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Problem Solving Strategies

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Problem Solving Strategies
Hello and welcome, In the last lecture I talked littlebit about an introduction into problem solving what all aspects problem solving involve andI also talked about things like how to represent the problem correctly in order to get a solutionget to solutions more easily. We also talked about an approach of situatedcognition wherein idea is lot of you know problems or lot of things that you learntto solve are in some sense related very closely to the context and it might be a sometimesdifficult to transfer learning in a specific context such as in a classroom to a real lifescenario and that it is advised that even classroom teaching for that matter shouldinvolve aspects that teach people be able to apply those problems in real life studiesso, that is basically how effective problem solving shall be taught.Today am going to start talking a little bit about problem solving strategies and we willtalk about how these you know how these strategies are efficient or inefficient.So, there are various strategies that people have used to to try and solve various kindsof problems and; obviously, different strategies are used for different kinds of problems andone of the things that determine your success in solving a particular problem is the choiceof the correct strategy. So, we will just take a couple of these kind of methods andso, strategies if you start discussing about strategies a some strategies might be verydirect, some strategies might be rather straight forward, direct that takes less time and veryefficiently and efficient at solving the problems. While there could be other kinds strategiesthat people might erroneously pick which basically might leads to spending a lot of times, spendinga lot of effort and still not really guaranteeing or giving us a good solution. So, one hasto be very careful one has to be very vary of the fact that correct kind of strategiesare selected to really as approach particular kinds of problems.So, algorithms are one of those kind of strategies, now an algorithm is just a method that willalways lead you to solve the problem that will always lead you to the almost a correctsolution to a particular problem, but then algorithm in the sense because they are detailedin stuff can sometimes be very inefficient and it generally would take a lot of time.Suppose you can take an algorithm as a very methodical approach to solving a particularproblem, but a lot of times and you can link this to your real life scenarios as well alot of times methodically and gradually solving a problem is not an option that we have andyou have lot of time pressure and sometimes you really want to achieve something veryquickly and then elaborate and elaborate algorithms even though they are almost guarantying yoursolution are not really chosen by individuals you know.So, in that sense error things algorithms will not be really very productive an exampleof such an algorithm could be you know something like an exhaustive search. Now an exhaustivesearch as the name suggests is when you are trying out all the possible answers usinga specified system. Suppose for example you are solving an algebraproblem and the algebra problem has let us say 2 variables X and Y and you have to solvefor X one of the sure short ways of really doing this kind of problems is basically justassuming start from X is equal to 0 Y is equal to 1 and just start putting each of thesevalues in the equation till you finally, reach particular kind of a solution.Now even though this method will certainly and in guaranteed fashion give you the solutionof equation, but the point is it is going to take lot of time and because it is goingto take lot of time and effort, it is not really very efficient way to solve that problem.In that sense algorithms are often really inefficient and are often unsophisticated,but there are also even more unsophisticated methods that can come up with possibilitiesand that offer you particular kinds of choices to reach particular kinds of solutions.Say for example, if you are given this task of finding out words from anagrams and stuffas suppose you will given this letter here this LSST and NEUIAMYUL and you have to figureout range in a particular way that you can figure out word that is made from these collectionof letters. Now what you would need to do is you have to kind of workout various permutationsand combinations if you not really aware of the correct word you will kind of spend alot of time if you are following things like exhaustive search mechanism you are goingto spend an inordinate amount of effort before you are even closer to solution because theyare so many words and it is very difficult because there are so many letters so, manypermutation and combination that you will need to finally, reach this.So, what you can do is you can actually pick up a strategy and a strategy could be supposefor example, I will just try and figure out the first 2 letters of whatever this big wordis and once you start figuring out the first 2 letters that could basically be just youknow 2 or 3 things. For example you can have s and t you can have s and u s and a s andi those kind of combinations and this one by the way from all the number of combinationspossible. Suppose if you are conducting exhaustive searchand it has been calculated that you would basically they could be almost 87 billionpossible arrangement of letters so; obviously, you know that is completely out of the question,but if you take such kind of a strategy just start by the first 2 letters and you knowkind of figure out how the rest of the word could be that could lead you to a solutionmuch easily in much more you know in much more efficiently and much less amount of time.So, even though this is a slightly unsophisticated way of doing it even though this does notreally guarantee your solution in some sense, but this is a quicker way of doing it.So, this kind of arrangement is basically referred to as what is called a heuristicsyou know. So, from all the possible solutions that might be there I picked up a method andI kind of bet my gut on it and said that there is a this person there is a next person chanceI will be able to solve this problem using this method and I started trying that outand eventually figure out what the solution is.These kind of methods these kind of general rules are basically referred to as heuristicsand these are usually correct you know in problem solving literature heuristics aretaken as strategies where you are; obviously, choosing to ignore some alternatives and kindof exploring only those alternatives that seem most likely to you to be able to producea solutions. So, it is almost kind of a gamble it does not really guarantee a solution justlike an exhaustive search kind of mechanism would give, but certainly offers a high chancegood chance of solving a particular problem in a slightly more efficient way.Psychologists have conducted a lot of research in heuristic psychologists have conducteda lot of research on kind of heuristics problem solvers used and much less on how what kindof algorithms they are. So, because a lot of problems in the real life you cannot reallycome up with an elaborate algorithm way to solve it I will you would see it most of peoplepick up a particular heuristic and then start using it.Say for example, if you have to select you know the most appropriate life partner thatyou would want to have and exhaustive search mechanism would actually involve you knowtesting all the possible you know partners that might be there, but then; obviously,nobody does that you kind of follow heuristic based on particular parameters and you knowkind of playing around with those parameters that will help you make this decision; obviously,this is also this is not really guarantee this correct solution that will might guaranteeyour solution, but that is completely you know impossible to do this one this heuristichere suppose for example, you can go with a you know the I know go with a various factorsthat might be a importance to you and they might help you in zeroing down on a particularperson. So, this is basically just to elaborate thedifference between what is heuristic and what in algorithm is like. So, let us discuss littlebit about different heuristic now one of the heuristics that people often use is referredto as the means ends heuristics. So, the idea is that it this one has 2 components, firstis that you divide the larger problem into a set of smaller problems or sub problems,then what you have to do is you have to try to reduce the difference between the initialstate and goal state. So, whatever steps or manipulations you haveto do basically you have to kind of start solving each of these sub problems eventuallyleading to solve the major problem. So, this is the goal state where you have you knowwhere you have to reach this the initial state where you start solving the problem and inbetween are the steps that you take or let us say there are so many sub problems thatyou need to solve in order to solve the eventual problems.Now the means ends heuristic is a is a rather appropriate heuristic because it requiresyou to identify the goal state or the ends the it also requires to figure out the meansthat is the steps that you would need to take reach those ends. When problem solvers usethe means ends heuristic they must focus their attention on the difference between the initialstate and the goal state. So, what you have to really pay attention to is where is thepoint that you want to reach, where is the point that you are and basically what arethe steps that you could take or to shorten this gap to close this gap.Researches emphasize this heuristic is one of the most effective and one of the mostflexible ways of problem solving because there are so many sub problems it is not like thatyour kind of you know just decided and set on a single path you have to do that in orderto solve problem you know, the difference of problems are contingent on so many differentfactors and you can be very flexible about which route to take which step to take andwhat point in order to eventually solve the problem.Now, and if you actually take a step back and think all the time we are using the meansends analysis you know very effectively and very often to solve so many problems I amreminded of the anecdotal story of the thirsty crow you know the crow is thirsty it is movingaround in a jungle and there is no water all the ponds and stuffs have dried up and thenhe figures out that this jar there and that jar has a little water at the bottom; obviously,the crow cannot get inside jar and drink it. So, the crow decides to do is the crow decidesto pick up stones and you know fill the pa jar up with stones so that the water comesup and the crow eventually is able to drink the water. Now what is the crow doing here,the crow is basically you know doing sort of a means ends analysis and then breakingthe larger problem of drinking water into 2 steps, the first step is you know locatethat there is water, the second is to bring that water up to a level that can be drunkusing the beak. So, the this kind of means ends analysis issomething that we are almost doing on a daily basis and we are kind of using this rathersuccessfully to solve a lot of problems that we encounter. So, when one uses the meansends heuristic to solve the problem one can proceed either in the forward direction fromthe initial state to goal state you just take series of cells 1, 2, 3, 4 to reach the stepor sometimes you can just you know deconstruct the journey.You can start from step 6 which is at goal state and start coming back ok this is whatI have to achieve just one step before is what just one step before is what and stufflike that both are possible and there has been lot of research on means ends heuristicsyou know researches have demonstrated that how people organized their problem into subproblems. So, it has been shown that a people do organizeyou know the information there is given a problem in shorter into smaller problems andthey use that to eventually reach good solution. Demonstration again from the Matlin's bookis Hobbits - and - Orcs Problem this is the one that is actually similar to the boat andcrocodile problem that I was referring to in the last lecture.So, there is this, the problem is that you know there are 3 Hobbits and 3 Orcs, Orcsare violin creatures. So, if both of these groups are here in one side of the river andthey just have one boat to go to cross river and go to the other side. Now the interestingthing is they can be only 2 persons that can travel on the sport and also what you haveensure is the fact that at any side if there are more Orcs and less Hobbits the Orcs willattack in each of the hobbits. So, the goals state of the problem is thateverybody crosses the river in a boat that has this capacity of 2 people and nobody endsup dead. Now one of the things that people use to solve this problem is basically thatthe larger problem is to go cross the river, but the smaller problem also is to ensurethat there are at any point that never more hobbits then more Orcs and Hobbits on eitherside of the river. So, that is how people would kind of break this problem down andthey kind of go about solving this big problem. So, they did this study Greeno in 1974 hedid this study and they kind of tried to examine how people are solving this Hobbits - and- Orcs problem and this study showed people do pause at particular points and they haveto try and tackle a sub problem you know now there are these number of Orcs and these numberof hobbits in left side and these number of Orcs and these number of hobbits on the rightside. Now how do I do it they sometimes plan ahead they sometimes come back and they kindof organize sequence of moves such that you know ensures the correct solution problem.Now in these kind of scenarios again just because I was talking about this in the lastlecture as well the working memory is specially active you know because all of these manipulationsand looking ahead and looking back is basically happening in your working memory and thisis what the you know when people this going on when people are planning one of these movessequences because you are have to in the real time evaluate whatever possible options arethere. So, this is just the demonstration of howpeople might be using the means ends heuristic, now a lot of research by the way confirmsthat sometimes people are you know reluctant to move away from goal state even if the correctsolution sometimes depends on taking the temporary detour. So, for example, the larger problemis crossing the river, but the you also have to tackle this sub problem because otherwisethere are more Hobbits at once there are more Orcs at one side and less hobbits they willbe eaten. Suppose for example, somebody decides thateven in first round itself 2 of the Hobbits you know jump up the boat and cross the atthe other side the point is ok this is leading to solution or the to the greater problem,but now on this side there is just one hobbits and 2 Orcs and 3 Orcs and they are just goingto eat this one up. So, the idea is a lot of times people would need to plan and thishappens in daily life as well if you have a larger goal at hand sometimes you wouldneed to plan in such a way that you are engaged in doing things that are not directly leadingto a solution, but eventually will lead you to a solution.So, the idea is these kind of detours these kind of plannings need to be done in orderto achieve good solutions to your problem . So, real life as well as I was saying theproblem as in the problem at hand it can sometimes be a very effective strategy to sometimesmove backwards and then you know move forward towards the goal state. Eventually you knowpeople do the lot of this kind of things in games for example, in chess for that matteryou know sometimes you would decide to sacrifice particular pons in order to achieve the largergoal. So, that is again a very similar to how youknow people solve problem in these abstraction scenarios as well. So, it might be a goodidea say another example classroom example I could take that you know it might be youmight kind of decide or debate this whether it is a good idea to submit a poorly doneassignment just that just to ensure that you are the first one to submit an assignmentor say for example, submit it just in time ah, but ensure that you are kind of you knowdoing it well and you are graded well for that.Finally, there is another heuristic that I would want to talk about that is the HillClimbing Heuristic, now the hill climbing heuristic is one of the straight forward moststraight forward ways of solving a particular problem, imagine say for example, there isa goal to follow a path way leading on the top of the hill now and there are 2 optionsthat you have present it one is the direct path one is the slightly bounding path. Whatyou would want to choose is that you will probably want to choose direct path, the pathwhich has the most steeper in climb because it is kind of guaranteeing it is kind of tellingyou that very quickly you will reach there, but and there is the other path which is boundingwhich is going to take lot of times. A lot of times what people would do is, theywill directly choose path that it has the steeping climb and you know gives the chanceof solving this problem correctly, but you know when people in even in real life matterwhen people reach such a choice point they use what is called you know this kind of scenariowhat is hill climbing heuristic to a pick up alternatives that seem to lead to the goalstate most directly you know quick quick fix solutions efficient and fast solutions.And the thing is that hill climbing heuristic can be useful when one does not really haveenough information about the alternative you know because you do not have really lot ofinformation about what is going to happen in future you might be able you might wantto you know take these kind of quick decisions but like many heuristics the hill climbingheuristic also can lead you a stray, you know the biggest drawback is the problem solversmust consistently choose that alternative that appears to be most direct, but in thatin doing that you are ignoring slightly slower slightly a less direct, but a better alternativeyou know. For example, the most direct path sometimemay come to ban abrupt end the most direct path may offer dangers of falling down andstuff like that. So, the idea is the hill climbing heuristic is in that sense slightlyrisky heuristic to take each; obviously, as being heuristic does not really offer youa guaranteed solution and it is in that sense a high risk kind of decision. So, the hillclimbing heuristic obviously, as I was saying is not guaranty that you will reach the goalstate it just kind of allows you that kind of solution.So, that is from, they solved from about heuristics and some of the strategies of problem solvingthat we discussed we will talk about more strategies of problem solving in the nextclass. Thank you .