P and NP is the problem that always comes out while we are studying algorithms, and usually, it comes up at the end of any algorithms book. The reason it comes out at the latest pages is that it is quite an advanced topic.

The book has been written by Cal Newport, a professor at the Georgetown University (Washington D.C). He wrote about the importance of the focusing and concentration on the work, by increasing the limit of the time we usually allocate for it. The Author writes a lot of different use cases for great historical people (some of them are still alive), how they have been going deep into their work. Who used what kind of technique, and how the technique was mastered. While going through the book I have realized that all of these characters had some similar points and patterns. Concentration Technique !!!

Problem

Given a graph which represents a flow network where every edge has a capacity. Also given two vertices source S and sink T in the graph. Find out the maximum possible flow from S to T with following constraints

Usually, the sorting algorithms determine the sort based on comparisons between the input elements. That is why they called comparison sorts algorithms. In here we would like to consider non-comparison sorts.

Algorithm is any well-defined computational procedure that takes some value, or set of values as input and produces some value, or set of values, as output.

The quicksort algorithm has a worst-case running time of O(n^2) on an input array of n numbers, and worst case happens when the array is sorted in descending order. Despite a worst-case running time, quicksort is often the best practical choice for sorting. Its average expected running time is O(n log n), and it has an advantage of sorting in place.

Merge sort is another sorting algorithm that applies the divide-and-conquer approach, where the problem is divided into sub-problems recursively. Keep dividing until the subproblem becomes primitive. After that, the results of the divisions are combined and formed the result for the upper caller and so on.

The i th *order statistic of a set of n elements is the i th smallest element. Simply saying the minimum of a set of elements is the first order statistic (i = 1) and maximum is the nth order statistic (i = n). Median is the informally considered as a “halfway point” of the set.

Insertion sort, which is an efficient algorithm for sorting a small number of elements. Insertion sort works the way many people do it by hand while playing a card game (Though personally i would not sort the cards while playing, because there are too many skill-full guys, who may take an advantage of it)