1628797080

A **Fenwick tree** or **binary indexed tree** is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers.

When compared with a flat array of numbers, the Fenwick tree achieves a much better balance between two operations: element update and prefix sum calculation. In a flat array of n numbers, you can either store the elements, or the prefix sums. In the first case, computing prefix sums requires linear time; in the second case, updating the array elements requires linear time (in both cases, the other operation can be performed in constant time). Fenwick trees allow both operations to be performed in O(log n) time. This is achieved by representing the numbers as a tree, where the value of each node is the sum of the numbers in that subtree. The tree structure allows operations to be performed using only O(log n) node accesses.

Binary Indexed Tree is represented as an array. Each node of Binary Indexed Tree stores sum of some elements of given array. Size of Binary Indexed Tree is equal to n where n is size of input array. In current implementation we have used size as n+1 for ease of implementation. All the indexes are 1-based.

On the picture below you may see animated example of creation of binary indexed tree for the array [1, 2, 3, 4, 5] by inserting one by one.

*Read this in other languages:* *Português*

TheOriginal Articlecan be found on https://github.com

*#javascript #algorithms #datastructures #tree*

1620466520

If you accumulate data on which you base your decision-making as an organization, you should probably think about your data architecture and possible best practices.

If you accumulate data on which you base your decision-making as an organization, you most probably need to think about your data architecture and consider possible best practices. Gaining a competitive edge, remaining customer-centric to the greatest extent possible, and streamlining processes to get on-the-button outcomes can all be traced back to an organization’s capacity to build a future-ready data architecture.

In what follows, we offer a short overview of the overarching capabilities of data architecture. These include user-centricity, elasticity, robustness, and the capacity to ensure the seamless flow of data at all times. Added to these are automation enablement, plus security and data governance considerations. These points from our checklist for what we perceive to be an anticipatory analytics ecosystem.

#big data #data science #big data analytics #data analysis #data architecture #data transformation #data platform #data strategy #cloud data platform #data acquisition

1628797080

A **Fenwick tree** or **binary indexed tree** is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers.

When compared with a flat array of numbers, the Fenwick tree achieves a much better balance between two operations: element update and prefix sum calculation. In a flat array of n numbers, you can either store the elements, or the prefix sums. In the first case, computing prefix sums requires linear time; in the second case, updating the array elements requires linear time (in both cases, the other operation can be performed in constant time). Fenwick trees allow both operations to be performed in O(log n) time. This is achieved by representing the numbers as a tree, where the value of each node is the sum of the numbers in that subtree. The tree structure allows operations to be performed using only O(log n) node accesses.

Binary Indexed Tree is represented as an array. Each node of Binary Indexed Tree stores sum of some elements of given array. Size of Binary Indexed Tree is equal to n where n is size of input array. In current implementation we have used size as n+1 for ease of implementation. All the indexes are 1-based.

On the picture below you may see animated example of creation of binary indexed tree for the array [1, 2, 3, 4, 5] by inserting one by one.

*Read this in other languages:* *Português*

TheOriginal Articlecan be found on https://github.com

*#javascript #algorithms #datastructures #tree*

1623066480

Hello! Today I would like to review what I’ve learned about search algorithms and the importance of each one in computer programming. I’ve never been great at writing preambles, so without further ado, let’s get started.

It’s safe to say we’ve all used some kind of search engine when browsing the web. Whether it’s Google, Bing, DuckDuckGo, etc., we have experienced the benefits of their search algorithms, individually and as a society. But how do search engines conduct these searches for optimized results from around the web? And how do they determine how results get sorted? The answer is more complicated than fundamental algorithms, though those still exist at the core of these search engine behemoths.

As I mentioned, Google’s search algorithms are more than simple lookup() methods but are still used at the most rudimentary level. One thing I can say confidently is that this first algorithm is not how Google executes searches. **_Linear search _**algorithms search a sorted structure, such as an array or a binary search tree, to find a match to the desired value. For example, if I had declared a sorted array as [0,1,2,3,4,5,6], and I ran a linear search for the value 6, our search algorithm would start the search at [0], then visit every index in the array, comparing each index’s value with our target value, until a match is found.

Linear Search is arguably the most rudimentary of search algorithms. But like every other algorithm, trade-offs exist when implementing this as a solution. This search algorithm would not be great in the use-case of an array with 1,000,000 indices to search through for a value, given its time complexity. You see, this search algorithm has a potential time complexity of O(n), or linear time complexity. The time complexity of this algorithm directly correlates to the size of the data structure (An array with one index can run a search in O(1) time, two indices in 0(2 + n) time, simplified to O(n), and so on). Unfortunately, this also means an array with 1,000,000 indices would execute a linear search for a value at index 300,000 in O(300,000 + n) time or, simplified, O(n) time. We needn’t worry about having to conduct linear searches through large amounts of data; there are, indeed, more optimal solutions available.

** Binary searches**, named after the trees they are programmed to search, search arrays in order, given that they are sorted. Binary searches work best when using a sorted array to build a binary search tree since we can create them effectively. To begin, the root node is defined as the median value of a sorted array. Going back to the previous array [1, 2, 3, 4, 5, 6, 7], this can be used to build a binary tree, which is more comprehensible for understanding and writing search algorithms. Does this look familiar to you?

This median key’s value gets compared to the search’s value to see if it is greater than or less than the target. Based on this comparison, a binary search algorithm will then search either array’s values to the left of the median if less than the median, or the right if greater. By now I’m hoping you remember that the lookup() method in a binary search tree works in this manner. The median value of a sorted array can be compared to the root node of a binary search tree, and lookup() for both require that the data structure is sorted. And, like with tree traversal, a binary search must visit every value in a sequence until a match is found. In a binary search tree with nodes valued [1,2,3,5,10,15,25,30,40,45,50], we would build a binary search tree using 15 as the tree’s root node, adding key values with lower values than the search value to the left, and ones with greater values to the right. If we were searching for a node with a value of 45, the algorithm would traverse in this order: root, left-child, right-child. An array representation of the nodes traversed for this would look like this: [15,25,40].

lookup(), as implemented in a binary search tree.

That’s all for now! In the next post, I will go over two more search algorithms: breadth-first search, and depth-first search, and how they are implemented in both trees and graphs. Be sure to check out https://visualgo.net for powerful visualizations of data structures and their algorithms, as well as a step-by-step breakdown of each of the latter. It’s probably the most useful learning aid I’ve used when learning.

#data-structures #trees #algorithms #javascript

1620629020

The opportunities big data offers also come with very real challenges that many organizations are facing today. Often, it’s finding the most cost-effective, scalable way to store and process boundless volumes of data in multiple formats that come from a growing number of sources. Then organizations need the analytical capabilities and flexibility to turn this data into insights that can meet their specific business objectives.

This Refcard dives into how a data lake helps tackle these challenges at both ends — from its enhanced architecture that’s designed for efficient data ingestion, storage, and management to its advanced analytics functionality and performance flexibility. You’ll also explore key benefits and common use cases.

As technology continues to evolve with new data sources, such as IoT sensors and social media churning out large volumes of data, there has never been a better time to discuss the possibilities and challenges of managing such data for varying analytical insights. In this Refcard, we dig deep into how data lakes solve the problem of storing and processing enormous amounts of data. While doing so, we also explore the benefits of data lakes, their use cases, and how they differ from data warehouses (DWHs).

*This is a preview of the Getting Started With Data Lakes Refcard. To read the entire Refcard, please download the PDF from the link above.*

#big data #data analytics #data analysis #business analytics #data warehouse #data storage #data lake #data lake architecture #data lake governance #data lake management

1621986060

If I ask you what is your morning routine, what will you answer? Let me answer it for you. You will wake up in the morning, freshen up, you’ll go for some exercise, come back, bath, have breakfast, and then you’ll get ready for the rest of your day.

If you observe closely these are a set of rules that you follow daily to get ready for your work or classes. If you skip even one step, you will not achieve your task, which is getting ready for the day.

These steps do not contain the details like, at what time you wake up or which toothpaste did you use or did you go for a walk or to the gym, or what did you have in your breakfast. But all they do contain are some basic fundamental steps that you need to execute to perform some task. This is a very basic example of algorithms. This is an algorithm for your everyday morning.

In this article, we will be learning algorithms, their characteristics, types of algorithms, and most important the complexity of algorithms.

Algorithms are a finite set of rules that must be followed for problem-solving operations. Algorithms are step-by-step guides to how the execution of a process or a program is done on a machine to get the expected output.

- Do not contain complete programs or details. They are just logical solutions to a problem.
- Algorithms are expressible in simple language or flowchart.

No one would follow any written instructions to follow a daily morning routine. Similarly, you cannot follow anything available in writing and consider it as an algorithm. To consider some instructions as an algorithm, they must have some specific characteristics :

**1. Input:** An algorithm, if required, should have very well-defined inputs. An algorithm can have zero or more inputs.

**2. Output:** Every algorithm should have one or more very well-defined outputs. Without an output, the algorithm fails to give the result of the tasks performed.

**3. Unambiguous:** The algorithm should be unambiguous and it should not have any confusion under any circumstances. All the sentences and steps should be clear and must have only one meaning.

**4. Finiteness:** The steps in the algorithm must be finite and there should be no infinite loops or steps in the algorithm. In simple words, an algorithm should always end.

**5. Effectiveness:** An algorithm should be simple, practically possible, and easy to understand for all users. It should be executable upon the available resources and should not contain any kind of futuristic technology or imagination.

**6. Language independent:** An algorithm must be in plain language so that it can be easily implemented in any computer language and yet the output should be the same as expected.

**1. Problem:** To write a solution you need to first identify the problem. The problem can be an example of the real-world for which we need to create a set of instructions to solve it.

**2. Algorithm:** Design a step-by-step procedure for the above problem and this procedure, after satisfying all the characteristics mentioned above, is an algorithm.

**3. Input:** After creating the algorithm, we need to give the required input. There can be zero or more inputs in an algorithm.

**4. Processing unit:** The input is now forwarded to the processing unit and this processing unit will produce the desired result according to the algorithm.

**5. Output:** The desired or expected output of the program according to the algorithm.

Suppose you want to cook chole ( or chickpeas) for lunch. Now you cannot just go to the kitchen and set utensils on gas and start cooking them. You must have soaked them for at least 12 hours before cooking, then chop desired vegetables and follow many steps after that to get the delicious taste, texture, and nutrition.

This is the need for algorithms. To get desired output, you need to follow some specific set of rules. These rules do not contain details like in the above example, which masala you are using or which salt you are using, or how many chickpeas you are soaking. But all these rules contain a basic step-by-step guide for best results.

We need algorithms for the following two reasons :

**1. Performance:** The result should be as expected. You can break the large problems into smaller problems and solve each one of them to get the desired result. This also shows that the problem is feasible.

**2. Scalability:** When you have a big problem or a similar kind of smaller problem, the algorithm should work and give the desired output for both problems. In our example, no matter how many people you have for lunch the same algorithm of cooking chickpeas will work every single time if followed correctly.

Let us try to write an algorithm for our lunch problem :

1. Soak chickpeas in the night so that they are ready till the next afternoon.

2. Chop some vegetables that you like.

3. Set up a utensil on gas and saute the chopped vegetables.

4. Add water and wait for boiling.

5. Add chickpeas and wait until you get the desired texture.

6. Chickpeas are now ready for your lunch.

The real-world example that we just discussed is a very close example of the algorithm. You cannot just start with step 3 and start cooking. You will not get the desired result. To get the desired result, you need to follow the specific order of rules. Also, each instruction should be clear in an algorithm as we can see in the above example.

#algorithms in data structure #data structure algorithms #algorithms