Intro to Divide and Conquer Algorithm

In the branch of computing and Engineering, data Technology and each one the associated branches among these fields the term “Divide associated Conquer” is an rule style paradigm supported the principle of formula ( multi-branched).BY the name “Divide and Conquer” we have a tendency to area unit ready to realize it are a few things regarding dividing a haul and obtaining an answer right, however however will it really work?. during this algorithmic approach, the rule designed works recursively by breaking down the matter in hand, into 2 or additional sub-problems or components supported the complexness of the matter till it’s easy enough to be solved directly. This sub-problems or components are referred to as atomic or fractions. This atomics or fractions area unit recursively weakened into additional and additional atomic or fractions till they are weakened into a kind which can be solved . once resolution these fractions or atomics they are however traversed back recursively however now instead of breaking down the matter , the {problems} area unit united back with their recursively broken counterparts then the desired resolution for that specific problem is generated.

Divide and Conquer Approach is split into 3 processes and these 3 processes kind the concept of divide and conquer paradigm for problem-solving

1) Divide

The first and foremost method for resolution any drawback exploitation Divide and Conquer paradigm. As advised by the name it’s perform is solely to divide the matter into sub-problem that in turn if area unit additional advanced then area unit {again|once additional} divided into more sub-parts. Basically , if we have a tendency to contemplate {for instance|as associate example|for example} binary search ( an example of Divide and Conquer approach ) the given list is broken ( beneath some specific contemplate outlined by its rule and user input ) into single parts among that then the part to appear is compared and so the user gets a prompt whether or not the part is within the list.

2) Conquer

This method is mentioned as ‘ Conquer ’ as a result of this method is what that performs the essential operation of a defined rule like type in cases of assorted types, finds the part to be searched simply just in case of binary search, multiplying of the numbers in Karatsuba rule and etc. however nearly among algorithms a minimum of the foremost basic ones that we have a tendency to study largely area unit thought-about to be solved throughout this half since the divide half breaks them into single parts which may be merely solved .

3) Merge

This is the last method of the ‘Divide’ and ‘Conquer’ approach whose perform is to recursively make the primary drawback however what we have a tendency to get now’s the solution to it drawback. In merge procedure, the solved parts of the ‘ Conquer ‘ area unit recursively united along a bit like the means they divided inside the initiative i.e. ‘ Divide’.

The steps ‘Conquer’ and ‘Merge’ work thus shut that typically they are treated mutually step. The Divide and Conquer area unit usually enforced in 2 ways:

1. Naturally i.e. by exploitation formula

2. expressly i.e. by exploitation information structures like stack and queues etc

How to establish Divide and Conquer issues

When we have a haul that appears almost like a celebrated divide & conquer rule (such as merge sort), it’ll be helpful.

Most of the time, the algorithms we have a tendency to style area unit aiming to be most nearly like merge type. If we’ve associate rule that takes a listing and will one thing with every part of the list, it would be ready to use divide & conquer.

For example, understanding the foremost necessary item of a listing . Given a listing of words, what proportion times will the letter “e” appear?

If we’ve associate rule that is slow which we might like to hurry it up, one in every of our initial choices is divide and conquer.

There isn’t any obvious tell-tale signs apart from “similar to a celebrated example”. however as we’ll see within the next section, we will check if it’s resolvable exploitation divide & conquer.

Pros of Divide and Conquer Strategy

1. Solves tough issues with ease.

2. Algorithms designed with Divide and Conquer methods area unit economical compared to its counterpart Brute-Force approach for e.g. if we have a tendency to compare time complexness of easy mathematical operation i.e. O(n3) that of Strassen’s mathematical operation i.e. O(n2.81).

3. Algorithms designed beneath Divide and Conquer strategy does not need any modification as they inhibit correspondence and will simply be processed by data processing systems.

4. It makes economical use of buffer store this happens thus as a result of that issues once divided gets thus little that they’ll be simply solved within the cache itself.

5. If we have a tendency to use floating numbers then the results could improve since spherical off management is very economical in such algorithms.

Cons of Divide and Conquer Strategy

1. Divide associated Conquer strategy uses formula that makes it slightly slower and if slightly error happens inside the code the program could enter into an infinite loop.

2. Usage of express stacks could build use of further area.

3. If activity a formula for no. times bigger than the stack inside the mainframe than the system could crash.

4. selecting base cases is additionally a limitation as choosing little cases may match if the cases area unit taken a lot of more than the capability of the system than issues could occur.

5. typically a case wherever the matter once attenuated leads to same subproblems which can needlessly increase the resolution time and further area could also be consumed.