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| Basic Strategies |
Basic Strategies
There are a number of basic problem-solving strategies that can be applied to most problems.
Top-down
With a top-down strategy, you begin with general principles and work towards specific examples that ultimately include the problem situation. The direction of general tospecific gives the strategy its name.
If you planned a meal using a top-down strategy, you might start with the nutritional requirements of an average adult and the nutritional values for a variety of foods, and eventually arrive at an appropriate shopping list, and finally a recipe for tonight’s supper.
The creation of legislation and governmental institutions in the United States of America has followed a top-down process. The Declaration of Independence was issued in June 1776. The new Constitution was written in 1787 and approved by congress in March 1789. This was followed in the same year by the passage of the Bill of Rights containing the first ten amendments to the constitution. Since that time, all other laws and governmental bodies of the United States have had to fit within the framework of the amended Constitution.
Most large computer programs are designed top-down, beginning with a detailed set of performance specifications. Then the primary and secondary features of the program are designed and specifications are created for exchanging information between parts of the program. The actual writing of computer code does not begin until the top-down design has been completed.
Bottom-up
As the name suggests, the bottom-up strategy is the opposite of the top-down. When using a bottom-up strategy for problem solving, you start with a specific aspect of a problem and then work towards a general solution.
If you want to improve your physical fitness, a top-down approach might include buying a new jogging suit and a book on weight lifting. A bottom-up approach might begin with skipping dessert and walking to work.
A bottom-up approach to home-building would begin with digging foundations and hammering nails. A top-down approach to home-building would begin with a site plan and an architectural design.
A trip to your family doctor for a yearly check-up would be part of a top-down approach to your health. A trip to the emergency department at your local hospital is usually a bottom-up strategy.
Left-right
The top-down and bottom-up approaches both imply that solving a problem involves an ordered sequence of events. The term ‘left-right’ is used here to imply that a problem can be approached from a number of different directions at the same time.
The left-right approach is commonly used in problem solving when you have a definite starting point and a definite goal. For instance, if you want to unravel a tangled ball of string, you often have to work alternately with one loose end, and then the other.
If you want to build a bridge across a river, it is often feasible to start construction from both banks with the goal of meeting in the middle.
Problems in deductive geometry often require a left-right approach. In these problems you typically begin with a given set of information and are seeking a particular conclusion. A left-right approach involves starting with the given information to see what other conclusions can be reached. Then you contemplate the ‘answer’ and work backwards; ‘If this statement is true, then what else must also be true?’ You work alternately from the ‘beginning’ and then the ‘end’ with the goal of finding a sequence of logical statements that will meet somewhere in the middle.
(Mathematicians, and wise students, then rewrite their solutions to make it seem as if there was a smooth and obvious deductive path from the given information to the desired conclusion.)
Trial-and-error
The trial-and-error approach involves making a reasonable estimate of what is required and then attempting to solve the problem using that estimate. The trial anderror approach is most effective when your problem is part of a well-behaved system.
Then the results tend to improve systematically as your estimates get closer to some optimum value. The key to success with a trial-and-error approach is to pause and analyze the results after each attempt at a solution. Then you can make systematic improvements in your estimates. Random guessing is generally a waste of time.
For equation solving, there are a variety of numerical techniques that make the trialand- error process as efficient as possible and ensure that no potential solutions are missed. The essential feature of ‘numerical methods’ is that successive trials are not random, but are based on computations that systematically lead towards a solution.
The ability of computers to rapidly carry out extensive and repeated computations makes them an ideal aid when using numerical methods for problem solving.
Trail-and-error methods should be avoided when dealing with delicate situations such as brain surgery, and when dealing with systems with critical values such as explosive devices.
There are a number of basic problem-solving strategies that can be applied to most problems.
Top-down
With a top-down strategy, you begin with general principles and work towards specific examples that ultimately include the problem situation. The direction of general tospecific gives the strategy its name.
If you planned a meal using a top-down strategy, you might start with the nutritional requirements of an average adult and the nutritional values for a variety of foods, and eventually arrive at an appropriate shopping list, and finally a recipe for tonight’s supper.
The creation of legislation and governmental institutions in the United States of America has followed a top-down process. The Declaration of Independence was issued in June 1776. The new Constitution was written in 1787 and approved by congress in March 1789. This was followed in the same year by the passage of the Bill of Rights containing the first ten amendments to the constitution. Since that time, all other laws and governmental bodies of the United States have had to fit within the framework of the amended Constitution.
Most large computer programs are designed top-down, beginning with a detailed set of performance specifications. Then the primary and secondary features of the program are designed and specifications are created for exchanging information between parts of the program. The actual writing of computer code does not begin until the top-down design has been completed.
Bottom-up
As the name suggests, the bottom-up strategy is the opposite of the top-down. When using a bottom-up strategy for problem solving, you start with a specific aspect of a problem and then work towards a general solution.
If you want to improve your physical fitness, a top-down approach might include buying a new jogging suit and a book on weight lifting. A bottom-up approach might begin with skipping dessert and walking to work.
A bottom-up approach to home-building would begin with digging foundations and hammering nails. A top-down approach to home-building would begin with a site plan and an architectural design.
A trip to your family doctor for a yearly check-up would be part of a top-down approach to your health. A trip to the emergency department at your local hospital is usually a bottom-up strategy.
Left-right
The top-down and bottom-up approaches both imply that solving a problem involves an ordered sequence of events. The term ‘left-right’ is used here to imply that a problem can be approached from a number of different directions at the same time.
The left-right approach is commonly used in problem solving when you have a definite starting point and a definite goal. For instance, if you want to unravel a tangled ball of string, you often have to work alternately with one loose end, and then the other.
If you want to build a bridge across a river, it is often feasible to start construction from both banks with the goal of meeting in the middle.
Problems in deductive geometry often require a left-right approach. In these problems you typically begin with a given set of information and are seeking a particular conclusion. A left-right approach involves starting with the given information to see what other conclusions can be reached. Then you contemplate the ‘answer’ and work backwards; ‘If this statement is true, then what else must also be true?’ You work alternately from the ‘beginning’ and then the ‘end’ with the goal of finding a sequence of logical statements that will meet somewhere in the middle.
(Mathematicians, and wise students, then rewrite their solutions to make it seem as if there was a smooth and obvious deductive path from the given information to the desired conclusion.)
Trial-and-error
The trial-and-error approach involves making a reasonable estimate of what is required and then attempting to solve the problem using that estimate. The trial anderror approach is most effective when your problem is part of a well-behaved system.
Then the results tend to improve systematically as your estimates get closer to some optimum value. The key to success with a trial-and-error approach is to pause and analyze the results after each attempt at a solution. Then you can make systematic improvements in your estimates. Random guessing is generally a waste of time.
For equation solving, there are a variety of numerical techniques that make the trialand- error process as efficient as possible and ensure that no potential solutions are missed. The essential feature of ‘numerical methods’ is that successive trials are not random, but are based on computations that systematically lead towards a solution.
The ability of computers to rapidly carry out extensive and repeated computations makes them an ideal aid when using numerical methods for problem solving.
Trail-and-error methods should be avoided when dealing with delicate situations such as brain surgery, and when dealing with systems with critical values such as explosive devices.
