Algorithmic Approach To Problem Solving

Algorithms and heuristics

Other means of solving problems incorporate procedures associated with mathematics, such as algorithms and heuristics, for both well- and sick-structured problems. Research in problem solving normally distinguishes between algorithms and heuristics, because each approach solves problems in different ways and with different assurances of success.

A problem-solving algorithm is a procedure that is guaranteed to produce a solution if it is followed strictly. In a well-known example, the "British Museum technique," a person wishes to find an object on brandish amongst the vast collections of the British Museum but does not know where the object is located. Past pursuing a sequential examination of every object displayed in every room of the museum, the person will eventually notice the object, but the approach is likely to consume a considerable amount of time. Thus, the algorithmic approach, though certain to succeed, is often tedious.

A problem-solving heuristic is an informal, intuitive, speculative procedure that leads to a solution in some cases merely non in others. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm. Thus, if one had an idea of where to look for the sought-after object in the British Museum, a swell deal of time could be saved by searching heuristically rather than algorithmically. But if one happened to be wrong about the location of the object, one would have to try some other heuristic or resort to an algorithm.

Although there are several problem-solving heuristics, a small number tend to be used frequently. They are known as means-ends analysis, working forward, working backward, and generate-and-test.

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In means-ends analysis, the problem solver begins past envisioning the end, or ultimate goal, and then determines the all-time strategy for attaining the goal in his current situation. If, for example, ane wished to bulldoze from New York to Boston in the minimum time possible, and then, at any given point during the drive, one would choose the route that minimized the time it would take to cover the remaining distance, given traffic weather, weather conditions, and so on.

In the working-forward approach, every bit the proper name implies, the problem solver tries to solve the problem from commencement to cease. A trip from New York City to Boston might exist planned simply by consulting a map and establishing the shortest route that originates in New York Urban center and ends in Boston. In the working-backward approach, the problem solver starts at the cease and works toward the beginning. For example, suppose one is planning a trip from New York Urban center to Paris. One wishes to arrive at one's Parisian hotel. To arrive, one needs to take a taxi from Orly Airport. To go far at the airdrome, 1 needs to fly on an airplane; and and so on, back to one's point of origin.

Often the least systematic of the problem-solving heuristics, the generate-and-test method involves generating alternative courses of action, ofttimes in a random fashion, and so determining for each course whether it will solve the problem. In plotting the road from New York City to Boston, one might generate a possible route and see whether it can get one expeditiously from New York to Boston; if then, ane sticks with that route. If not, one generates another road and evaluates it. Eventually, one chooses the route that seems to work best, or at least a route that works. Every bit this case suggests, it is possible to distinguish betwixt an optimizing strategy, which gives one the best path to a solution, and a satisficing strategy, which is the first acceptable solution one generates. The advantage of optimizing is that information technology yields the best possible strategy; the advantage of satisficing is that it reduces the amount of fourth dimension and energy involved in planning.

Obstacles to effective thinking

A better understanding of the processes of thought and problem solving can be gained by identifying factors that tend to foreclose effective thinking. Some of the more common obstacles, or blocks, are mental gear up, functional fixedness, stereotypes, and negative transfer.

A mental set, or "entrenchment," is a frame of heed involving a model that represents a problem, a problem context, or a procedure for problem solving. When problem solvers have an entrenched mental fix, they fixate on a strategy that normally works well but does not provide an effective solution to the particular problem at paw. A person tin become so used to doing things in a certain fashion that, when the approach stops working, it is hard for him to switch to a more than effective way of doing things.

Functional fixedness is the disability to realize that something known to take a particular use may likewise be used to perform other functions. When one is faced with a new problem, functional fixedness blocks i'due south ability to use old tools in novel means. Overcoming functional fixedness first allowed people to use reshaped coat hangers to get into locked cars, and it is what offset allowed thieves to pick simple bound door locks with credit cards.

Another block involves stereotypes. The most common kinds of stereotypes are rationally unsupported generalizations most the putative characteristics of all, or nearly all, members of a given social group. About people acquire many stereotypes during childhood. One time they become accustomed to stereotypical thinking, they may non be able to come across individuals or situations for what they are.

Negative transfer occurs when the procedure of solving an before problem makes later problems harder to solve. Information technology is assorted with positive transfer, which occurs when solving an earlier problem makes it easier to solve a later trouble. Learning a foreign language, for example, can either hinder or help the subsequent learning of another language.