LECTURE 21
OF THE DIVIDE-AND-CONQUER ALGORITHM
In this particular lecture, I seek to explain the divide-and- conquer algorithm and also to set a good foundation for the next lecture. For the sake of those seeing this term for the first time, I will try as much as possible to explain it in the simplest language. Myself, it was in the study of Discrete Mathemathics and Combinatorics that I first met with this concept and yours truly, the word ‘Algorithm’ itself is a mathematical invention. It projects from the name of the famous Persian Mathematician, Muhammad ibn Musa Al-Kwarizmi, referred in mathematics circles as the father of Algebra (al-jabr). Actually, the surname of this mathematician, Al-Kwarizmi was rendered in Latin as Algoritmi and hence the english word Algorithm.
Now to begin with, let’s look at what an algorithm is in general. An algorithm is simply a finite number of steps that solves a computational problem. The problem need not necessarily be computational. It can be any problem at all. But once we are able to find a terminating or a finite number of steps, which is very well-defined (or should we say general) and efficient in solving that problem, then what we really have is an algorithm. And all we seek or anticipate from a classic algorithm is that, it should be able to solve our problem (be it computational, or whatsoever) anytime it is fed with inputs from a well defined set. Knowing this, I shall proceed to explain what the divide-and-conquer Algorithm is.
Well, the divide-and-conquer algorithm is a special type of Algorithm, typically used in mathematics and computer science. This algorithm specializes in solving bigger problems or computational problems with rigid austerities. It does so by breaking the PARENT PROBLEM into fragments or sub-problems of the same type and then solving them independently or recursively until the problem is simpler enough to be dealt with directly. It then combines the solutions of those fragments or sub problems to be the solution of the bigger problem.
To render it concise and simpler, let’s say the divide-and- conquer algorithm solves a problem mainly by DIVIDING the problem into smaller bits, and then dealing with those bits. Like the name implies, it conquers a problem first by dividing it. And if I must say, most of our daily activities are a perfect models of the divide-and- conquer algorithm. Even in eating, we apply the same technique; we attack our meals by swallowing them down in bits. We equally cover our long distances by taking our steps in bits. Just think of any activity at all, and you will be able to trace the DAC in it. Nature does mimick or say portray this algorithm in all its dealing Even in separating and dividing the men of Shinar whose intention were to build a huge tower unto the heavens, the Lord did employ a similar technique. He, by creating a language barrier, defeated their vain purpose. Truly, unity is strength and division is weakness. We always divide to conquer. However, unity may not always project strength, in that satan does unite us at times to conquer us. Nevertheless, unity by far is strength.
Concluding on the DAC, we may but say it is an algorithm of nature and that a product of God’s Creation. For wisdom does also beckon us, that if we will DIE IN PEACE, then we first ought to DIE IN PIECES. And truly so, if we would rightly estimate our graves and dig it in bits, our final retirement into them will be but a simple consolation.
For “If we die in part every day of our lives”, says the 18th century saint, Archbishop Fenelon, “we shall have but little to do on the last”.
“O how utterly,” declared he in earnest, “will these little daily deaths destroy the power of the final dying.”
Advisibly so, if death will lose its hideous sting, then it first ought to be broken into bits or pieces. If we will faithfully divide the grave, we will conquer it for sure. Wherefore is the divide-and-conquer algorithm a very useful algorithm. It is more spiritual than mathematical.