Form W4 (2013: Fill & Download for Free

Wow, this post is long!Here is the tl,dr; version:We start with the 21 candidates.We show a simple lemma that can give us some lower bound for the number of questions we need.We design a simple recursive algorithm to check all possible ways of asking the questions. We use the above lemma to prune almost all branches of the search.Within the simple algorithm, we use a solver of linear programs to check whether an answer is still feasible.The smallest number of questions is indeed 6.Jaimal Ichharam explains nicely how we can reduce the number of possible answers to 21. In fact, it is impossible to reduce it any further: for each of those 21 options it is possible to construct a set of 8 weights such that it is the (only) answer.Now, the number 21 can be used to prove that we need at least 4 questions in the worst case. This is not an optimal lower bound (as we shall see later), but the proof is very simple. The argument is the same information-theoretic one that can be used to prove that searching in a sorted array is [math]\Omega(\log n)[/math] and that comparison-based sort is [math]\Omega(n\log n)[/math]: in order to distinguish among many possibilities, you need enough information, and for that you need to ask enough questions.Lemma: Any deterministic algorithm that solves the "8 bags problem" and always makes at most [math]q[/math] questions can distinguish between at most [math]2^{q+1}-1[/math] different candidates.Proof: The number is the maximal number of different outputs our program can produce. And if there are more candidates than possible outputs, some candidate is never output, and therefore the program cannot be correct.Why is that the maximum number of possible outputs? We'll prove that by using induction. If [math]q=1[/math], we get to ask 1 question, and then we can give 3 different answers: one in the case the left side of the scale was lighter, one if it was heavier, and one if they were equal. (In the last case, the answer would be that this is the split we are looking for.)In the general case with [math]q[/math] questions, after the program asks the first question, there are three branches. If the two pans were equal we know the answer and terminate. In each of the other two cases we have [math]q-1[/math] questions left and thus (by the induction hypothesis) we can give at most [math]2^q - 1[/math] different outputs. Thus the total number of different outputs for a program that asks [math]q[/math] questions is at most [math]1+2(2^q-1)[/math], q.e.d.(Note that a very similar lemma can be used in any other problem where our questions can receive the answers <, =, >, and where getting the answer = uniquely determines the correct answer. Do you see the similarity to binary search?)Corollary: If we ask at most 3 questions, we can have at most 15 different outputs. Therefore we need at least 4 questions to distinguish among 21 candidates.Even though the lemma does not give a tight lower bound, it is still important: we will use it later to prune our search.Our ultimate goal will be to implement a brute force search that will consider all orders in which we can ask the questions. The schema of the algorithm is very simple:is_solvable(number_of_questions, past):  count the answers that are consistent with the past  if there is at most one, return True  if we are down to 0 questions left, return False  for each possible answer A:  p1 = past + [ when weighing A left pan is lighter ]  p2 = past + [ when weighing A left pan is heavier ]  if is_solvable(number_of_questions-1, p1)  and is_solvable(number_of_questions-1, p2): return True  return False That is it. In each possible situations, consider all possible (meaningful) questions you could ask next. The current situation is solvable in [math]q[/math] questions if and only if you can now ask a question such that regardless of the answer you get you can guarantee solving the new state in [math]q-1[/math] questions.One additional optimization of this algorithm is our use of the above lemma. Instead of "if we are down to 0 questions left (and have more than 1 candidate), return False" we can have the more general check "if the number of candidates is too large for the number of questions, return False".The only "building block" we now need is the check whether a given candidate is consistent with a given set of answers we already have. So let's take a look at that.What do we have at the beginning? Eight unknown weights: [math]0\leq w_1<w_2<\cdots<w_8[/math]. Now, each time we ask a question and don't find the correct split, we get a new information of the following form:[math] w_1 + w_3 + w_4 + w_8 < w_2 + w_5 + w_6 + w_7[/math]Now, what does it mean when we say that an answer is still feasible? It means that the above system of inequalities is consistent with equality in that particular case.(Technical note: To be completely correct, our check for feasibility should find such values of weights that not only is there equality in our case, but at the same time there must be inequalities in all other cases. However, this is trivially true: whenever we have weights such that more than one split would balance the scales, we can apply some small random perturbation to the weights so that there would only be equality in the one case we want. Details are left as an exercise.)In order to do the above checks I use an LP solver (lp_solve in particular). Checking whether a system of inequalities and equalities has a solution is pretty close to linear programming. The only technicality we need to deal with are the sharp inequalities. Luckily, in our case we can simply turn them into less-than-or-equal inequalities by simply requiring the difference to be at least 1. (Note that the weights can always be scaled.)Here is a sample linear program:min: w8; w1+1 <= w2; w2+1 <= w3; w3+1 <= w4; w4+1 <= w5;  w5+1 <= w6; w6+1 <= w7; w7+1 <= w8; w1+w3+w6+w8+1 <= w2+w4+w5+w7; w1+w2+w3+w8+1 <= w4+w5+w6+w7; w1+w2+w4+w8 = w3+w5+w6+w7; Without the last constraint this program is feasible. One possible assignment of weights is (0,2,3,4,5,6,7,8). With the last constraint the program stops being feasible, so the corresponding way of splitting the bags cannot be the solution any more after those two weighings.(Note that I chose minimizing the maximum weight as the goal of the LP. This is pretty much arbitrary, any positive linear combination of our variables would do, as we are only interested in the existence of a solution.)Code posted here: http://ideone.com/xnivHM(Runs for about 3 minutes on my laptop, verifies that there is no solution with fewer than 6 questions in the worst case, and finds one with 6. Keeping the past in sorted order and adding memoization brings runtime down under a minute.)Some simple modifications of the code above can give us an optimal strategy as well. Here's one that I found by making some arbitrary choices:The first three questions will always be the same: 1567 vs. 2348, 1458 vs. 2367, and 1368 vs. 2457. If one of them is the solution, we are done. Otherwise, we get one of 8 possible combinations of < and >. Each of them will correspond to at most 7 candidates. These are the feasible answers at this point:<<<: 1468 1568 1278 1378 1478 1578 1678  <<>: 1268 1278  <><: 1278 1378  <>>: 1238 1248 1348 1258 1358 1268 1278  ><<: 1467 1468 1278 1378 1478  ><>: 1267 1367 1467 1268 1278  >><: 1456 1457 1467 1278 1378  >>>: 1467 1258 1358 1268 1278  If 1368 < 2457, compare 1378 vs. 2456 as the fourth question, otherwise compare 1268 vs. 3457 as the fourth question. In most cases you'll be left with at most 3 feasible solutions, and that is trivial to solve in two questions. There are only two cases that are harder:: <<<<: 1468 1568 1478 1578 1678 <>>>: 1238 1248 1348 1258 1358 Both of these can again be solved in two questions, an optimal strategy is left as an exercise.

CPA Affiliate Networks are getting widely popular nowadays.Daily a new CPA network is born in the industry with some special innovative offers to lure publishers & marketers.Are you looking for a Premium CPA Affiliate networks with the highest paying offers for your niche?Let’s start…Maximum bloggers have started to implement Affiliate marketing on their blogs over Google Adsense and traditional display Ads methods. Almost all Internet marketers know the potential of CPA and affiliate marketing, and hence the online affiliate industry is growing at rocket speed.Here we are with Top 9+ CPA Affiliate network list which is best for global traffic and is rated best among all pro Marketers.There are more than thousands of legit CPA networks and every company is having different unique benefits which can’t be compared in this blog post hence we are only reviewing the Best 9+ CPA Affiliate Networks for 2019 which will enable you to make real money from your traffic easily.What is a CPA Affiliate network?CPA stands for “cost per action” or “cost per cost per acquisition” which means you will be paid commission or incentives when some product or service gets purchased from your affiliate (referral) link. There is another term called “CPL” which stands for cost per lead, so when a user fills a form or complete any survey or download some application from your affiliate link, you will be paid commission. Let’s see in details.CPA networks are scattered over the web and some famous networks arePeerfly, Maxbounty, GlobalWideMedia, admitad, ShareASale, JVzoo, Clickbank etc…These networks have thousands of direct offers from advertisers from almost all countries. As these great networks are direct contact between advertisers, hence you get more pay-out per lead or action.CPA Affiliate networks are companies which work on numerous verticals like cost per action, cost per mile, cost per view, cost per install & cost per sale. It’s a platform to connect advertisers with publishers. You can sign up on any CPA network, promote offers listed with them and make real money out of it.Best 9+ CPA Affiliate Networks {2019 Edition}You may register an account with these CPA Affiliate Networks as they are most authentic, they are a bigger company, they sponsor the maximum of affiliate networking events and conferences and pay their publishers on time without any single delay.Getting approved in some of the CPA companies is hard as they require lots of experience to get you in their network but if you are already working with some affiliate networks now and earning a decent amount, then it’s quite easy to get approved.ClickbankClickbank is online retailer with a global presence, secure payment processing, reliable tracking and payouts, and an extensive affiliate network. Vendors can create and sell both digital products (such as ebooks, software, and membership programs) and physical goods through ClickBank.When you find a product that you wish to promote, either by searching the ClickBank marketplace or at a vendor's website, you will be provided with a unique link which you can use to direct customers to the product page2: admitad (Global Affiliate Network)admitad is a Cost Per Action based network that delivers all your advertising needs. admitad offers reliable sources of sales and publishers with new business models to ensure monetization of traffic. Established in Germany in 2009 (Launched in 2010), currently, it is present globally.admitad Affiliate networkIt has its own innovative in-house platform, premium payments on request starting from $20$, a variety of modern tools and globally known brands!admitad essential features & benefits:Web address: Admitad is an affiliate network◾Weekly payments, premium payments on request;◾User-friendly interface and a natural sign-up process◾The primary segments: finance, mobile, e-commerce, travel, online games;◾Minimum payout is $20.◾Fast decision-making and centralized organizational structure◾Forms of payment: PayPal, e-payments and wire transfer.◾Main technical advantages: antifraud technologies, cross-device tracking, fingerprint tracking, advertiser toolbox, anti-cookie technologies, deep linking options, cross-device monitoring, in-house platform;◾Business model: admitad does not take fees and provides its affiliates with regularly renewed statistics and analytics.◾Territorial coverage: network with a global presence, TOP brands, and multiple GEOs worldwide.admitad has global traffic and works with international offers. Currently, it supports over 1300 affiliate programs, and over 550000 publishers trust the company.◾Global corporate events for admitad publishers◾Free and on-time statistical and analytical reports available for all publishers◾Friendly and multi-language support.admitad-banneradmitad prefers to support you during the entire CPA marketing journey. The network develops every publisher and helps every affiliate to grow within the admitad network and increase his or her revenues with us.admitad houses thousands of fresh, campaigns in numerous niches. From eCommerce, Web, finance to Travel, admitad have best campaigns with excellent payouts and their quick link technology enables auto monetization of website traffic by their innovative tools. I am using admitad on many of my websites. Its a must try Network.It’s time to raise the bar and get the payouts you know you deserve – admitad is always open to help you to gain and grow a successful business!3: CPALeadCPALEAD is world’s largest incentive CPA network having more than 2000+ offers. They invented content locking first which is now used by all major CPA Content Locking networks. They have the highest payout rates in the industry and have invented a lot of tools for publishers such as custom landing pages, pre-built Niches to promote, etc..CPALeadCPALEAD is used by people all over the world, and they have the maximum number of users and traffic. They love their publishers by sending them free gifts, goodies and inviting them to the grand party every year.CPAELAD is my favorite, and I am using it since 2013. They have never done late in any single payment till now. The company has ranked as one of the top affiliate networks in the world by mThink and recognized as one America’s top 40 fastest growing companies by INC 500 .They pay weekly for mobile apps install, surveys, ZIP/Email submit, etc with minimum payment of $10 in NET 30, NET 15, weekly and even early payment by request. They pay through Check, PayPal, Wire, Payoneer, ACH (Direct Deposit)CPALEAD offers high-quality lead generation, Exclusive offer inventory, mobile app installs and offers for all countries with 100% fill rates.If you are looking to simply make money from by sharing files or tools or want to work with PPD (Pay per download) method, then CPALead is the best premium content locking CPA network to choose.4: MaxBountyMaxBounty is another highly popular CPA Affiliate network for Pro internet marketers who earn more than 5000$ per month. To be honest its quite hard to get approved on MaxBounty as they have lots of requirements and only approved selected users who are making huge revenue already.MAXBountyMaxBounty is not for newcomers in affiliate marketing. It’s merely the most reliable network I have been a part of so far as they pay on time every week.They have their In-house tracking system and have more than 1000+ offers from CPA, CPL and CPS. The company is offering performance-based affiliate marketing since 2004 and ensures both sides of performance marketing spectrum should be treated equally. They have been rated #1 since years by top industry professionals.MaxBounty has a minimum payment of $50 and pays weekly and NET-15 for the first month. Payment methods on MaxBounty are Check, wire, Payoneer, PayPal, and ACH. They are also offering $1000 bonus to new affiliates, Once your account is approved, Contact your AM (Affiliate manager) to know more about this promotion.MaxBounty comes under the premium list. Their exclusive offers, higher payouts differ from others. Join MaxBounty to receive premium payouts and exclusive campaigns optimization on your traffic by their account managers.5: Adscend MediaIt’s one of the oldest and stable CPA Network since 2008. Adscend Media was more into content locking and offer walls. However, over the time the network has strived and changed a lot to go with the flow,The company houses over 1850+ offer globally in verticals like CPL, CPA, and CPV. It has mostly offered which gets converts quickly like email submits, click on buttons. So obviously these type of campaign have a low payout, but it converts very fast and can give you very high ROI.Adscend media have to offer walls and also offers API which lets you import its campaigns ion your software, app or networks.Adscend Media is undoubtedly op CPA Affiliate network with a vast number of offers on all categories, all verticals, and allows global traffic.If you are looking for an incent allowed offers, Adscend Media allows incent or points on most of it CPA campaigns.6: ShareASaleShareASale which is now part of Awin is a leading performance marketing network form past 19 years. with thousands of sale and leads affiliate program from almost all niches like technology, e-commerce, travel, hosting, health, beauty, etc..The network houses over 3900+ direct affiliate programs and publisher support directly via call. They have some features like coupons and deals, data feeds, custom links creating, Real-time reports and video creatives.No matter, which niche you are working, ShareASale have affiliate programs to suit your audience. They have some innovative tools to scale your earnings higher.ShareASale have direct advertisers and have premium payout rates. They have an in-house tracking inventory. Payments are paid via PayPal, Payoneer, direct ACH transfers, Wire and Checks.7: GlobalWideMediaGlobal Wide media (Formerly NeverBlue ) offers data driven marketing solutions for modern affiliate marketers.It is one of the oldest and very premium CPA networks for serious marketers. They have the highest CPA offers form broad categories and also offers extra high payout rate which you won’t get on any other systems. Their Affiliate support teams help you to promote better offers by optimizing your traffic.GWM has multiple offices around the globe and multiple platforms for different locations to signup as a publisher. Some of their premium clients include Hotels.com - Deals & Discounts for Hotel Reservations from Luxury Hotels to Budget Accommodations, Aliexpress, Booking.com: The largest selection of hotels, homes, and vacation rentals, ford, uber, Walmart, etc.Minimum payout is $100 and methods are PayPal, Check Wire and ACH Direct deposit for many countries. Global Wide media is an excellent choice for foraffiliate marketers who wills to make more than 1000$ per month as they only need serious publishers.GlobalWideMedia is no doubt a premium CPA Network dealing in many verticals with great payouts as they have tons of direct advertisers and companies.8: ClickBoothClickbooth is another famous CPA network which has already earned lots of industry awards for its excellence in service. Clickbooth connects advertisers with publishers to drive new customers on CPA, CPL, CPE, CPS, CPC pricing model.ClickBooth is NOT for beginners as they have a pretty robust system for approval for affiliates. Only serious marketers are allowed onboarding at ClickBooth. With experienced Affiliate manager, guaranteed weekly payments, friendly affiliate technology: Clickbooth has ranked on the top list in a short period.Register today on Clickbooth to sneak peek their exclusive partner affiliate offers and get payouts in a week.9: MobIdeaAs the name suggests, MobIdea is a CPA network specialized in mobile offers. With innovative tools and technology, Mobidea is the #1 platform for free CPA offers and Push notification CPA offers.They have the highest number of top affiliate offers for mobile traffic in almost all geos.MobIdea features at a glance◾MobIdea is the first affiliate network to offer all the capabilities of a tracker within the mobidea platform and it’s free forever.◾Weekly payments via PayPal, ePayments, FirstChoicePay, paxum, and Wire.◾Real-time optimization with an advanced algorithm for top converting offers.◾7 days a week support in 5 languages for Affiliates.◾100% support from MobIdea experts to guide you to monetize your traffic better with their proven optimization techniques.◾offers wall and API data feeds for automation.If you have mobile or push traffic, Convert it with best premium CPA mobile affiliate offers with MobIdea.How to get the higher payout for your affiliate offers:We all work for money, and a better payout is we all need. If you are promoting a campaign and you think you deserve better rates….Follow these tips to negotiate for better ratesAt first, you need to check other CPA affiliate networks for the same offer if you are getting a good payout don’t just switch your traffic to another system but contact your affiliate manager and tell that you are getting the higher rate on another network, They will undoubtedly increase prices for you.This is the simplest way to get desired. Payouts, But keep in mind that unless you don’t promote and convert your campaigns in good numbers, You won’t be entertained to negotiate payouts.It is always better to keep in touch with your affiliate account manager and ask him/her about new offers, discuss strategies with them as most of the time they have premium payouts rates for some particular offers and they can offer you best rates for some affiliate campaigns for your traffic. So in last its all about building a relationship with your account managers. 🙂Understanding CPA Terminology:What is CPA (Cost per acquisition)?Cost per acquisition simply means you have to sell some product or service by promoting it on your blog, social media, emails or through your affiliate link and when the sale or subscription happens you get paid with a commission which is decided by the advertiser for different products.For Example, I am promoting Fiverr services by writing its review on my blog, and when anyone buys any service from Fiverr from my link, I will be paid $14 commissions for the sale happened.What is CPL (cost per lead)?Cost per lead is mainly used for content locking. Many smart bloggers share some premium stuff with their readers for free like Game cheats, Premium eBooks, etc.instead of giving its direct download link to their users the embed their download link in CPL affiliate networks, So when a user tries to download he/she have to complete a small survey or offer and in this case the author earns money by just providing free download of premium Stuff.CPL networks have also increased since the last decade. Daily a new cost per lead network or you may call it PPD (pay per download) site is born. PPD sites usually provide content locking solution with attractive landing pages for locking your content, and the offers are automatically displayed to the user depending on their country so one can earn huge revenue via PPD methods too. I will write another post for guiding you on how to make money from Pay per download sites with an in-depth tutorial.Also we have free E-book on CPA Marketing that help out with leads, downloads and emails.Some extra Top ranked CPA Affiliate Networks which should not be missed:While we have shared the top CPA Networks list for 2019 above, here are extra performance marketing networks which work on CPA pricing model and have been ranked in top 20 for 2019 by Think BlueBook. Let’s check it out.Dr.Cash:If you are looking to promote products for beauty, and health (Nutra vertical ), then Dr.cash is no doubt the best all in one Nutra Affiliate program which houses more than 2300+ premium affiliate offers worldwide.Dr.Cash Affiliate NetworkDr.Cash is innovative Affiliate Network for Nutra vertical which is leading the industry in Nutra niche since 2016. They have specific Nutra campaigns with almost every geo. Higher payout rates, 24/7 partner support, twice a day payout, fantastic dashboard with real-time conversion reports, have made them #1 Affiliate Network in the highest paying vertical (Nutra)Beauty and health are one of the best niches to promote. With the maximum of people in the world looking for weight loss, health problems, proper diet, beauty products, Nutra affiliate offers are blessings for internet marketers.When almost all wide Affiliate networks are not heavily promoting Nutra offers, It is always better to go with the industry leader and exclusive Nutra Affiliate program where you get the best revenue on your conversions. Get started with Dr.cash today to scale your Affiliate earnings. They have over 14000+ publishers.Dr.Cash works in over 100+ goes and have premium affiliate campaigns for over 50+ beauty and health niches.Madrivo is the most robust digital agency in lead generation, Affiliate marketing, and online advertising. It’s a gold winner of Marcom Awards, Madrivo enables all verticals in CPA categories. The company has grown over 400% this year and have generated over $150 Million for advertisers globally.Madrivo is a premium CPA Network which invites only. Hence newcomers in this industry won’t be entertained with Madrivo. You need to have an invitation from MmadRivo team for registering on their network as publishers. However, you can also contact them here to request an invitation. (Their approval process is pretty hard).Madrivo houses premium CPA Affiliate offers for their exclusive advertisers, and hence they bring credibility to the world of online advertising. The company have invested a lot in research and understanding online consumers and utilizes its data for successful online marketing strategies.AdWorkMedia enables you to earn money from your websites, Apps, links, domains, content, etc. With innovative monetizing tools like content locking, offer wall, product lockers, Adworkmedia enables higher monetization with more excellent conversions ratios.AdworkMedia have over 2500+affiliate campaigns for over 250+ countries. They have their own mobile-friendly targeting automated monetization tools for better conversion rate.AdworkMedia offers 7 days a week support and flexible payment options to choose from.W4 Performance Ad Market enables the high standard of CPA performance market. The premium affiliate network was founded on the difference to give respects to smart publishers which they deserve. They have direct premium advertisers like Amazon, Vonage, Norton, Microsoft, Audible, etc. with guaranteed best payouts by their direct advertisers. The network is super-premium and only works with qualified affiliates who are serious and want to scale their own revenues.Mundo MediaIts, a global leader in User Acquisition and Monetization. It also uses blockchain technology and has the global reach with a single point to 35,000+supply partners from over 150+ countries. The platform is built in optimization algorithms and data-driven analysis to increase the control and performance of comedians.The Network is entirely transparent on ad placement, performance and cost. One can become Mundo Media publisher partner and get access to thousands of top performing offers from many GEO’s as well as private crypto offers to promote.