Here's how to quickly create a shared album for wedding photos or family trip that your friends or family can add photos or videos to.

How to create shared albums on Google Photos | Technology News - The Indian Express

Google will start applying minimum and maximum attributes for processing time across Shopping ads and free listings.

Google unveils Merchant Center updates to improve delivery times

Google expands its presence in India with a new office in Pune's Koregaon Park Annex, focusing on advanced enterprise cloud technologies. The facility accommodates over 1,300 employees, offering amenities like a well-stocked cafe, game zone, and recreation room. , Pune News, Times Now

Pune Google Office: Watch: Sneak Peek Inside Google's Newly-Opened Pune Office | Pune News, Times Now

Watch the virtual tour video of Google’s Pune office given by a Samsung software engineer. Explore the facilities and amenities available for Google employees in Pune.

Virtual Tour of Google’s Pune Office with Samsung Software Engineer | - Times of India

But this is what happened with a Google employee recently, as revealed by Arvind Srinivas, CEO of the San Francisco-based Perplexity AI startup. In the Big Technology Podcast show, Srinivas told Alex Kantrowitz about his experience hiring a Google employee. Google counteroffered the employee ...

A 4X salary hike offer: Why Google's counteroffer to existing employee is making waves | Zee Business

The initiative, titled Tech Accord to Combat Deceptive Use of AI in 2024 Elections, was announced at the prestigious Munich Security Conference (MSC), where tech giants pledged to tackle the proliferation of harmful AI-generated content that could influence voter opinions

Meta, OpenAI, X, Google, Microsoft to Combat Deceptive AI Content Ahead of 2024 Elections: Will It Work? - News18

The Shark Tank judge criticised them for engaging in unfair trade practices., Technology & Science News, Times Now

East India Company: Shark Tank Judge Anupam Mittal Says Google And Apple Are The New 'East India Company' - Here's why | Technology & Science News, Times Now

The news of Google's generous salary offer comes at a time when Google CEO Sundar Pichai has been vocal about the need for the company to make 'tough choices' to pave the way for future investments. - Google Offers 300% Salary Hike To Stop An Employee From Joining Rival AI Company Headed By ...

Google Offers 300% Salary Hike To Stop An Employee From Joining Rival AI Company Headed By IIT-Madras Alumni

Arsh Goyal, a software engineer working with Google, gave a tour of the company's newly-opened office in Pune. The office is located in the city's Koregaon Park Annexe area.

Software engineer gives tour of Google's new office in Pune. Watch

Google, LLC is an American multinational technology company that specializes in Internet-related services and products, which include online advertising technologies, a search engine, cloud computing, software, and hardware.

Google (Alphabet)

It's been a busy few weeks, with each of the tech behemoths reporting their earnings for the third quarter of the year. Here's a quick recap of the billions each one of them made: -parent saw a whopping 11% year-over-year in its revenue during the three months ended Sept. 30. The tech titan made a profit of $19.69 billion on revenues of $76.69 billion in the preceding quarter, compared to a profit of $13.91 billion on revenues of $69.09 billion in the same period of 2022. Google Alphabet increase The increases were driven by "meaningful growth in Search and YouTube, and momentum in Cloud," Alphabet CFO Ruth Porat said in a statement. too reported an in its revenues and profit for the three months ended Sept. 30. The Windows maker generated $56.52 billion in revenue and $22.29 billion in income last quarter, compared to the $50.12 billion in revenue and $17.56 billion in net income in the same quarter last year. Microsoft increase As with Google, Microsoft attributed a momentum in cloud computing as a catalyst for the increased sales. Meanwhile, over at Mark Zuckerberg's Meta, the Menlo Park, Calif.-based social media giant had an eye popping . The company made $34.15 billion in revenue, up 23% year over year, but the breakthrough was of course, the profit: up more than 2.5x to $11.58 billion from the $4.40 billion a year ago. turnaround story Topping things off, said its net sales increased 13% year over year to $143.1 billion during the most recent quarter while net income was to $9.9 billion from $2.9 billion a year ago. Amazon up Despite raking in billions, each of these companies of people this year in a bid to save cost and even out the lack of growth from the COVID-19 days when their businesses were booming. laid off thousands Google ranked #6 on HackerNoon's Tech Company Rankings this week. Microsoft ranked #8 while Meta was on the #24 spot. ⛲ Amazon, Google's Plan to Beat ChatGPT: Invest in Its Competitor It looks like Google is partnering with Amazon in funding a startup that promises to compete head to head with Microsoft-backed OpenAI's ChatGPT. We are, of course, talking about Anthropic, the San Francisco-based generative AI startup that received an inflow of $1.25 billion from Amazon last month with promises of another cool $2.75 billion. Well, Anthropic is now Google to its list of investors, as the search giant too is investing a cool half a billion dollars in the startup with commitments of up to $1.5 billion in the future. adding The combined $6 billion from Amazon and Google, while nothing to scoff at, is still less than half the $13 billion Microsoft has reportedly into OpenAI ever since it shook hands with the company in 2019. injected What's also interesting is the fact that, as opposed to OpenAI, Anthropic has garnered interest from two major tech giants who compete against each other in the cloud space. It just might seem that companies that are lagging behind in the AI space are trying to play catchup and catch lightning in a bottle, similar to how Microsoft did with its investment in OpenAI. Also, an interesting fact: Anthropic was co-founded by former OpenAI executives and siblings Dario and Daniela Amodei. Exciting times ahead! 👋 You’re reading of HackerNoon's Tech Company News Brief, a weekly collection of tech goodness that combines HackerNoon's proprietary data with internet trends to determine which companies are rising and falling in the public consciousness. went live yesterday. Prefer reading the whole thing a day early AND in one go? No problemo! Just subscribe to receive the newsletter in your inbox every Tuesday. part 2 Part 1 here complete In Other News.. 📰 Resident Evil Village on the iPhone could be a preview of Apple’s gaming future — via . The Verge Google CEO Sundar Pichai to testify in US antitrust trial — via . Reuters Amazon’s Tye Brady discusses generative AI, humanoid robots and mobile manipulation — via . TechCrunch A look back at Elon Musk’s first year owning Twitter, in tweets — via . CNN Fidelity has marked down the value of Twitter/X by 65% — via . Axios Biden unveils U.S. government’s first-ever AI executive order — via . CNBC And that's a wrap! Don't forget to share this newsletter with your family and friends! See y'all next week. PEACE! ☮️ — Sheharyar Khan, Editor, Business Tech @ HackerNoon *All rankings are current as of Monday. To see how the rankings have changed, please visit HackerNoon's page. Tech Company Rankings

The Tech Company News Brief: How Much Money Did Tech Companies Make Last Quarter? 

টেক কোম্পানির সংবাদ সংক্ষিপ্ত: টেক কোম্পানিগুলো গত ত্রৈমাসিকে কত টাকা উপার্জন করেছে?

The Tech Company News Brief: Wie viel Geld haben Technologieunternehmen im letzten Quartal verdient?

Resumen de noticias de The Tech Company: ¿Cuánto dinero ganaron las empresas de tecnología el último trimestre?

The Tech Company News Brief : Combien d’argent les entreprises technologiques ont-elles gagné au dernier trimestre ?

टेक कंपनी समाचार संक्षिप्त: टेक कंपनियों ने पिछली तिमाही में कितना पैसा कमाया?

テクノロジー企業ニュース概要: テクノロジー企業は前四半期にどれくらいの利益を上げましたか?

기술 회사 뉴스 개요: 기술 회사는 지난 분기에 얼마나 많은 돈을 벌었나요?

Resumo das notícias da The Tech Company: Quanto dinheiro as empresas de tecnologia ganharam no último trimestre?

Краткий обзор новостей технологических компаний: сколько денег технологические компании заработали в прошлом квартале?

Tech Company Haber Özeti: Teknoloji Şirketleri Son Çeyrek Ne Kadar Para Kazandı?

Bản tin tóm tắt về công ty công nghệ: Các công ty công nghệ đã kiếm được bao nhiêu tiền trong quý vừa qua?

科技公司新闻简报：科技公司上季度赚了多少钱？

Now that the Threads craze has come and gone and failed to kill Twitter/X/Everything™ like the technology pundits would have you believe, it bears mentioning that Musk is opening up a new front in his war against competitors, now also targeting Microsoft-backed OpenAI, the creator of ChatGPT. Musk's everything app ambition is kinda like his wish to be anywhere and everywhere (sometimes quite literally), so it shouldn't surprise anyone that the billionaire entrepreneur also wants a piece of the artificial intelligence pie. Just recently, the world's richest man the launch of an AI startup called xAI. announced Long-time readers may have noticed that xAI sounds a lot different than the "TruthGPT" Musk had said he was naming his AI startup all the way back in April but the Tesla owner is uh.. Weirdly with the alphabet "X" so just roll with it. obsessed Musk's foray into AI is both a business decision and a way to get even with OpenAI, which he co founded and then left years ago over "differences" in the direction the startup was headed. Musk even went as far as to on OpenAI earlier this year for an immediate pause of at least 6 months in the training of AI systems more powerful than GPT-4. call "The goal of xAI is to understand the true nature of the universe," the company's states, adding that xAI will work closely with X (Twitter), Tesla, and other companies to make progress towards its mission. website ranked #16 on HackerNoon's this week while was on the #97 spot. Microsoft Tech Company Rankings Tesla 🤖 Make AI Safe Again Tech heavyweights including -parent and creator are to make artificial intelligence safe. Joining them are , , OpenAI (of course), and a host of other tech companies who have committed to watermarking AI-generated content in a bid to make the technology safer. Google Alphabet Facebook Meta banding together Microsoft Amazon Exactly how and where the watermark will appear is unclear, but the idea is to embed it within content so users can easily spot deep-fake images or audios, Reuters reported. AI safety has taken center stage ever since the release of ChatGPT, with world governments consulting companies developing the technology to develop guard rails lest the robots take over. As major governments develop AI regulation, tech companies have begun self regulation. In fact, OpenAI has already to "steer and control AI systems much smarter than us" and prevent it from going rogue. created a new research team The U.S., which reportedly lags behind the EU in tackling artificial intelligence regulation, is looking to develop bipartisan legislation on AI technology under President Joe Biden who has been meeting with AI companies for consultations. Facebook ranked #3 on HackerNoon's this week while Amazon was on the #37 spot. Tech Company Rankings 👋 You’re reading of HackerNoon's Tech Company News Brief, a weekly collection of tech goodness that combines HackerNoon's proprietary data with internet trends to determine which companies are rising and falling in the public consciousness. went live yesterday. Prefer reading the whole thing a day early AND in one go? No problemo! Just subscribe to receive the newsletter in your inbox every Tuesday. part 2 Part 1 here complete In Other News.. 📰 OpenAI's Sam Altman launches Worldcoin crypto project — via . Reuters It’s Spotify’s turn to increase prices — via . The Verge Threads has lured some creators who never loved Twitter — now Meta has to keep them— via . CNBC With the rise of AI, social media platforms could face a perfect storm of misinformation in 2024 — via . CNN Twitter co-founder Jack Dorsey urges ‘calm’ after Elon Musk eliminates the last traces of his original company — via . Fortune Leaders, experts offer artificial intelligence advice for real people — via . Axios And that's a wrap! Don't forget to share this newsletter with your family and friends! See y'all next week. PEACE! ☮️ — Sheharyar Khan, Editor, Business Tech @ HackerNoon

Elon Musk Sets His Sights on a Different Competitor 

এলন মাস্ক একটি ভিন্ন প্রতিযোগীর উপর তার দৃষ্টি স্থাপন করে

Elon Musk hat einen anderen Konkurrenten im Visier

Elon Musk pone su mirada en un competidor diferente

Elon Musk jette son dévolu sur un autre concurrent

एलोन मस्क एक अलग प्रतियोगी पर अपनी नजरें गड़ाए हुए हैं

イーロン・マスク氏、別の競合他社に目を向ける

Elon Musk는 다른 경쟁자를 겨냥합니다.

Elon Musk está de olho em um concorrente diferente

Elon Musk gözünü farklı bir rakibe dikti

Elon Musk đặt mục tiêu của mình vào một đối thủ cạnh tranh khác

埃隆·马斯克将目光投向了不同的竞争对手

There are plenty of articles and reviews of companies that talk about companies where everyone would like to work. But giving so much attention to the companies that have the best reputations, the best employee benefits, and the most positive reviews, I thought maybe companies on the other end of this specter also deserve some of your attention. After all, there are companies you want to join and there are ones you , right? would prefer not to So today I am going to talk about tech companies that are most famous for being hated by many people and having a bad reputation. Most hated tech giants Seems like you can’t avoid talking about the American tech giants no matter if it’s an article about the best employers in tech or about the worst ones. As you may know, many people tend to hate or dislike the American tech behemoths, each member of the Big Five list, which is Alphabet, Apple, Amazon, Facebook, and Microsoft (with Netflix lately often being considered as a new member of this club). So it should come as no surprise that each member of the ‘Big Five’ would have made it to the top of tech companies with the worst reputations. The only question that is left is: who would be the winner? If I had to make a top 5 list of the most hated American tech giants, here is how I would place them. No 5 - Microsoft Let’s be honest, the software giant never had such a spotless reputation. For years and decades, Microsoft is hated by many people around the world for various reasons: launching low-quality, unfinished, and just plain defective products to the market , acquiring and slowly murdering previously great products , willingness to collaborate with authoritarian regimes (Microsoft’s research branch in China on three A.I. research papers for the military. The research topics included facial recognition, which could help the Chinese government monitor and oppress its citizens), and loads of other things. (hi, Windows Vista) (hi, Skype) had worked But, being objective here, I have to say that in recent years Microsoft’s reputation has been more on the improving side. As Mark Hurst, tech journalist and author, , lately Microsoft makes a lot of effort to present itself as “the kinder, friendlier, Big Tech giant.” It’s not like they manage to fool anybody, but among other tech behemoths, these days Microsoft probably is the least hated one. Good job, software giant! said No 4 - Amazon Today Amazon is an undisputed leader in North America’s online retail, but the company is also doing business in resale, meal delivery, cloud computing, video streaming, and a number of other niches all around retail and tech. So it should come as no surprise that in the U.S., Amazon can easily compete for the crown of the most hated tech giant. Jeff Bezos’s company is widely criticized for its ‘last mile’ shipping operations, leading to multiple burnouts, among its employees, who are mostly working for a minimum wage. Not only that, Amazon is also heavily criticized for paying to the U.S. federal budget and looking for even more tax breaks when conducting a very public search for a second headquarters. But since Amazon is hated mostly just in North America, 4th place only. injuries, and deaths little to no income taxes No 3 - Facebook Facebook, on the other hand, in recent years has been actively gaining weight, so to speak, as one of the most hated tech giants globally. Mostly Facebook is being criticized for how it handles user data, as well as fake news, hate speech, and all kinds of political content. All kinds of data breaches and privacy scandals have also affected Mark Zuckerberg’s reputation. In the public consciousness, the founder of Facebook has turned from a charming robot-like nerd who accidentally created the world’s most popular social network while trying to get laid in college into just another tech billionaire, whose main concern is profits above anything else. This puts Facebook in the 3d spot in our little top. No 2 - Google/Alphabet The ultimate Internet giant, Google its famous ‘Don’t Be Evil’ slogan in 2015, and they did it for a good reason. From an innovative company trying to make the world a little bit better, Google became just another giant corporation, fighting for market dominance and focused on increasing revenue at any cost. eloquently dropped In recent years Google/Alphabet went through a number of scandals, from its employees Google working on Pentagon’s drone AI program and , to internal dissent and discussion at its famous TGIF all-company meeting. protesting against censoring Chinese search engine shutting down No 1 - Apple But when it comes to the most hated tech company in the world, Apple is definitely the champion. The American consumer electronics maker is hated (as well as loved, let’s acknowledge that) all around the world for a long time and passionately, especially since the beginning of the iPhone era. There are so many reasons to hate Apple that describing everything would take the whole article, maybe not even one. Here are just a few major reasons I decided to give Apple the top spot: leveraging cheap labor in China and relying on third-party Chinese contractors with the worst reputations, such as Foxconn (this company has a whole devoted to the epidemic of suicides among its employees exclusively), very active “ ”, consistently decreasing quality of their products, overinflated end-product prices, and, of course, all American tech giants’ favorite gig: to spy on its citizens. Money definitely doesn't stink for companies like Apple. Wikipedia page patent bullying helping authoritarian governments Other tech companies with the worst reputation There are more than enough well-hated tech companies with questionable reputations besides the Big Five, of course. They can be infamous for numerous reasons, such as toxic corporate culture, controversial business models, active political participation, abusing employees, and other nasty stuff. Having so many different criteria to judge upon makes it almost impossible to make a more or less objective rating, so here’s just a number of companies that in our opinion deserve to make it to such a list. Oracle Oracle, current Java’s happy parent (Oracle in 2010), gets quite a lot of criticism over its copyright policies and employee treatment. The biggest reputation-crashing scandal for Oracle is the copyright battle against Google when for infringing copyright in the Java API. According to Cory Doctorow, a famous tech journalist, “Oracle’s mission to copyright APIs is a terrifying example of the worst kind of tech issue: something totally boring and esoteric and simultaneously incredibly important.” Well-said. acquired Java Oracle sued Google Right now Oracle is going through its biggest round of layoffs in over ten years, which is another major factor damaging this company’s reputation. “Oracle is now a next-gen cloud company and everyone in sales who is not cloud savvy will no longer have a job,” according to the . reports Salesforce Salesforce is mostly being chastised for its extremely demanding and harsh corporate culture. Here’s one anonymous employee review of the company: “Working here is like being in a cult. You are expected to dedicate your life to the cause 24-7, on weekends and vacations. People swear and shout all the time because of stress and frustration. Age discrimination abounds with seasoned professionals being passed over for promotions in favor of younger millennials.” IBM IBM is a company that should definitely get a spot in any list of the worst tech businesses in the world just for infamously supplying punch card technology to nazis and enthusiastically helping them to . A lot of time passed since then, but IBM didn’t get any better. Awful treatment of employees, users' private data, , and significant strategic focus on tax evasion: IBM is a deeply toxic company that seems to be getting even worse. organize and facilitate the Holocaust secretly stealing constant layoffs Uber The world’s largest taxi-hailing app is also not without sin, to say the least. Over its rather brief history (the company was founded in 2009) Uber has been accused of lots of things: secretly and breaching privacy rules, toxic , creating an extremely unfair business model where Uber , and a number of other things. stealing personal data corporate bro-culture treats non-employee workers like customers “It’s hard to think of a company that has shown more disdain for governmental authority, or for the safety and welfare of its drivers, riders, and employees,”  said Lindsey Barrett, a professor from Georgetown University Law Center. Tencent / Baidu And for the final one, I probably should mention Tencent and Baidu as two giants of the Chinese Internet. Baidu, the biggest in China search engine, works basically as a censorship tool directly in line with the Communist Party of China’s policies. Tencent is the owner of WeChat, China’s most popular messaging app (has more than ), and it does pretty much the same thing: censoring its content and fully collaborating with the communist government of China in terms of sharing its user’s data. 1.25 billion monthly users Also published here .

World’s Worst Tech Employers

Artificial intelligence is truly turning out to be a tale of two cities. With the launch, and , of OpenAI's , the world has split into two distinct camps: on one hand, you have the "doomsday bros" who fear the rise of the machines and are warning of an impending end (or at the very least, replacement) of the human species as we know it. On the other hand, we have the "wield-it bros" who are heralding the launch of AI as the next industrial revolution and seek to benefit and profit off of it. subsequent success ChatGPT As the world at large with the implications of artificial intelligence, the person responsible for giving birth to AI as we know it is sounding the alarm, calling the rise of machines a more urgent threat to the world than climate change. grapples Geoffrey Hinton, widely known as one of the "godfathers of AI", is the co-author of a seminal paper that represented a milestone in the development of the neural networks undergirding AI technology. He recently quit -parent to espouse the threat posed by AI, perhaps because he knew the would befall him as the senior software engineer who claimed Google’s artificial intelligence chatbot LaMDA was a self-aware person. Google Alphabet same fate Free from his employer's grips, Hinton has been sharing his thoughts, unfiltered, to the media at large, and recently Reuters that the AI threat "might end up being more urgent" than climate change. told "With climate change, it's very easy to recommend what you should do: you just stop burning carbon. If you do that, eventually things will be okay. For this it's not at all clear what you should do," Hinton said. Suffice to say, Hinton is part of the "doomsday bros" group, which includes the . While it is easy to shrug Musk's comments about AI, particularly considering that he's developing his , the same cannot be said about Hinton who rubbished an open letter signed by thousands, including Musk, to of systems more powerful than OpenAI's recently-launched GPT-4. likes of Elon Musk own generative AI model temporarily pause development “It’s utterly unrealistic,” he said. “I'm in the camp that thinks this is an existential risk, and it’s close enough that we ought to be working very hard right now, and putting a lot of resources into figuring out what we can do about it.” Hinton's comments come just days after the CEOs of Google, , and OpenAI with the Biden administration to chart a path forward for AI. Ironically, the White House has tasked the companies themselves to "ensure the safety and security of their products", as if self-regulation is going to work. Nonetheless, the administration warned the companies that it would be open to new regulations and legislation to cover artificial intelligence. Microsoft met AI has been a for Microsoft. The company reaped billions more in profit during the first quarter of the year thanks to its deep partnership with OpenAI, which let it roll out generative AI capabilities across its suite of products soon after ChatGPT became public. Those capabilities made Microsoft's products more attractive to enterprise customers, who are always a sucker for streamlining and automating their processes. boon On the other hand, AI has been a for Google, which is so terrified by the rise of ChatGPT that it fears its entire existence may be under threat. The fact that Google is lagging behind Microsoft has for both the company and its CEO Sundar Pichai. curse spelled disaster Meanwhile, the likes of and are trying to on the potential of AI, offering services powered by their own takes on generative AI models to reap some of that sweet . All of this must be quite horrifying to Hinton, who has already said he regrets his life's work Amazon Meta cash in AI profit “I console myself with the normal excuse: If I hadn’t done it, somebody else would have,” Hinton said during a with . lengthy interview The New York Times Perhaps, to Hinton, it's a race to the bottom to see who gets to destroy humanity first. Microsoft ranked #67 on HackerNoon's this week. Google was #4; Meta was #23; and Amazon was #70. Tech Company Rankings 👋 You’re reading of HackerNoon's Tech Company News Brief, a weekly collection of tech goodness that combines HackerNoon's proprietary data with internet trends to determine which companies are rising and falling in the public consciousness. goes live tomorrow. Hate waiting? No problemo! Just subscribe to receive the newsletter a day early in your inbox. part 1 Part 2 here complete In Other News.. 📰 as many Switch as it used to. Sales of the company's wildly successful console were down 22.1% in the year ended March 31st. The company ranked #84 on HackerNoon's Tech Company Rankings this week. Nintendo isn't selling AI can now create music! has removed tens of thousands of songs that it believed were generated using AI. The has more to do with copyright more so than the fact that the songs were created using machines. Spotify removal : the amount is paying to feature its content. $100 million Google The New York Times Airbnb will now let users single rooms. rent out Utah now requires users to before visiting adult websites. verify their age LinkedIn more than 700 jobs as part of its decision to leave China. cut And that's a wrap! Don't forget to share this newsletter with your family and friends! See y'all next week. PEACE! ☮️ — Sheharyar Khan, Editor, Business Tech @ HackerNoon Featured image generated using Kadinsky 2 with the following prompt(s): humanoid machines, wielding weapons, fighting, terminator 2, planet earth, climate change

AI Is a More Urgent Threat to the World Than Climate Change 🌡️

AI হল জলবায়ু পরিবর্তনের চেয়ে বিশ্বের জন্য আরও জরুরি হুমকি 🌡️

KI ist eine dringendere Bedrohung für die Welt als der Klimawandel 🌡️

AI는 기후 변화보다 세계에 더 긴급한 위협입니다 🌡️

Yapay Zeka Dünya İçin İklim Değişikliğinden Daha Acil Bir Tehdit 🌡️

Investing is a good way to set aside money that will work for you while you go about your daily business. Basically, the goal of investing is to make your money work in one or more types of investment instruments with the hope of it growing over time. Now choosing which stock to invest in is a question every beginner should be asking. So, to make it easier for you, we did some research on the best stocks to buy in 2022. Here in this article, we will present the top 10 best stocks beginners should be looking to buy now. But before that, let’s share with you 4 tips that stock trading beginners should know about. 4 Tips for Stock Trading Beginners Should Know About Finding the best stock trading website for beginners or best brokers for beginners is quite a task, especially when you are just starting out. We suggest making it a habit of following these 4 tips: 1. Choosing the Right Broker Before starting to choose an online broker, you will need to answer a few questions about your investing goals, i.e. what are your investment goals. Only after you know what types of investments you are interested in, you can proceed to evaluate brokers by based on several factors, including: broker reviews Commissions - You should take a look at commissions and what investment options brokers offer. Some of the brokers will offer access to cryptocurrencies, futures, and options trading. Reliability - You should always choose to work with a reliable broker, i.e. the broker has to be regulated.  So make sure your broker is properly licensed and regulated. The security of your deposit is always a top priority. Account minimum - For many mutual funds even if you can open a brokerage account with a small amount of money, you may find it difficult to invest it. Account fees - Most brokers are charging a fee for transferring out investments or cash, or for closing an account. Tools, education, and features - If you are a beginner in investing, you should look at a brokerage company that offers free educational resources, such as live webinars, detailed how-tos, video tutorials, glossaries, and more. Be sure to find out how well the broker supports their clients by helping them understand the risks associated with such strategies. This could mean guidance from the customer support team on duty, a live chat feature, or clear and detailed instructions on how to use these investment products responsibly. Promotions - To entice new customers, online brokers run promotions, such as a cash bonus on certain deposit amounts. It isn’t wise to choose a broker solely on its promotions, but if you’re stuck between two options, a promotion may sway you one way or the other. 2. Don’t Skip The Learning Curve Never stop learning. Check out online webinars, read educational articles, research new , and watch video lessons. trading strategies 3. Learn to Control Your Emotions Emotional traders find it difficult to adhere to trading rules and strategies. Overly stubborn traders may not get out of losing trades fast enough because they expect the market to turn in their favor. When a trader realizes his mistake, he should leave the market with the least possible loss. Waiting too long can result in a significant loss of capital. After exiting a trade, traders should be patient and re-enter the market when the opportunity arises. 4. Have a Trading Plan The main reason you need to develop your own trading plan template is to be able to replicate our good trades. The trading plan should include all the necessary trading rules: Consider the preferred time frame you wish to trade. It comes down to the commitment to work and personal preference. Do you want to trade in the direction of the trend, i.e. a trend following strategy, or do you want to be a countertrend trader and trade reversal patterns? It would help to look for an entry signal. You can use price action, support and resistance, indicators, or a combination of those. Consider your risk management strategy and your position size per trade. We recommend a maximum risk of 1% or 2% of the total account value per trade. When you are just starting out and learning a new trading system, do you trade much lower than this one? The Best Stocks You Should Consider Buying Right Now One of the most time-intensive aspects of investing is finding the best stocks to buy that fit your investment strategy. After all, there are a huge number of different stocks to choose from. With so many choices, finding the answer to "what is the best stock to buy” is tough. The list below outlines the top stocks to buy this month. 1. Amazon Amazon (AMZN) stock is currently trading near 3133.94, but with a share split that will take place in June or so, and the split kicks in, the share price will drop, some predict, around $166. the goal is to make its shares more accessible for retail traders. It also gives employees more flexibility in how they manage their equity. Amazon has said Share split might be a signal of the company’s intentions for the future. For example, it could expand the shareholder base to reduce other shareholders' influence, which can be beneficial for, as mentioned earlier, retail traders, who buy shares while the price is relatively low. Overall, Amazon has done well during the pandemic, and the company is one of a handful with over a $1 trillion valuation. That swell already had many investors wondering whether they should buy Amazon stock, so with the company's announcement of a 20-for-1 stock split, the interest picked up. 2. Google Alphabet’s Google controls nearly 92% of the online search market share. That's a one. Google search is not the only place where Alphabet makes money from advertising. Alphabet controls over 31% of all online advertising by revenue and is the world's largest online advertising network, . according to Statista Alphabet has had a stellar run over the past year. However, early 2022 declines have brought the stock to a more reasonable valuation, setting the stage for a strong rebound ahead. It's a good time to invest. 3. Disney The pandemic really hurt Disney's theme parks and movie business but helped their streaming service, Disney+, which has grown into a powerhouse a few years earlier than Disney expected. In 2022, the demand for Disney theme parks and movies will rise again like never before. Disney+ is focused on expanding its platform. In fact, Disney could be the perfect combination of a re-opening game and a booming business fueled by the pandemic. The amazing stability makes it arguably the safest stock on this list. However, it has huge growth potential as it develops new lines of business. 4. Apple With a market capitalization of over $2.6 trillion, the tech giant is one of the largest companies in the world and is the largest company listed on the Dow Jones Industrial Average. Apple's revenue and earnings growth remain strong, and it is these numbers that underlie the highly favorable opinion of analysts about the stock. Of the 27 analysts covering AAPL stock, 22 recommend it as a buy, four as a hold, and one as a sell, with an average target price of $181.40 per share, representing more than 12% upside potential, according to TipRanks. Despite the recent volatility, the stock is currently trading at a relatively high valuation compared to the industry average. However, similar to the other big tech companies on this list, the high equity-related valuation is offset by strong revenue and earnings growth that many believe will continue for the foreseeable future. 5. Netflix There are many competitors in the field, but it's hard to bet against a first mover, especially with a long history of investing in content, technology, and marketing strategies that have paid off. The current slowdown in subscriber numbers is likely nothing more than a bump in the road, though it's worth noting that Netflix may not be able to achieve a sharp increase in subscribers again. Perhaps further declines are ahead. This is probably why many analysts have abandoned their optimistic views on the stock. However, the average price target is overwhelmingly bullish at $521.04, representing more than 40% upside potential. Netflix is ​​a great investment for the right investor. While there is a risk that the company will not be able to stem the growth in subscribers, if it does, the stock could rise significantly. So if you have a strong appetite for risk and believe in the pioneer of streaming entertainment, it's time to take the plunge. Whether you are looking to invest in the stock market for the first time or looking to balance your portfolio to take advantage of the hottest trends on Wall Street, the stocks we listed above are worth your consideration.

Top 5 Stocks For Beginners To Buy in 2022

While many have analyzed the Facebook move into the “Metaverse” more from a corporate political standpoint, here we’ll look at another key aspect for long-term survival and thrive: When Facebook announced Meta, the company highlighted: Distribution! "The metaverse will feel like a hybrid of today’s online social experiences, sometimes expanded into three dimensions or projected into the physical world. It will let you share immersive experiences with other people even when you can’t be together — and do things together you couldn’t do in the physical world." All nice words, but what does that mean? Understanding the attention merchant business model Facebook, together with Google, is the most profitable attention merchant. The company has emulated successfully the Google advertising machine. The most powerful money-making machine ever created on the Internet. Yet with a couple of slight differences in their business models. First, Facebook’s ads are pushed to the users via targeting, wherein in Google’s case these ads are pushed based on contextual search. This, if at all, is an advantage to Facebook, which growth potential is even greater than Google. In fact, Google has been trying to emulate that unsuccessfully in the last decade. The power of the Facebook advertising machine stands in the fact that it can be easily adopted by the masses. You don’t have to be a nerd to use Facebook Ads. Quite the opposite. While to understand Google Ads, you need to understand the nuances of search, algorithm scoring. And most of all how search intent works. In an asymmetric business model, the organization doesn’t monetize the user directly, but it leverages the data users provide coupled with technology, thus having a key customer pay to sustain the core asset. For example, Google makes money by leveraging users’ data, combined with its algorithms sold to advertisers for visibility. This is how attention merchants make monetize their business models. Second, where Google’s distribution passes through ownership of hardware (Google manufactures the Pixel), browser (Google owns Chrome), mobile operating system (Google runs Android), and search. Thus, Google (Alphabet) is way more vertically integrated. What does that imply? We need to look at the digital supply chain. In business, vertical integration means a whole supply chain of the company is controlled and owned by the organization. Thus, making it possible to control each step through customers. in the digital world, vertical integration happens when a company can control the primary access points to acquire data from consumers. The interesting part is that a supply chain where the raw materials are data gets flipped upside down compared to a traditional/physical supply chain. In a data supply chain the closer the data to the customer the more we’re moving downstream. For instance, when Google produced its own physical devices. While it moved upstream the physical supply chain (it became a manufacturer) it moved downstream the data supply chain as it got closer to consumers using those devices, so it could gather data directly from the market, without intermediaries. In fact, in a data supply chain, the hardware component is also a data harvesting tool, as it usually runs a closed operating system controlled by the same company together with a hybrid marketplace (closed in terms of rules who are defined centrally by the organization, and open in terms of developers that can participate in creating applications on top of the marketplace). Therefore, where Google has tight control over the supply chain, both on desktop and mobile. Facebook’s distribution is primarily based on strong brand names. With the acquisitions of Instagram, WhatsApp, and Oculus, Facebook has kept a strong distribution, yet primarily based on the strength of these brands. This leads to the next point. Metaverse and market expansion theory The market expansion consists in providing a product or service to a broader portion of an existing market or perhaps expanding that market. Or yet, market expansions can be about creating a whole new market. At each step, as a result, a company scales together with the market covered. A market expansion usually consists of building new markets, out of existing ones. These new markets use the previous as a foundation, yet they develop their own logic. And are prone to wider mass adoption. And in turn, the business people operating there will need to master a whole new business playbook. Why does it matter here? Well, because the Metaverse would give Facebook both the defense to keep its distribution strong; and an attack to build a wider market than mobile. To do that though, it will need to create a business ecosystem and what I like to call a “ business platform” which is something different from a technical platform: A business platform like in the example above is the combination of hardware, and software, combined with a developer’s and entrepreneurial ecosystem. It’s a hybrid model of closed and open. Thus, from here we can really really explain the swift move that Facebook made into the Metaverse. Blitzscaling into the Metaverse We can argue that Mark Zuckerberg’s Meta is in a . In short, he’s both trying to defend its business model, and attack the market, by creating a whole new industry, potentially bigger than mobile, as explained above. In fact, Apple’s changes in privacy are affecting badly all the main mobile advertising players. The ones that will survive in the long-term are those who have their own physical and distribution pipeline. And Facebook is not among those! Blitzscaling mode By June 2021, Apple announced all its changes to the UI to enhance privacy. The new Apple’s privacy control panel (Source: Apple) As Craig Federighi, Apple’s senior vice president of Software Engineering : announced "Privacy has been central to our work at Apple from the very beginning, every year, we push ourselves to develop new technology to help users take more control of their data and make informed decisions about whom they share it with. This year’s updates include innovative features that give users deeper insights and more granular control than ever before." The App Privacy Report (Source: Apple) This move by Apple already started to erode the digital advertising industry. And it’s hitting the most, those players that do not have control over the supply chain of data. Among them, Snapchat. As Evan Spiegel, Snapchat’s CEO explained: Our advertising business was disrupted by changes to iOS ad tracking that were broadly rolled out by Apple in June and July,” CEO Evan Spiegel said during a call with analysts. “While we anticipated some degree of business disruption, the new Apple provided measurement solution did not scale as we had expected, making it more difficult for our advertising partners to measure and manage their ad campaigns for iOS. Players like Facebook and Snapchat, therefore, are the most involved and those who need to move fast into the metaverse! Zuckerberg’s Bill Gates moment? As we saw, unless Facebook, now Meta succeeds in building up the Metaverse it might really face a survival threat in the coming years. In fact, while many look at this moment for Marck Zuckerberg, like the Bill Gates moment, there is a huge difference. For a bit of context in 1995 Bill Gates realized the importance of the Internet, thus moving the whole company in the direction of what he called the “Information Superhighway.” However, the “Information Superhighway” was a term used by “ business intellectuals” to describe more interactive TV on the web. Rather, the web how it really evolved. Therefore, it was more like a linear projection of the future. However, native and much simpler, bottom-up applications turned out to be the killer apps of the web: browsing and searching. As Bill Gates realized that, Microsoft turned to its distribution strenght to take over the browser market, dominated by Netscape. In fact, the initial version of Internal Explorer (a knock-off of Netscape) took immediately traction, as it was bundled together with Microsoft office, and therefore a no-brainer for most PC users. Yet, this was a clear abuse of dominating position, which attracted the attention of the antitrust, and it led Bill Gates to sit for hours and hours in a courtroom, toasted by antitrust lawyers. This was 1998. And Bill Gates, eventually drained by the antitrust. Slowly passed the reins (we don’t really know what happened in the backstage, and it might be possible that Bill Gates had to leave as CEO to prevent Microsoft to be broken up) to Steve Ballmer. A slowed, threatened Microsfot eventually lost the browser war, the search war, and the social media war. And yet, it survived all this, thanks to its distribution advantage (if you run a startup, you might be surprised to figure that many large corporations still run Microsoft Office). And eventually, what won was not the top-down, linear model where you pour billions and bring the TV online. On the opposite side, the content of web 1.0 (1995-the 2000s) was much more amateurish, yet it was not centrally controlled, which made it way more appealing. Only much much later on, as Internet speed, and other complementary tech picked up, players like Netflix fully transitioned to streaming (around 2007), thus proving the viability of what Bill Gates had in mind. And also then, the format was not the same as TV. The content model and formats had completely changed, and the “Hollywood Model” didn’t longer apply. This was particularly clear, when Kevin Spacey, Speaking at the Edinburgh Television Festival urged the industry to nurture talent and give audiences: “what they want, when they want it.” And Kevin Spacey continued: “If they want to binge then we should let them binge.” He stressed how the media industry could learn from the unlearned lesson from the music industry as it tried to resist the unstoppable rise of the web: “Give people what they want, when they want it, in the form they want it in, at a reasonable price, and they’ll more likely pay for it rather than steal it.” To sum up, the most important lesson here is that we completely lack imagination when it comes to reinventing the future (and we can argue the more “business experts” we are the more we lack it) and that we apply to the future a linear innovation model. Where you take the future tech and without imagination, we stuck the old tech on top of it. Therefore, in the case of the Information Highway, here the TV was supposed to be brought online. Instead, the bottom-up model saw the first real web players (Google going forward) take over. In fact, the first Internet players like AOL were still managed as walled gardens with a centralized and controlled user experience and a subscription-based monetization model. The new web players instead succeeded because they enabled billion of users to generate amateurish content in a messy way (which over time evolved into pro content, yet a completely different format than TV – see Netflix). There is a huge difference, therefore, between Facebook of today and Microsoft of the time. Microsoft in 1995, while running after the Internet, already owned and controlled the distribution (Microsoft today is among the most valuable companies on earth, still thanks to its distribution advantage). Facebook today does not own the distribution or the billions of hardware consumer devices coupled with an operating system, and a marketplace, which instead other tech giants do have. The only parallel we can make here is that today like then, we’re using a buzz term like Metaverse, to describe the future. And players like Facebook are trying to design a whole ecosystem top-down, by pouring in billions of dollars. And Facebook today, like Microsoft back then (Microsoft invested $1 billion back then to ramp up the Information Highway) is investing over $10 billion into the Metaverse (some might argue cynically and they might be also right that Facebook is doing these investments to clean its brand from all the scandals of the last years appealing to the EU with a massive cash infusion, as a “lobbying investment”). This leads us to the Metaverse, which is the survival escape for Facebook. Inside the Metaverse Supply Chain Let’s now try to answer on how the Metaverse supply chain might look like. As reported by uploadvr.com, Facebook CEO Mark Zuckerberg and VP AR/VR Andrew Bosworth on Instagram, in which they explained: hosted a live Ask-Me-Anything session "These new platforms are so different from everything that’s come before it – not just the input, but the app model, how you’re going to discover things, how tightly they need to be optimized. If you’re building a pair of glasses that need to look like normal glasses, you need to have the system be so tightly optimized so you can basically do all the computation that you would expect from a modern computer, but do it on someone’s face within a thermal envelope and a power envelope that can last all day long. So that’s a very big challenge." The team is pretty far along in this, at this point. We’re building a microkernel-based operating system, which is the architecture that you want to segment the pieces to make it as secure as possible. That way you have a small [set] of pieces that you know are going to be fundamentally trustworthy that you can build on top of. But at the end of the day, we need to basically be able to and customize every layer of the stack in order to build out the performance and efficiency that we need in order to deliver these systems.” design And they highlighted how the company is building a “reality operating system.” Andrew Bosworth, transitioning as CTO of Meta will play a key role in this development. However, as Andrew Bosworth also highlighted in an interview for : The Verge "There’s lots of things that you can do in the metaverse by yourself as experiences and that’s going to be great. But a lot of it is going to be quite new because I think the metaverse is largely a synchronous experience. You’re there with people in real time having an experience in real time. There’s something meaningful about it." This is a key point, as it highlights what makes the whole Metaverse different. And questioned about how crypto and NFTs fit into the puzzle he highlighted: When you think about interoperability, entitlements, as we would call it in the game industry, is an important concept. Like who owns this thing and what rights do they have to it? Can they make copies of it? Can they sell it? Can they take it with them into every single location? What locations can they take it into? And that’s not hard to do with the database if the entire metaverse is controlled by one company, which we don’t want it to be. And we don’t think it can be. It’s not necessarily hard to do with a database if we have a really good standardized schema and you can pick which database it’s in and it goes here and there and everyone kind of has access to that. But another way to do it, that could be really strong, is NFTs and crypto, where you’ve got the ledger. Therefore, the blockchain might work as a decentralized ledger for goods that exist in the Metaverse. And: Instead of having to store it in a database somewhere, which has its own downsides, you store it in the blockchain. Let me describe how this chain might look like, from the bottom up: Data Layer : the raw data might consist of the universe of things that metaverse users will do within the virtual environment, plus all the actions performed and items/virtual spaces they own. Raw data that data need to be portable. So that users can transfer it anywhere in the metaverse/parallel metaverses. As this data might represent the whole digital identity of the user it’s critical that this is also transferable to the blockchain, so that it can be controlled by the user. Portable data: : while the Metaverse company might have the right to use the data for advertising purposes. An advertising marketplace will have to reward users for the data used and also enable them opt-in mechanisms for how this data is getting used in the advertising process. Owned data : the Metaverse might also bring data from the real world into the digital world through AR and make it interoperable. Mixed data Operating Layer Initially, as a viable option, a minimal operating system integrating all the pieces of a virtual and mixed experience will need to be highly optimized to track the user movements and the interactions across the digital worlds. Applications Layer In the application layer, the development ecosystem will be able to build worlds and things that can be done by users in each digital environment. Ownership Layer The ownership layer might be a mixture of data marketplace combined with blockchain. So that it can be controlled, it must be portable and it can be tokenized, to be reused in many other ways. So that the digital identity is not tied to a single platform, but it can be reused across the Metaverse. Key takeaways Rather than looking at Facebook’s move into the Metaverse from just a rebranding standpoint, this is a distribution move. And a move to guarantee the survival of the company. The swift move by Apple’s new privacy policy is accelerating the investments in AR/VR as a few tech companies (Facebook and Snapchat primarily) might face survival threats in the comings years. This, in turn, might lead to a forced development of the “Metaverse” and the reshaping of the whole tech industry’s landscape. A Metaverse might be much more of what was envisioned by Facebook, to comprise an additional layer of ownership through blockchain technologies, to enable ownership to be distributed, decentralized, portable, and controlled by each user. Graphics Copyright: FourWeekMBA

As Facebook and Apple Battle for User Identity, The Metaverse Supply Chain Grows

When thinking of AI (artificial intelligence), mixed emotions often come to mind. For movie buffs, we might immediately see images of Will Smith battling it out with humanoid AI creatures in IRobot or the even more realistic looking depiction of artificial intelligence in the movie aptly called AI. In our human minds, AI is something that could potentially lead to a catastrophic apocalypse as machines take over the world. This is not just hearsay as with some things. According to a , 2,000 Americans were asked what they thought the potential impact of machines learning for themselves would have on life as we know it. 34% claimed it could be harmful, while 12% pointed to the possibility of complete human extinction. Truth be told, computer systems and AI have become a significant part of our lives without most people actually realizing it. Companies the world over use AI in their everyday practices and here are just a few examples. recent study about AI and marketing Image courtesy of Statista.com Amazon We all know it, and most of us have used Amazon at some point in our lives. This powerhouse company has utilized AI for many years with the introduction of Alexa, but AI is not limited to this helpful little device. Amazon seems to know what we are thinking even before we choose to look something up. It’s not a magic trick, but AI programs using . Amazon is tracking what you look at to help predict what products may be beneficial to you in the future. Predictive Analytics Amazon has reached a bit further with this concept through —the no lines or checkout convenience store concept is remarkable as the user simply fills up their bags while walking through the store. The customer is charged via the app and cameras throughout the store track other items you may pick up and then put down continually monitoring what you like and logging that data for future store visits. Amazon Go Alibaba Where Amazon is more prevalent in some parts of the world, China-based Alibaba is actually much larger. It currently sells more products than eBay and Amazon combined and they too do much more than work to predict what customers might buy in the future. Their format, known as , is being used to help alleviate traffic jams by monitoring each vehicle within smaller cities. Alibaba Cloud is another project from the company designed to help farmers monitor field yields and improve their cost-cutting measures throughout their operation. City Brain Project Facebook Facebook is a social media giant, but due to backlash from countless and other problems within their self-post system, the company has had to put efforts into helping keep these posts from ever reaching the internet. When posting pictures on Facebook, Deep Text is employed to analyze the photo immediately to determine if it is appropriate. It utilizes face recognition that is highly advanced to catch and remove any image that is deemed a violation of their terms and conditions. revenge porn posts Apple One of the most significant users of AI in the world is, you got it, Apple. The iPhone is the leading smartphone device on the market ( .) and with each passing year, it gets a bit more advanced. Current iPhones use FaceID to ensure a user who is accessing the device is the actual owner. In addition, Siri is a part of every Airpod, Apple Watch, and HomePod product you purchase. In Q3 2019, 13 percent of all worldwide smartphone sales were an Apple iPhone Baidu The Chinese version of Google has a that is remarkably adaptable and can learn voices with just 3.7 seconds of audio played. This tool is used for reading books in which the author’s voice is cloned and used to provide a more authentic read. Deep Voice tool IBM This company has been using IA for decades with the first computer, Deep Blue, to beat out a world chess champion over 20 years ago. Watson was the next world-famous computer from IBM and was a featured player and winner of Jeopardy. Their newest AI-inspired computer system is known as and it is designed to formulate human arguments and win debates against some of the world's greatest known debaters. Project Debater Microsoft Products such as Cortana, Bing, Office 365, and Skype are AI programs from Microsoft. It is the goal of Microsoft to introduce smart devices into every service they offer. They are currently one of the largest AIaaS ( ) users. AI as a Service JD.com Drone deliveries are one of the latest offerings from big companies such as Amazon, but JD.com, a Chinese based online retailer, has been using drone deliveries for four years successfully. They use big data to help their robotics division move the company into the realm of 100% automation. Currently, the warehouses for JD.com run wholly on automated systems. Tencent China has its own social media format called Tencent. This company aims to be the most respected internet enterprise and is working toward that goal with the help of AI. Currently, its 1 billion users use the app WeChat, but the company is reaching into other avenues such as digital assistants, self-driving cars, live streaming, education and many other avenues. Their slogan seems to say it all, “AI in all.” Alphabet-Google Alphabet-Google is the parent company to projects such as Waymo, DeepMind, and Google Duplex. Each of these mediums utilizes AI differently. is responsible for self-driving taxis in California while DeepMind is a self-learning applications designed to play games with notable accomplishments such as beating out a professional Go player and learning 49 Atari games on its own. Google Duplex works remarkably like an AI-based assistant making phone calls or scheduling phone calls on the user’s behalf. Waymo These are just a few examples of how AI has become a part of everyday business and personal lives. It is everywhere, and even though the concept of the world being taken over by computers is a bit concerning, we must face the fact that AI is not going anywhere anytime soon.

How Companies Are Actually Using AI in Everyday Practices

Google Interview Questions Deconstructed: The Knight’s Dialer (Logarithmic Time Edition) This is the second post in my series where I lay out my favorite interview questions I used to ask at Google until they were leaked and banned. This post is a continuation of , so if you haven’t taken a look yet, I recommend you read it first and come back. If you don’t feel like it, I’ll still do my best to make this post sensible, but I still recommend reading the first one for some background. the first one First, the obligatory disclaimer: while interviewing candidates is one of my professional responsibilities, this blog represents my personal observations, my personal anecdotes, and my personal opinions. Please don’t mistake this for any sort of official statement by or about Google, Alphabet, or any other person or organization. Apologies for the delay, by the way. In the time since I published the first part of this series, I’ve gone through a number of (very positive) changes in my life, and as a result writing sort of fell by the wayside for a while. I’ll share what I can as things become public. This post goes above and beyond what I would expect to see during a job interview. I’ve personally never seen anyone produce this solution, and I only know it exists because my colleague mentioned that the best candidate he had ever seen had blasted through the simpler solutions and spent the rest of the interview trying to develop this one. Even that candidate failed, and I only arrived at this solution after weeks of on-again, off-again pondering. I’m sharing this with you for your curiosity and because I think it’s a cool intersection of mathematics and programming. way With that out of the way, allow me to reintroduce the question: The Question Imagine you place a knight chess piece on a phone dial pad. This chess piece moves in an uppercase “L” shape: two steps horizontally followed by one vertically, or one step horizontally then two vertically: Suppose you dial keys on the keypad using only hops a knight can make. Every time the knight lands on a key, we dial that key and make another hop. The starting position counts as being dialed. How many distinct numbers can you dial in hops from a particular starting position? N At the end of , we had developed a solution that solves this problem in linear time (as a function of the number of hops we’d like to make), and requires constant space. This is pretty good. I used to give a “Strong Hire” to candidates who were able to develop and implement the final solution from that post. However, it turns out we can do better if we use a little math… the previous post Adjacency Lists The crucial insight of the solutions in the involved framing the number pad as a graph in which each key is a node and the knight’s possible next hops from a key are that node’s neighbors: previous post In code, this can be represented as follows: <a href="https://medium.com/media/21565d1630d681ecc89193307871af60/href">https://medium.com/media/21565d1630d681ecc89193307871af60/href</a> This is a fine representation for a number of reasons. First off, it’s compact: we represent only the nodes and edges that exist in the graph (I include number 5 for completeness, but we can remove it without any repercussions). Second off, it’s efficient to access: we can get the set of neighbors in constant time via a map lookup, we can iterate over all neighbors of a particular node in time linear to the number of neighbors by iterating over the result of that lookup. We can also easily modify this structure to determine the existence of an edge in constant time by using a sets instead of tuples. This data structure is known as an , named after the explicit listing of adjacent nodes to represent edges. This representation is by far the most common method of representing graphs, chiefly because of its linear-in-nodes-and-edges space complexity as well as its time-optimal access patterns. Most computer scientists would look at this representation and say “pack it up, that’s about as good as it gets.” adjacency list Mathematicians, on the other hand, would not be so happy. Yes, it’s compact and fast to operate on, but mathematicians are (by and large) not in the business of pragmatic ease of use like most computer scientists and engineers. A computer scientist might look at this graph data structure and say “how does this help me design efficient algorithms?” whereas a mathematician might look at it and say “how does this representation allow me to use the rest of my theoretical toolkit?” With that question in mind, the mathematician might be disappointed by this representation. Personally, this representation of a graph rhymes with nothing I’ve encountered during my mathematical education. It’s useful for writing algorithms, but that’s pretty much it. Graphs as Matrices There is another, more fruitful, way to represent a graph, though. You’ll notice a graph is all about relationships between nodes. In the case of an adjacency list, we relate each node with the nodes it’s connected to. Why not instead focus on pairs of nodes? Instead of asking “what nodes are connected to one another with an edge,” you can ask “given a pair of nodes, is there an edge that connects them?” If this seems like a sort of “six of one, half dozen of another” situation, it is. But the second formulation is magical because it calls into focus something that’s invisible in the adjacency list representation: suddenly we’re very interested in pairs of nodes that have edges. Rather than starting with nodes and computing only the relevant pairs, we start with , and decide whether or not they are relevant later. don’t all possible pairs We can reframe the adjacency list as follows. Note for each pair (A, B), NEIGHBORS_MAP[A][B] will be 1 if that pair represents an edge in the graph and 0 otherwise: <a href="https://medium.com/media/e2a2ba2ac8115ad18ce0fee90f4dc4c0/href">https://medium.com/media/e2a2ba2ac8115ad18ce0fee90f4dc4c0/href</a> Why would we do this? Certainly not to create a more efficient data structure. Our space complexity has gone from being proportional to the number of edges to the number of edges, which means squared, where is the number of nodes. Iterating over neighbors also just got more expensive: for a given node we get a bunch of irrelevant zeros that we have to filter through. possible N N A mathematician, on the other hand, just got interested. Anyone beyond the junior year of a mathematics undergrad should look at this and immediately say “that’s a matrix!” (For the sake of brevity, I’ll assume here that you know enough about linear algebra and matrix multiplication to follow along with this post. If you don’t, you can find a great introduction .) here The wonderful thing about matrices is that they support an algebra. Matrices can be added, subtracted, and multiplied with one another, according to some simple rules. What this particular representation lacks in compactness, it more than makes up for in abstract ease of manipulation. An Aside A slight digression: “okay cool”, you might say, “we’ve represented the graph as a matrix. And that matrix can be multiplied by another matrix. What does this have to do with the graph? Who cares?” This is a much more valid question that you may realize, and the answer is “nothing, yet.” Undergrads are my intended audience, so I feel obligated to put you in the right frame of mind before I continue because I’m afraid this might otherwise be more discouraging than enlightening. After you finish reading this logic presented in the rest post, you may be tempted to ask yourself “how the hell was I supposed to come up with that?” I certainly had that reaction time and time again while reading proofs and textbooks. The short answer is: you’re not. At least not immediately. The more proofs and theorems you learn, the more you’ll find you’re able to spot patterns and apply your knowledge. I suggest treating this post as just another tidbit to know and hopefully apply later. Down to Business Alright, now that that’s out of the way, let’s get down to the solution. First we’ll explore the structure of this matrix a little. (Note all indices are offsets from zero. This is a departure from mathematical tradition, but this is a CS-oriented post, so let’s go with it.) In this matrix, each row represents the destinations accessible from each key: row 0 has a 1 in position 4 to show you can hop from 0 to 4. It has a 0 in position 9 to show you can’t hop from 0 to 9. The rows also have a meaning. While the rows represent where you can go the corresponding position, the columns represent how can get each position. If you look closely, you’ll notice that the rows and columns look strikingly similar: the -th position in each row is the same as the -th position in each column. This is because this graph is undirected: each edge can be traversed in both directions. As a result, the entire matrix can be flipped along its main diagonal and emerge unchanged (the main diagonal is formed by the positions where the row and column numbers are equal). from to i i Now that we’ve introduced representing the graph as a matrix, it’s no longer an algorithmic object but an algebraic one. The particular algebraic operation we’ll be concerned with is matrix-vector multiplication. What happens when we multiply this matrix by a vector? Recall that the formula for multiplying an row by column matrix with an -length column vector (short for a matrix with rows and 1 column) is: R C A C v C In words, this means that the resulting -length vector can be computed by taking each row, multiplying each element of that row by the corresponding element in the vector, and adding the component values together. The results are then placed in a vertical, -by-one matrix, or a -length vector for short. C C C This may seem uninteresting at first glance, but that algebraic relation up there is actually the crux of this entire solution. Consider what it means. Each row represents the numbers you can reach from that row’s corresponding key. With this in mind, matrix multiplication is no longer an abstract algebraic operation, . it’s a means of summing values corresponding to destinations from a given key on the dialpad To make the implications clear, recall the recurrence relation from my previous post: caption: Remember represents the number of distinct sequences you can dial from key in hops T K N This is nothing more than a weighted sum of values corresponding to destinations from a given key on a dialpad! This framing ignores edges that aren’t in the graph by not even considering them in the iteration, whereas the matrix-oriented one includes them, but only as multiplications by zero that don’t affect the final sum. The two statements are equivalent! So then what is the meaning of the vector in all this? So far we’ve been talking almost entirely about the matrix, and we’ve mostly ignored the vector. We can choose any we want, but we want to choose one that will be meaningful in this calculation. The recurrence relation provides us with a hint: in that case, we start with , which is always 1 because in zero hops we can only dial the starting key. Let’s see what happens with a where all the entries are 1: v v T(K, 0) v Multiplying the transition matrix by the 1 vector gives us a vector where each element corresponds to the count of numbers that can be dialed in 1 hop. Multiplying again, we can: Now each element in the resulting vector equals the count of numbers that can be dialed from the corresponding key in 2 hops! We’ve just developed a new linear-time solution to the Knight’s Dialer Problem. In particular: Logarithmic Time But this solution is still linear. We need to multiply by the vector again and again and again, times. If anything, this solution is actually slower than the dynamic programming solution we developed in the previous post because this one requires unnecessarily multiplying by zero a whole bunch of times. A v N There is, however, another algebraic property we can use: matrices can be multiplied, and anything that can be multiplied can be exponentiated (to an integer power). Our solution becomes the following: Again, I won’t be defining matrix multiplication, so if you need a refresher, take a look at . this post How do we compute ? Naturally, one way is to repeatedly multiply by itself. However, this is somehow even more wasteful than multiplying by the vector: rather than multiplying one vector by again and again, we multiply all the columns of again and again. There is a better way: exponentiation by squaring. A^N A A A As you probably know, every number has a binary representation. If you’ve been studying computer science you already know that this the preferred way of representing a number in hardware. In particular, every number can be represented as a sequence of bits: Where k is the largest nonzero bit. For example, 49 in binary is “110001,” or: Something interesting happens when we perform this expansion for in our matrix exponentiation solution: N Recall that addition in the exponent translates to multiplication underneath it This results in a total of matrix multiplications. How does relate to ? is equal to the number of bits required to represent , which as you may already know is equal to . Instead of requiring a number of multiplications that grows linearly in , we only need a logarithmic number of matrix multiplications! This hinges on a few useful facts: k k N k N log2(N) N A to the power of zero is the identity matrix. Multiplying any matrix by the identity matrix results in the original matrix. As a result, if any bit is zero, we’ll end up multiplying by the identity matrix, and it’ll be as though we ignored it. We can compute to any power of two by squaring the result again and again. squared is times . to the 4th is squared times squared, etc. A A A A A A A This is it! We now have a logarithmic solution. While this solution requires a little more code than the previous ones on account of the definition of matrix multiplication, it’s still quite compact: <a href="https://medium.com/media/4d6e764c0c25d12ab53a0ea6a599ac92/href">https://medium.com/media/4d6e764c0c25d12ab53a0ea6a599ac92/href</a> Wrapping Up On the face of it, this solution seems awesome. It features logarithmic time complexity and constant space complexity. You might think it really doesn’t get any better than that, and for this particular problem you would be right. However, this matrix exponentiation-based approach has one glaring drawback: we need to represent the entire graph as a (potentially very sparse) matrix. This implies we’ll have to explicitly store a value of every possible pair of nodes, which requires space quadratic in the number of nodes. For a 10-node graph like this one, that isn’t a problem, but for more realistic graphs which might have thousands if not millions of nodes, it becomes hopelessly infeasible. What’s worse, the matrix multiplication I gave up there is actually in the number of rows (for square matrices). The best-known matrix multiplication algorithms like Strassen or Coppersmith–Winograd have sub-cubic runtimes, but either require extreme memory overhead or feature constant factors that negate the effects for matrices of reasonable size. A cubic-time matrix multiplication starts to become unreasonable with graphs with sizes around the ten thousand range. cubic At the end of the day, none of these limitations really matter in my mind. Let’s be honest: how often are you going to be computing this on any realistic graph? Feel free to correct me in the comments, but I personally can’t think of any practical application of this algorithm. The main purpose of this problem is to evaluate candidates on their algorithm design chops and coding skills. If a candidate makes it anywhere the things I discussed in this post, they’re probably a lot more qualified for the Google SWE job than I am… near If you liked this post, applaud or leave a response ! I’m writing this series to educate and inspire people, and nothing makes me feel quite as good as receiving feedback. Also, if this is the sort of stuff you enjoy, and if you’re all the way down here there’s a good chance it is, give me a follow ! There’s a lot more where this came from. Also, you can find runnable the code for this and the previous post . here Next Steps After this question was banned I felt like I wanted to start asking a more straightforward programming question. I searched far and wide for a question that was simple to state, had a simple solution, allowed for many levels of followup questions, and had an obvious tie to Google’s products. I found one. If that sounds like something you’d like to read about, stay tuned…

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