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Posted on : June 13, 2025 By Tech World Times Development and Testing  Rate this post Sorting helps organize data in a specific order. It is used in search, reports, and efficient storage. Different sorting algorithms offer different performance. In this article, we will explain the Time Complexity of Sorting Algorithms in simple words. We will cover Python, Java, and C++ examples. 1. What Is Time Complexity? Time complexity tells how fast an algorithm runs. It measures the number of steps as input grows. It is written in Big-O notation. For example, O(n²) means steps grow with the square of inputs. 2. Types of Time Complexity Here are common types: O(1): Constant time O(n): Linear time O(n log n): Log-linear time O(n²): Quadratic time We will now apply these to sorting. 3. Bubble Sort Bubble Sort compares two numbers and swaps them if needed. It repeats until the list is sorted. Time Complexity: Best Case: O(n) (if already sorted) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef bubble_sort(arr): n = len(arr) for i in range(n): for j in range(n - i - 1): if arr[j] > arr[j+1]: arr[j], arr[j+1] = arr[j+1], arr[j] Java Example: javaCopyEditvoid bubbleSort(int arr[]) { int n = arr.length; for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) { int temp = arr[j]; arr[j] = arr[j+1]; arr[j+1] = temp; } } C++ Example: cppCopyEditvoid bubbleSort(int arr[], int n) { for (int i = 0; i < n-1; i++) for (int j = 0; j < n-i-1; j++) if (arr[j] > arr[j+1]) swap(arr[j], arr[j+1]); } 4. Selection Sort This sort picks the smallest number and places it at the front. Time Complexity: Best Case: O(n²) Average Case: O(n²) Worst Case: O(n²) Python Example: pythonCopyEditdef selection_sort(arr): for i in range(len(arr)): min_idx = i for j in range(i+1, len(arr)): if arr[j] < arr[min_idx]: min_idx = j arr[i], arr[min_idx] = arr[min_idx], arr[i] 5. Insertion Sort This algorithm builds the final list one item at a time. Time Complexity: Best Case: O(n) Average Case: O(n²) Worst Case: O(n²) Java Example: javaCopyEditvoid insertionSort(int arr[]) { for (int i = 1; i < arr.length; i++) { int key = arr[i]; int j = i - 1; while (j >= 0 && arr[j] > key) { arr[j + 1] = arr[j]; j = j - 1; } arr[j + 1] = key; } } 6. Merge Sort Merge Sort splits the array into halves and merges them back in order. Time Complexity of Sorting Algorithms like Merge Sort is usually better. Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n log n) Python Example: pythonCopyEditdef merge_sort(arr): if len(arr) > 1: mid = len(arr) // 2 left = arr[:mid] right = arr[mid:] merge_sort(left) merge_sort(right) i = j = k = 0 while i < len(left) and j < len(right): if left[i] < right[j]: arr[k] = left[i] i += 1 else: arr[k] = right[j] j += 1 k += 1 arr[k:] = left[i:] + right[j:] 7. Quick Sort Quick Sort picks a pivot and places smaller numbers before it. Time Complexity: Best Case: O(n log n) Average Case: O(n log n) Worst Case: O(n²) C++ Example: cppCopyEditint partition(int arr[], int low, int high) { int pivot = arr[high]; int i = low - 1; for (int j = low; j < high; j++) { if (arr[j] < pivot) { i++; swap(arr[i], arr[j]); } } swap(arr[i+1], arr[high]); return i + 1; } void quickSort(int arr[], int low, int high) { if (low < high) { int pi = partition(arr, low, high); quickSort(arr, low, pi - 1); quickSort(arr, pi + 1, high); } } 8. Built-in Sort Methods Languages have built-in sort functions. These are well-optimized. Python: sorted() or list.sort() uses TimSort Time Complexity: O(n log n) Java: Arrays.sort() uses Dual-Pivot QuickSort Time Complexity: O(n log n) C++: std::sort() uses IntroSort Time Complexity: O(n log n) These are better for most real-world tasks. 9. Time Complexity Comparison Table AlgorithmBestAverageWorstStableBubble SortO(n)O(n²)O(n²)YesSelection SortO(n²)O(n²)O(n²)NoInsertion SortO(n)O(n²)O(n²)YesMerge SortO(n log n)O(n log n)O(n log n)YesQuick SortO(n log n)O(n log n)O(n²)NoTimSort (Python)O(n)O(n log n)O(n log n)YesIntroSort (C++)O(n log n)O(n log n)O(n log n)No 10. How to Choose the Right Algorithm? Use Merge Sort for large stable data. Use Quick Sort for faster average speed. Use Insertion Sort for small or nearly sorted lists. Use built-in sort functions unless you need control. Conclusion The Time Complexity of Sorting Algorithms helps us pick the right tool. Bubble, Selection, and Insertion Sort are simple but slow. Merge and Quick Sort are faster and used often. Built-in functions are highly optimized. Python, Java, and C++ each have their strengths. Understand your problem and input size. Then pick the sorting method. This ensures better speed and performance in your code. Tech World TimesTech World Times (TWT), a global collective focusing on the latest tech news and trends in blockchain, Fintech, Development & Testing, AI and Startups. If you are looking for the guest post then contact at techworldtimes@gmail.com

Asus ROG Xbox Ally, ROG Xbox Ally X to Start Pre-Orders in August, Launch in October – Rumour A new report indicates that the ROG Xbox Ally will be priced at around €599, while the more powerful ROG Xbox Ally X will cost €899. Posted By Joelle Daniels | On 16th, Jun. 2025 While Microsoft and Asus have unveiled the ROG Xbox Ally and ROG Xbox Ally X handheld gaming systems, the companies have yet to confirm the prices or release dates for the two systems. While the announcement  mentioned that they will be launched later this year, a new report, courtesy of leaker Extas1s, indicates that pre-orders for both devices will be kicked off in August, with the launch then happening in October. As noted by Extas1s, the lower-powered ROG Xbox Ally is expected to be priced around €599. The leaker claims to have corroborated the pricing details for the handheld with two different Europe-based retailers. The more powerful ROG Xbox Ally X, on the other hand, is expected to be priced at €899. This would put its pricing in line with Asus’s own ROG Ally X. Previously, Asus senior manager of marketing content for gaming, Whitson Gordon, had revealed that pricing and power use were the two biggest reasons why both the ROG Xbox Ally and the ROG Xbox Ally X didn’t feature OLED displays. Rather, both systems will come equipped with 7-inch 1080p 120 Hz LCD displays with variable refresh rate capabilities. “We did some R&D and prototyping with OLED, but it’s still not where we want it to be when you factor VRR into the mix and we aren’t willing to give up VRR,” said Gordon. “I’ll draw that line in the sand right now. I am of the opinion that if a display doesn’t have variable refresh rate, it’s not a gaming display in the year 2025 as far as I’m concerned, right? That’s a must-have feature, and OLED with VRR right now draws significantly more power than the LCD that we’re currently using on the Ally and it costs more.” Explaining further that the decision ultimately also came down to keeping the pricing for both systems at reasonable levels, since buyers often tend to get handheld gaming systems as their secondary machiens, Gordon noted that both handhelds would have much higher price tags if OLED displays were used. “That’s all I’ll say about price,” said Gordon. “You have to align your expectations with the market and what we’re doing here. Adding 32GB, OLED, Z2 Extreme, and all of those extra bells and whistles would cost a lot more than the price bracket you guys are used to on the Ally, and the vast majority of users are not willing to pay that kind of price.” Shortly after its announcement, Microsoft and Asus had released a video where the two companies spoke about the various features of the ROG Xbox Ally and ROG Xbox Ally X. In the video, we also get to see an early hardware prototype of the handheld gaming system built inside a cardboard box. The ROG Xbox Ally runs on an AMD Ryzen Z2A chip, and has 16 GB of LPDDR5X-6400 RAM and 512 GB of storage. The ROG Xbox Ally X, on the other hand, runs on an AMD Ryzen Z2 Extreme chip, and has 24 GB of LPDDR5X-8000 RAM and 1 TB of storage. Both systems run on Windows. Tagged With: Elden Ring: Nightreign Publisher:Bandai Namco Developer:FromSoftware Platforms:PS5, Xbox Series X, PS4, Xbox One, PCView More FBC: Firebreak Publisher:Remedy Entertainment Developer:Remedy Entertainment Platforms:PS5, Xbox Series X, PCView More Death Stranding 2: On the Beach Publisher:Sony Developer:Kojima Productions Platforms:PS5View More Amazing Articles You Might Want To Check Out! Summer Game Fest 2025 Saw 89 Percent Growth in Live Concurrent Viewership Since Last Year This year's Summer Game Fest has been the most successful one so far, with around 1.5 million live viewers on ... Asus ROG Xbox Ally, ROG Xbox Ally X to Start Pre-Orders in August, Launch in October – Rumour A new report indicates that the ROG Xbox Ally will be priced at around €599, while the more powerful ROG Xbo... Borderlands 4 Gets New Video Explaining the Process of Creating Vault Hunters According to the development team behind Borderlands 4, the creation of Vault Hunters is a studio-wide collabo... The Witcher 4 Team is Tapping Into the “Good Creative Chaos” From The Witcher 3’s Development Narrative director Philipp Weber says there are "new questions we want to answer because this is supposed to f... The Witcher 4 is Opting for “Console-First Development” to Ensure 60 FPS, Says VP of Tech However, CD Projekt RED's Charles Tremblay says 60 frames per second will be "extremely challenging" on the Xb... Red Dead Redemption Voice Actor Teases “Exciting News” for This Week Actor Rob Wiethoff teases an announcement, potentially the rumored release of Red Dead Redemption 2 on Xbox Se... View More

Game Pass – will it continue forever? (Microsoft) The Monday letters page struggles to predict what’s going to happen with the PlayStation 6, as one reader sees their opinion of the Switch 2 change over time. To join in with the discussions yourself email gamecentral@metro.co.uk Final Pass I agree with a lot of what was said about the current state of Xbox in the Reader’s Feature this weekend and how the more Microsoft spends, and the more companies they own, the less the seem to be in control. Which is very strange really.The biggest recent failure has got to be Game Pass, which has not had the impact they expected and yet they don’t seem ready to acknowledge that. If they’re thinking of increasing the price again, like those rumours say, then I think that will be the point at which you can draw a line under the whole idea and admit it’s never going to catch on. But would Microsoft ever shut down Game Pass completely? I feel that would almost be more humiliating than stopping making consoles, so I can’t really imagine it. Instead, they’ll make it more and more expensive and put more and more restrictions on day one games until it’s no longer recognisable.Grackle Panic button Strange to see Sony talking relatively openly about Nintendo and Microsoft as competition. I can’t remember the last time they mentioned either of them, even if they obviously would prefer not to have, if they hadn’t been asked by investors.At no point did they acknowledge that the Switch has completely outsold both their last two consoles, so I’m not sure where their confidence comes from. I guess it’s from the fact that they know they’ve done nothing this gen and still come out on top, so from their perspective they’ve got plenty in reserve. Expert, exclusive gaming analysis Sign up to the GameCentral newsletter for a unique take on the week in gaming, alongside the latest reviews and more. Delivered to your inbox every Saturday morning. Having your panic button being ‘do anything at all’ must be pretty reassuring really. Nintendo has had to work to get where they are with the Switch but Sony is just coasting it.Lupus James’ LadderJacob’s Ladder is a film I’ve been meaning to watch for a while, and I guessed the ending quite early on, but it feels like a Silent Hill film. I don’t know if you guys have seen it but it’s an excellent film and the hospital scene near the end, and the cages blocking off the underground early on, just remind me of the game. A depressing film overall but worth a watch.Simon GC: Jacob’s Ladder was as a major influence on Silent Hill 2 in particular, even the jacket James is wearing is the same. Email your comments to: gamecentral@metro.co.uk Seeing the future I know everyone likes to think of themselves as Nostradamus, but I have to admit I have absolutely no clue what Sony is planning for the PlayStation 6. A new console that is just the usual update, that sits under your TV, is easy enough to imagine but surely they’re not going to do that again?But the idea of having new home and portable machines that come out at the same time seems so unlikely to me. Surely the portable wouldn’t be a separate format, but I can’t see it being any kind of portable that runs its own games because it’d never be as powerful as the home machine. So, it’s really just a PlayStation Portal 2? Like I said, I don’t know, but for some reason I have a bad feeling about that the next gen and whatever Sony does end up unveiling. I suspect that whatever they and Microsoft does it’s going to end up making the Switch 2 (and PC) seem even more appealing by comparison.Gonch Hidden insight I’m not going to say that Welcome Tour is a good game but what I will say is that I found it very interesting at times and I’m actually kind of surprised that Nintendo revealed some of the information that they did. Most of it could probably be found out by reverse engineering it and just taking it apart but I’m still surprised it went into as much detail as it did.You’re right that it’s all presented in a very dull way but personally I found the ‘Insights’ to be the best part of the game. The minigames really are not very good and I was always glad when they were over. So, while I would not necessarily recommend the game (it’s not really a game) I would say that it can be of interest to people who have an interest in how consoles work and how Nintendo think.Mogwai Purchase privilege I’ve recently had the privilege of buying Clair Obscur: Expedition 33 from the website CDKeys, using a 10% discount code. I was lucky enough to only spend a total of £25.99; much cheaper than purchasing the title for console. If only Ubisoft had the foresight to see what they allowed to slip through their fingers. I’d also like to mention that from what I’ve read quite recently ,and a couple of mixed views, I don’t see myself cancelling my Switch 2. On the contrary, it just is coming across as a disappointment.From the battery life to the lack of launch titles, an empty open world is never a smart choice to make not even Mario is safe from that. That leaves the upcoming ROG Xbox Ally that’s recently been showcased and is set for an October launch. I won’t lie it does look in the same vein as the Switch 2, far too similar to the ROG Ally X model. Just with grips and a dedicated Xbox button. The Z2 Extreme chip has me intrigued, however. How much of a transcendental shift it makes is another question however. I’ll have to wait to receive official confirmation for a price and release date. But there’s also a Lenovo Legion Go 2 waiting in the wings. I hope we hear more information soon. Preferably before my 28th in August.Shahzaib Sadiq Tip of the iceberg Interesting to hear about Cyberpunk 2077 running well on the Switch 2. I think if they’re getting that kind of performance at launch, from a third party not use to working with Nintendo hardware, that bodes very well for the future.I think we’re probably underestimating the Switch 2 a lot at the moment and stuff we’ll be seeing in two or three years is going to be amazing, I predict. What I can’t predict is when we’ll hear about any of this. I really hope there’s a Nintendo Direct this week.Dano Changing opinions So just a little over a week with the Switch 2 and after initially feeling incredibly meh about the new console and Mario Kart a little more playtime has been more optimistic about the console and much more positive about Mario Kart World.It did feel odd having a new console from Nintendo that didn’t inspire that childlike excitement. An iterative upgrade isn’t very exciting and as I own a Steam Deck the advancements in processing weren’t all that exciting either. I can imagine someone who only bough an OG Switch back in 2017 really noticing the improvements but if you bought an OLED it’s basically a Switch Pro (minus the OLED). The criminally low level of software support doesn’t help. I double dipped Street Fighter 6 only to discover I can’t transfer progress or DLC across from my Xbox, which sort of means if I want both profiles to have parity I have to buy everything twice! I also treated myself to a new Pro Controller and find using it for Street Fighter almost unplayable as the L and ZL buttons are far too easy to accidently press when playing. Mario Kart initially felt like more of the same and it was only after I made an effort to explore the world map, unlock characters and karts, and try the new grinding/ollie mechanic that it clicked. I am now really enjoying it, especially the remixed soundtracks. I do however want more Switch 2 exclusive experiences – going back through my back catalogue for improved frame rates doesn’t cut it Nintendo! As someone with a large digital library the system transfer was very frustrating and the new virtual cartridges are just awful – does a Switch 2 need to be online all the time now? Not the best idea for a portable system. So, the start of a new console lifecycle and hopefully lots of new IP – I suspect Nintendo will try and get us to revisit our back catalogues first though.BristolPete Inbox also-rans Just thought I would mention that if anyone’s interested in purchasing the Mortal Kombat 1 Definitive Edition, which includes all DLC, that it’s currently an absolute steal on the Xbox store at £21.99.Nick The GreekI’ve just won my first Knockout Tour online race on Mario Kart World! I’ve got to say, the feeling is magnificent.Rable More Trending Email your comments to: gamecentral@metro.co.uk The small printNew Inbox updates appear every weekday morning, with special Hot Topic Inboxes at the weekend. Readers’ letters are used on merit and may be edited for length and content. You can also submit your own 500 to 600-word Reader’s Feature at any time via email or our Submit Stuff page, which if used will be shown in the next available weekend slot. You can also leave your comments below and don’t forget to follow us on Twitter. Arrow MORE: Games Inbox: Is Mario Kart World too hard? GameCentral Sign up for exclusive analysis, latest releases, and bonus community content. This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply. Your information will be used in line with our Privacy Policy

Over the past few months, I’ve had the pleasure of testing out the reMarkable Paper Pro. You can read my full review here, but in short, it gets everything right about the note taking experience. Despite being an e-ink tablet, it does get quite pricey. However, there are certainly some fantastic parts of the experience that make it worth comparing to an iPad Air, depending on what you’re looking for in a note taking device for school, work, or whatever else. Updated June 15th to reflect reMarkable’s new post-tariff pricing. Overview Since the reMarkable Paper Pro comes in at $679 with the reMarkable Marker Plus included, it likely makes most sense to compare this against Apple’s iPad Air 11-inch. That comes in at $599 without an Apple Pencil, and adding in the Apple Pencil Pro will run you an additional $129. The equivalent iPad setup will run you $50 more than the reMarkable Paper Pro. Given the fact that iPad Air‘s regularly go on sale, it’d be fair to say they’re roughly on the same playing field. So, $679 for a reMarkable Paper Pro setup, versus $728 for a comparable iPad Air setup. Which is better for you? Obviously, the iPad Air has one key advantage: It runs iOS, has millions of apps available, can browse the web, play games, stream TV shows/movies, and much more. To some, that might end the comparison and make the iPad a clear winner, but I disagree. Yes, if you want your tablet to do all of those things for you, the iPad Air is a no brainer. At the end of the day, the iPad Air is a general purpose tablet that’ll do a lot more for you. However, if you also have a laptop to accompany your tablet, I’d argue that the iPad Air may fall into a category of slight redundance. Most things you’d want to do on the iPad can be done on a laptop, excluding any sort of touchscreen/stylus reliant features. iPads are great, and if you want that – you should pick that. However, I have an alternative argument to offer… The reMarkable Paper Pro does one thing really well: note taking. At first thought, you might think: why would I pay so much for a device that only does one thing? Well, that’s because it does that one thing really well. There’s also a second side to this argument: focus. It’s much easier to focus on what you’re doing when the device isn’t capable of anything else. If you’re taking notes while studying, you could easily see a notification or have the temptation to check notification center. Or, if you’re reading an e-book, you could easily choose to swipe up and get into another app. The best thing about the reMarkable Paper Pro is that you can’t easily get lost in the world of modern technology, while still having important technological features like cloud backup of your notes. Plus, you don’t have to worry about carrying around physical paper. One last thing – the reMarkable Paper Pro also has rubber feet on the back, so if you place it down flat on a table caseless, you don’t have to worry about scratching it up. Spec comparison Here’s a quick rundown of all of the key specs between the two devices. reMarkable Paper Pro‘s strengths definitely lie in battery, form factor, and stylus. iPad has some rather neat features with the Apple Pencil Pro, and also clears in the display category. Both devices also offer keyboards for typed notes, though only the iPad offers a trackpad. Display– 10.9-inch LCD display– Glossy glass– 2360 × 1640 at 264 ppi– 11.8-inch Color e-ink display– Paper-feeling textured glass– 2160 × 1620 at 229 ppiHardware– 6.1mm thin– Anodized aluminum coating– Weighs 461g w/o Pencil Pro– 5.1mm thin– Textured aluminum edges– Weighs 360g w/ Marker attachedStylus– Magnetically charges from device– Supports tilt/pressure sensitivity– Low latency (number unspecified)– Matte plastic build– Squeeze features, double tap gestures– Magnetically charges from device– Supports tilt/pressure sensitivity– Ultra-low latency (12ms)– Premium textured aluminum build– Built in eraser on the bottomBattery life– Up to 10 hours of web browsing– Recharges to 100% in 2-3 hrs– Up to 14 days of typical usage– Fast charges to 90% in 90 minsPrice– $599 ($529 on sale) for iPad Air– $129 ($99 on sale) for Pencil Pro– $679 bundled with Marker Plus Wrap up All in all, I’m not going to try to convince anyone that wanted to buy an iPad that they should buy a reMarkable Paper Pro. You can’t beat the fact that the iPad Air will do a lot more, for roughly the same cost. But, if you’re not buying this to be a primary computing device, I’d argue that the reMarkable Paper Pro is a worthy alternative, especially if you really just want something you can zone in on. The reMarkable Paper Pro feels a lot nicer to write on, has substantially longer battery life, and really masters a minimalist form of digital note taking. Buy M3 iPad Air on Amazon: Buy reMarkable Paper Pro on Amazon: What do you think of these two tablets? Let us know in the comments. My favorite Apple accessory recommendations: Follow Michael: X/Twitter, Bluesky, Instagram Add 9to5Mac to your Google News feed.  FTC: We use income earning auto affiliate links. More.You’re reading 9to5Mac — experts who break news about Apple and its surrounding ecosystem, day after day. Be sure to check out our homepage for all the latest news, and follow 9to5Mac on Twitter, Facebook, and LinkedIn to stay in the loop. 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