method.

list.sort(reverse=True) Example 1

The following program sorts the list elements in ascending and descending order using the sort() method −

lst

[

]

lst

sort

(

)

(

“Sorting list items in ascending order: “

lst

)

lst

sort

(

reverse

True

)

(

“Sorting list items in descending order: “

lst

)

Output

On executing, the above program will generate the following output −

Sorting list items in ascending order: [1, 4, 5, 9, 10, 12] Sorting list items in descending order: [12, 10, 9, 5, 4, 1]

In this case, we’ve given a list of random values. The sort() method was then applied to the list, which sorted the given list in ascending order and printed the list in ascending order. The same list was then sorted in descending order by passing an additional key to the sort() function, reverse=True, and the list was printed in descending order.

Example:2 For a list containing string values

The following program sorts the list elements(string) in ascending and descending order using the sort() method −

lst

[

‘hello’

‘this’

‘is’

‘tutorials’

‘point’

‘website’

‘welcome’

‘all’

]

lst

sort

(

)

(

“Sorting list items in ascending order: “

lst

)

lst

sort

(

reverse

True

)

(

“Sorting list items in descending order: “

lst

)

Output

On executing, the above program will generate the following output −

Sorting list items in ascending order: ['all', 'hello', 'is', 'point', 'this', 'tutorials', 'website', 'welcome'] Sorting list items in descending order: ['welcome', 'website', 'tutorials', 'this', 'point', 'is', 'hello', 'all']

We can see that all the elements are sorted in alphabetical order

Method 2: Using sorted() method

The sorted() function returns a sorted list of the iterable object given.

You can choose between ascending and descending order. Numbers are sorted numerically, while strings are arranged alphabetically.

Syntax sorted(iterable, key=key, reverse=reverse) Parameters

iterable − It is a sequence

key − A function that will be executed to determine the order. The default value is None.

reverse − A Boolean expression. True sorts ascending, False sorts descending. The default value is False.

Example

The following program sorts the list elements in ascending and descending order using the sorted() method −

lst

[

]

(

“Sorting list items in ascending order: “

sorted

(

lst

)

(

“Sorting list items in descending order: “

sorted

(

lst

reverse

True

)

Output

On executing, the above program will generate the following output −

Sorting list items in ascending order: [1, 4, 5, 9, 10, 12] Sorting list items in descending order: [12, 10, 9, 5, 4, 1]

In this example, we’ve provided a set of random numbers. We gave the list as an argument to the sorted() method, which sorted and printed the given list in ascending order. The same list was then sorted in descending order by giving an additional key, reverse=True, to the sorted() method, and the list was printed in descending order.

Conclusion

In this article, we learned how to sort list objects/elements using the functions i.e sort() and sorted (). We also learned how to use the same functions to sort a list of items in descending order. We also discussed how the list will be sorted if it contains strings as objects.

How To Structure And Set Goals

What are the essential parts of a marketing plan template?

A marketing plan is a strategic document that specifies your organization’s target markets, marketing objectives, programs, and activities to achieve them, expected timescales, resources to be utilized, according to defined budgets, and how success will be measured.

What is the purpose of a marketing plan?

The purpose of a marketing plan is to define strategies to engage audiences in order to achieve business objectives.

The goal of a marketing plan is to ensure marketing activities are structured, relevant, and timely to achieve an organization’s objectives.

It’s a plan defining your company’s sustainable competitive position, structuring and setting marketing goals, and defining the resources necessary to achieve your business vision.

Context of a marketing plan

Here’s another way of understanding the context of a marketing plan, to put it into context with other types of plans, as shown in this table:

When to use a marketing plan?

The process of marketing planning within an organization will differ, depending on whether a strategic marketing plan or an operational marketing plan is utilized. Here are the differences between the two:

A strategic marketing plan outlines the overall strategy within a market, connecting customers, competitors, and what the organization is capable of achieving. It is typically created at divisional or company level.

In an organization’s planning process, marketing links:

Customers’ needs and wants

Competitor value proposition and actions

Strategic direction

Organizational objectives

If you’re just starting out and you haven’t got a plan at all, we recommend starting with our RACE Growth System, which is structured around a 5-step multichannel marketing framework. Our RACE Growth System enables large and small businesses alike to pinpoint their priorities for growth across focused 90-day planning cycles. So you can plan, manage, and optimize your marketing activities in less than 3 months.

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What should be included? / How should a marketing plan be structured?

A marketing plan should include:

The current position, priorities, and direction of your organization

Its position in relation to external environmental factors

A critical analysis of your organization’s strengths, weaknesses, opportunities, and threats

Clearly defined objectives and a way to benchmark their success

The means by which to achieve those objectives

Relevant and timely actions and responsibilities by function, product or service, and market segment

The finances and resources required and forecasted revenues

Regular measurement of progress and outcomes against benchmarks

A solid marketing plan has:

Clear, realistic goals which you can be confident of hitting

The best strategy to achieve these goals against your competition

Sufficient details of the tactics and actions needed to translate the strategy into action

A method to check you are on track with your plans

Check out the 18 most important digital marketing techniques to make sure you’re not missing any opportunities.

Which types of businesses use marketing plans?

Marketing planning will assist in the day-to-day running of any size, type or age of business. The targets and milestones set will help organizations, from small start-ups to large corporates, to effectively:

Allocate resources and budget

Motivate teams

Manage the performance of staff members and marketing efforts

Marketing plans for small businesses

In smaller businesses, the scope of a plan is typically annual and for the whole business. Typically, SMEs are working with smaller budgets and tighter turnaround times.

A marketing plan for a small business typically looks to identify where to prioritize the investment of time and available budget to generate results.

Smaller organizations typically have:

Small market shares

Owners involved in all aspects of strategic and operational management

Independence

A high degree of uncertainty

Difficulty innovating owing to limited resources

Such differences between large and smaller organizations tend to be reflected in the development of marketing plans.

When establishing a small start-up, marketing planning is an essential element. A small number of these businesses launch and grow, but for those that are successful, a strategic marketing approach will ensure continued development.

Marketing plans for large organizations

In large organizations, its focus will change, depending on the type of organization. A separate marketing plan might be:

Geographically-based

Product-based

Business unit based

Focused on segmentation

A marketing plan in a large organization may integrate a number of plans, specific to individual parts of the business. It is practical planning that takes place at a divisional, business unit, or individual company level.

Larger organizations with clearly defined management structures and a wealth of resources will make use of marketing principles very differently from smaller organizations.

Structure an effective marketing plan with RACE

Did you know – nearly half of companies don’t have a clearly defined digital marketing strategy? These companies are missing opportunities for better integration and risk losing customers due to out-of-date processes.

Savvy marketers and Smart Insights members already recognize that a practical, integrated marketing plan is essential for business growth in 2023 and beyond.

If you’re looking for a quick marketing plan structure to hone your performance and strategize your approach to marketing, why not download our free RACE Growth System template?

That’s why our RACE Growth System is structured across a simple 5-step marketing and sales funnel which can be applied to every size of business from startups to multinational corporations.

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How does a marketing plan relate to other plans?

The plan should not be formulated or used in isolation; it should be informed by the corporate objectives identified in your organization’s business plan.

Integrated with a marketing plan may also be a digital plan, multi-channel plan and campaign plan, for example. The marketing plan informs these plans and vice-versa.

An effective marketing plan will ensure the integration of activities, the scheduling of requirements, distinguishing responsibilities and the provision of benchmarks for measuring success.

Different organizations will utilize differing plans, covering different areas and timeframes. What is crucial in a business is that the plans being utilized, the timeframes allocated, and how they integrate with each other are collectively established.

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