From organizing your closet to paying bill for dinner with friends, we face many mathematical problem solving in real life. It makes up large part of our daily life. When solving a problem choose the right approach to arrive at the best solution, especially when it comes to planning a future career. Adopting an algorithm is an effective technique to find the best possible solution that resolves the issue. One such problem solving algorithm is divide and conquer.
What is Divide and conquer?
It is an algorithmic paradigm, also a military strategy which can be used to deal with painful tasks in daily life. It is a very simple technique in which the main problem is sub divided into smaller and manageable segments. These sub segments can be easily solved and ultimately the bigger problem is conquered. One cannot beat the whole beast all at once. One needs a strategic way to take over and so the path of success becomes easier.
Method of divide and conquer:
- Divide the problem into a number of sub problems that are smaller instances of the same problem.
- Conquer the sub problems by solving them recursively. If they are small enough, solve the subproblems as base cases.
- Combine the solutions to the sub problems into the solution for the original problem.
Strategy of Divide and Conquer:
UNDERSTAND the problem:
- Analyse the situation carefully. You can take mental notes on the key points of the existing problem.
- Record all the data present in the problem. It is always a necessary part to track down the source or origin of the problem.
- Restate the problem in other ways in order to clarify what needs to be solved.
PLAN a solution strategy:
- Try to divide the problem into various sub divisions.
- Map out your strategy in a diagram or list it out. Either mentally or with the help of pen and paper.
- Apply one or more of the strategic solutions to each of the sub problems so that the base cases are solved. Look for a pattern so that the sub cases can be solved with reference to one another.
EXECUTE your strategy:
- Write down the steps of your solution as you carry out your plan so as to organize your thoughts.
- Double-check your steps in order to avoid propagating errors.
- Assess your progress.
- Don’t spin your wheels! – if you find yourself bogged down, step away from the problem and return to it later.
REFLECT on your result:
- Does your final answer correspond to common sense?
- Check the consistency of your answer by testing it on the cases
- Take note of successful methods you employed to further expand your toolbox of problem solving techniques.
So basically, divide any big problem into smaller problems (to make our life easy), solve individual problems and combine the solution of small problems to get the solution to big problem.
Also learn the general problem solving strategy here. You can understand the way of approaching any problem. Apply this divide and conquer method to solve problems.
Solve one part at a time. It is sometimes possible to make a problem easier to solve by attacking one part at a time! Practice it then no problems can left you stranded!