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In this tutorial we learn about ways to measure performance of an Algorithm . By measuring performance of an algorithm we can determine which algorithm is better than the other one. Performance of an algorithm is usually represented by the Big O Notation . Follow along and learn more about measuring performance of an algorithm .
I am in a Big problem!
I just received a birthday gift from my elder sister and I want to send a thank you message to her. But, the thing is I am running short on time. I want to get this task done as soon as possible. I’ve listed three ways in which I can solve this problem.
1) Sending a thank you note through post/mail.
2) I could ring her phone or compose an email to convey the message.
3) Or drive to her house and thank her in person.
But, which approach do you think would be fastest?
Approach 2, right? Yes, I was thinking the same.
My end goal of sending a thank you message can be easily accomplished by few clicks or a with one phone call.( Big assumption: Gossip time on the phone not counted )
Similarly, in order to solve any problem in computer science, we write programs. Every program — though can be written in a different programming language — like the one discussed above, can be solved in many ways. In the programming world, we call these ways/solutions as Algorithms .
Oh, yeah, big word alert: What is an algorithm? An algorithm is nothing but a bunch of steps we undertake to achieve some goal, sister getting a thank you message in our above example. Let’s take our third approach to send thank you message to big sister.
Wait, you might be wondering, does that count as an algorithm? Sure it does!
Similarly, before jumping to write a program in computer science, we always write an algorithm; a bunch of steps required to accomplish the task or solve the problem .
But, you may ask: We had multiple solutions to our thank you message problem. How do we decide/analyze which algorithm is fastest and best to solve our problem?
Before I answer your previous questions, let’s try to solve an immediate issue which popped up. I will get back to how do we go about analyzing algorithm after solving this immediate issue.
Imagine this, you just joined a new development team and were given a piece of code. As you look through the code, you find two methods sort_1 and sort_2 . Both these methods take same input in the form of an array of unsorted integer . And the function/method returns a sorted array i.e integers returned are in an order. Without going into code details, we can write the pseudo code as
Something like Input Given: An array of unsorted numbers like [8, 2, 10, 1]
Output Expected: Sorted array like [1, 2, 8, 10]
Someone from the team comes and tells you, “ Ah, one of this sorting method is faster than the other. But which one I can’t remember. Can you find out for me ? ”
Newbies can’t say no. So, time to put on our Testing Caps.
Something which is very clear is that we still don’t know any full proof approach which will give us an accurate result. We might have to do a repeated test to get a good average result.
Test Plan : Let’s create an array of 100 random numbers. Let us call this sort_1 function inside a loop which runs 1,000 times and log time taken to sort numbers. Refer to the below pseudo code:
Test Result: After running this test, you’ll find, log times are pretty close.A difference of few percents maybe. We've got a fair idea how long these functions/methods each take to sort 100 numbers.
Side Note: The small difference in time is because sorting 100 numbers is a fairly small task for machines. Any algorithm you choose, unless extremely inefficient, you will find a difference of a few milliseconds only.
But, did it solve our problem yet? We still can’t figure out which one is fastest or better than other.
Test Plan: Instead of creating 100 random numbers and calling the sort function 1000 times, why not create a single large random number array and call the sort function only once.
Test Result : Ah, this test did the job for us. With the humongous amount of data, you may find that one method beats other. Not just by few percents. Rather by a dramatic huge margin. One method could sort the array within a fraction of seconds and other is still sorting it for us.
I am sure you might be wondering is this even possible?
So, let me break this to you: this kind of result is not at all unusual. And this is one of the major reason and core challenges one faces with algorithm analysis.
The ( correct ) algorithms we write are neither slow or fast in itself. It would be very easy that way. It also very much depends on how much data we are asking these algorithms to work on .
But, I ran both these tests on my computer. What if, I ran this algorithm on a supercomputer. Will the result still be same?
Factors like the speed of the processor, programming language used to implement it and hardware will drastically impact the run time of the algorithm.
So, now the main question is: how do we go about analyzing/measuring/estimating the time taken by algorithms to run ignoring low-level hardware details and subject to varied input sizes?
( Also, problem fondly known as how do we go about measuring Time Complexity of an algorithm)
Not-So-Boring-Math to the rescue!
Mathematical notation called as Big O Notation/ Big O Complexity at our rescue.
What the heck is Big O Notation?
In computer science, we use Big O to classify algorithm where we express how quickly the run-time or space requirements grows relative to input , as the input size grows arbitrarily large .
Let me break the definition down into simpler words:
Sorry, it’s difficult to jot down the exact run time of an algorithm. Why you may ask. Remember, our computer vs supercomputer issue. Different hardware, processor speed affects total run-time of the algorithm. So instead of talking about run time directly, we use Big O to talk about how quickly the run time grows when the data ( read: input ) given to our algorithm increases.
Yes, I agree logging time would have been hassle free. But, since, we’re measuring how quickly our run time grows, we need to measure speed in terms of something else.
In Big O , we use the :
So, you’d often find us saying, “ Hey, the run time of that algorithm grows on the order of the size of the input i.e O(n) ”. Or something like, “ on the order of the square of the size of the input i.e O(n²) ”.
If all this explanation seems abstract so far, don’t worry. Let’s look at some examples analyzing our code with Big-O notation for more clarity.
When analyzing algorithms/operations, we often consider the worst-case scenario . What’s the worst that can happen to our algorithm and when does our algorithm will do some serious heavy-lifting work?
Let’s say you have a cabinet full of files. You may have many tasks like finding files, getting rid of duplicates etc. You also know that if there are more files in the cabinet, longer it will take you to accomplish your task.
Assuming we’ve to perform some of the task mentioned above. Here are few scenarios and ways in which we can find the file from the cabinet and their corresponding order of notation( operation’s time complexity ).
Scenario/Problem : Let's say we want to find a particular file in the cabinet. But, the files stored in the cabinet are not sorted or alphabetized. How can we search for our file?
Approach: We will have to look at each and every file present in the cabinet till we can find our file.
Worst-Case Scenario & Complexity Explanation:
Scenario/Problem : You need a file and remember exact location where you had kept the file.
Approach : Open the cabinet, pick the file from the location. End of the story.
Scenario/Problem : You’ve duplicate files in the cabinet and you want to remove them. But, you’ve no idea how many duplicate copies of each file lies in the cabinet.
Approach : We will have to pick the first file, check it against all the other files. Then take file number 2 and repeat the same action until you got to the last file.
Scenario: The files in the cabinet are in the order. We’ve to search a file marked with a label .
Approach : We can start in the middle, see in which half should be in, go to the middle of the half and repeat the steps until we found our file.
Let’s take a small algorithm where we’ve to calculate the complexity of the equation by throwing away:
If you can remember or scroll back to the definition of Big O, there’s a term in bold which states that when input size( n ) grows arbitrarily large.
As n gets really big, adding 200 or dividing by 10 has a decreasingly significant effect. So, we can safely throw these terms out. We only concentrate on a principal activity which has the most impact.
( I know, I know this is the biggest Big O definition explanation in the history of mankind. This is the final concept I promise! )
We need to analyze or care about memory cost( space complexity ) just like we did for our precious time. Best part there isn’t much difference between them.
Space complexity is space taken by algorithm to complete its algorithm relative to its input size.
Space Complexity = Constant Space + Auxiliary Space
Let’s see few code examples to simplify our definition:
We know, Space complexity = Constant Space + Auxiliary Space
Constant space is local variables & inputs i.e variable x, y, z and r in our case.
Auxiliary Space is for the temporary variable. Not used in above example. We consider 1 unit for each variable present in our algorithm
Space complexity = 1 + 1 + 1 + 1 + 0 = 4 = O(1) ( remember, our constant time Big O notation? )
Now, above method has an input of array and another input gives size/length of that array. An array has n elements, each will hold 1 unit of memory. So space taken by an array is ( 1n ) where n = number of elements in the array
Constant space = Space taken by array + variable n + variable r
Auxiliary Space = Space taken by temporary variable i
Space Complexity = (n * 1) + 1 + 1 + 1 = O(n)
Big O is a powerful tool, but one should use it wisely. Sometimes there’s a tradeoff between saving time and saving space , so one has to take a crucial decision on what needs to be optimized.
Like Big O royally ignores constants and less significant terms. But, sometimes they matter too. Imagine, if we have got a script that goes on for 5 hours, an optimization that divides the runtime by 10 might not affect Big O, but it can still save us few hours of waiting. Also, beware of premature optimization.
Hence, it is rightly said that one must develop the skill to optimize time and space complexity as well as be wise enough to judge if these optimizations are worthwhile.
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Head of Product, Atlassian Intelligence
Artificial intelligence (AI) solutions are advanced technologies that use algorithms, data analysis, and computational power to automate processes, make predictions, and learn from data without explicit programming.
Offering unprecedented efficiency, accuracy, and innovation, AI has reshaped how many industries operate. Keep reading to learn more about how AI works and the benefits of using AI solutions.
AI mimics human intelligence using algorithms and data. These processes rely on machine learning, where computers learn patterns and make decisions without necessarily being programmed for each scenario. Think of it like teaching a computer to recognize cats in pictures: instead of giving it a list of rules about what makes a cat, you’d show it pictures of cats and let it learn the common features on its own.
There are different types of AI, but one common approach is supervised learning. In this method, the computer is given a dataset with labeled examples, like pictures of cats and dogs with labels saying which is which. It uses these examples to learn the patterns and make predictions on new, unseen data.
Another important aspect of AI is neural networks, which are inspired by the human brain. These neural networks have layers of interconnected nodes, each processing and transforming data differently. Through training, neural networks adjust the connections between nodes to improve their performance on specific tasks.
Many businesses are unleashing the power of AI , with AI solutions used in various applications, from recognizing speech and images to powering recommendation systems and even autonomous vehicles, making our lives easier and more efficient.
Artificial intelligence solutions come in many forms, each with its own applications. Here are a few of the different categories or branches of AI solutions:
Machine learning teaches computers to learn from examples. When shown data, computers can recognize patterns and make predictions without explicit instructions. This technology is used to make recommendations for movies on your favorite streaming platforms or to predict trends in finance.
NLP helps computers understand and generate human language. It’s what makes virtual assistants like Siri or Alexa able to understand your commands and respond naturally. NLP also powers language translation tools and sentiment analysis in social media.
Computer vision lets machines “see” and understand visual information. It’s used in facial recognition systems, self-driving cars to recognize objects on the road, and in quality control for manufacturing processes.
Predictive analytics uses AI to forecast future outcomes based on past data patterns. It’s handy in finance for predicting stock prices, healthcare for anticipating patient outcomes, and marketing for identifying potential customers.
RPA automates repetitive tasks, allowing machines to handle mundane jobs and streamline workflows. It’s used in industries like banking to process transactions, logistics to manage inventory, and customer service to answer common queries.
AI data solutions are already majorly impacting many areas of our lives. Here are some of the applications of AI solutions and how it’s helping in different fields:
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Artificial intelligence solutions offer numerous benefits and positive impacts across various domains, contributing to the following:
While AI solutions have tremendous potential, their adoption and deployment can present challenges and ethical considerations organizations must address. These include:
Leveraging AI solutions in your organization can be transformative but requires thorough planning, execution, and integration with existing frameworks. Here are the steps you can follow to use AI in your organization:
Read industry news and attend relevant events to stay updated on the latest advancements. Project collaboration between AI experts and domain specialists will become crucial for driving innovation and solving complex challenges.
Ethical considerations like fairness and transparency will play a significant role in AI development and deployment. Prioritize ethical AI practices to ensure the responsible use of these technologies. Invest in talent development to cultivate a workforce with the skills to use AI effectively. By staying informed, collaborating across disciplines, and prioritizing ethics, businesses can confidently navigate the future of AI solutions and drive positive impact.
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What industries can benefit from ai solutions.
Industries like software development , finance, retail, manufacturing, and marketing can benefit from AI solutions. Even project management can see improvements with AI, like predicting project risks and optimizing schedules.
AI solutions are highly scalable and can grow to handle larger tasks or datasets. Scalability depends on factors like enough computational resources, a robust data infrastructure, and the organization’s readiness to implement and manage AI effectively.
Examples of AI solutions include:
These examples show how AI can be applied across different areas to streamline processes and improve outcomes.
COMMENTS
We can evaluate an algorithm's performance in four ways in Artificial intelligence. Completeness; Optimality; Time complexity; Space complexity; Time and space complexity are always considered with respect to some measure of the problem difficulty. In theoretical computer science, the typical measure is the size of the state space graph, |V | + |E|, where V is the set of vertices (nodes) of ...
Finally, the performance measures are averaged across all folds to estimate the capability of the algorithm on the problem. For example, a 3-fold cross validation would involve training and testing a model 3 times: #1: Train on folds 1+2, test on fold 3. #2: Train on folds 1+3, test on fold 2. #3: Train on folds 2+3, test on fold 1.
There are basically three types of problem in artificial intelligence: 1. Ignorable: In which solution steps can be ignored. 2. Recoverable: In which solution steps can be undone. 3. Irrecoverable: Solution steps cannot be undo. Steps problem-solving in AI: The problem of AI is directly associated with the nature of humans and their activities.
Problem Solving Agents and Uninformed SearchAn intelligent agen. act to increase their performan. Four general steps in problem solving: Goal formulation - deciding on what the goal states are. - based on current situation and agent's performance measure. cessful world states Problem formulation - - how can we get to the goal, without ge.
The problem solving agent chooses a cost function that reflects its own performance measure. The solution to the problem is an action sequence that leads from initial state to goal state and the ...
Problem-solving in AI involves a wide range of tasks. These tasks can be as simple as sorting data or as complex as diagnosing diseases or optimizing logistical operations. The goal of AI problem-solving is to replicate and improve upon human abilities to analyze, deduce, and make decisions. This journey from basic intuitive problem-solving to ...
3.3 Search Algorithms. A search algorithm takes a search problem as input and returns a solution, or an indication of failure. We consider algorithms that superimpose a search tree over the state-space graph, forming various paths from the initial state, trying to find a path that reaches a goal state.
Image recognition is another cognitive domain where algorithm performance is often assessed against humans. For image recognition, AI performance is typically benchmarked in a competition using the ImageNet database [9]. ... We induce that for similar production management decisions for which the same criteria apply, AI will be equally able to ...
Measuring Your Algorithm's Performance. Summary. Understanding how to evaluate and manage algorithmic performance could be the difference between success and failure. This article outlines a six ...
Problem solving in artificial intelligence refers to the process of finding solutions to complex problems using computational systems or algorithms. It involves defining and structuring the problem, formulating a plan or strategy to solve it, and executing the plan to reach the desired solution.
It leverages a combination of algorithms, models, and data to mimic the human ability to reason, learn from experience, and apply knowledge to new and unseen scenarios. AI problem-solving capabilities span various domains, from simple tasks like solving puzzles to complex decisions in financial analysis, healthcare diagnostics, and beyond.
performance measure • This can be simplified if the agent can adopt a goal and aim at satisfying it • Goals help organize behaviour by limiting the objectives that the agent is trying to achieve • Goal formulation, based on the current situation and the agent's performance measure, is the first step in problem solving
Performance of different AI algorithms can be defined as how well they complete their tasks and the confidence levels for predictions in some situations, which means for every AI the performance ...
Conclusion. To sum up, the foundation of AI problem-solving is comprised of the ideas of problems, problem spaces, and search. In AI issue solving, efficient search algorithms are crucial for efficiently navigating vast and intricate problem spaces and locating ideal or nearly ideal answers. They offer an organized method for defining ...
Figure 1: A simplified road map of part of Romania. The problem is to travel from Arad to Bucharest in a day. For the agent, the goal will be to reach Bucharest the following day.
The initial stage of problem-solving always involves setting a goal. This goal serves as a reference point, guiding the intelligent agent to act in a way that maximizes its performance measure ...
ch to a definite goal from a present state or condition."According to computer science, a problem-solving is a part of artificial intelligence which encompasses a number of. chniques such as algorithms, heuristics to solve a problem.Therefore, a problem-solving age. atisfying the goal.Steps performed by Problem-solving agentGoal Formu.
The model's iterative learning process, known as contextual bandits, a form of reinforcement learning, involves picking a potential solution, getting feedback on how good it was, and then trying again to find a better solution. This data-driven approach accelerated MILP solvers between 30 and 70 percent without any drop in accuracy.
Artificial intelligence (AI) problem-solving often involves investigating potential solutions to problems through reasoning techniques, making use of polynomial and differential equations, and carrying them out and use modelling frameworks. A same issue has a number of solutions, that are all accomplished using an unique algorithm.
Computational thinking is a term that has been developed on the basis of problem solving, as well as enabling today's technologies to be used effectively in different areas (Wing, 2006). Even though there is no consensus among the organizations, they have expressed the need for problem solving and the effective use of information and ...
In Big O, we use the : size of the input/data which we denote as "n". O stands for the order. So, you'd often find us saying, " Hey, the run time of that algorithm grows on the order of the size of the input i.e O (n) ". Or something like, " on the order of the square of the size of the input i.e O (n²) ".
AI projects fail, because they fail to deliver value. The root cause of failure is applying AI to the wrong use cases. The solution for finding the right use cases is with three measures: Measure the problem magnitude; Measure the solution accuracy retrospectively; Measure the solution accuracy in real time; These steps should be investigated ...
Artificial intelligence (AI) solutions are advanced technologies that use algorithms, data analysis, and computational power to automate processes, make predictions, and learn from data without explicit programming. Offering unprecedented efficiency, accuracy, and innovation, AI has reshaped how many industries operate.