apart from giving us the framework of divide and conquer methodology also gives us a methodology that we follow repeatedly during this course.

This way of breaking down the problem has found wide application in sorting, selection and searching algorithms.

search problem aims at finding the smallest as well as the biggest element in a vector A of n elements. By the steps of Divide and Conquer, the vector can be divided into sub-problem as shown below.

is an equation or inequality that describes a function in terms of its value on smaller inputs.

we guess a bound and then use mathematical inductiont prove our guess correct.

converts the recurrence into a tree whose nodesrepresent the costs incurred at various levels of the recursion. We use techniques for bounding summations to solve the recurrence

provides bounds for recurrences of the form

T(n) = aT(n / b) + f(n)

which involves breaking a big issue into smaller subproblems that may be solved individually and then combining their solutions to solve the original problem

It is a classic case of the use of the divide and conquers methodology.

It is an efficient technique for *1/1 searching in a sorted array. It works by comparing a searching element „e" with the array's middle element A(mid).

This is another method of sorting that uses a different methodology to arrive at the same sorted result. It "Partitions" the list into 2 parts but not necessarily at the center, but an arbitrarily "pivot" place and ensures that all elements to the left of the pivot element are lesser than the element itself and all those to the right of it are greater than the element

It is a method of choosing a subset of a dataset as the solution set that results in some profit.

It is a technique for designing algorithms that consists of decomposing the instance to be solved into a number of smaller sub instances of the same problem, solving successively and independently each of these sub instances, and then combining the sub solutions thus obtained obtain the solution of the original instance

It is a process of arranging a set of elements in some order. We can apply the divide-and-conquer method to the sorting problem.

1st step to perform the divide and conquer technique

starts with the least cost edge. Then, it chooses another edge that is adjacent to this edge and is of least cost and attaches it to the first edge.