please see discussion below and respond with 150 words or more.
Today ill choose the main two sorting algorithms in the background materials to answer the first question.
Lets discuss how Selection and Quicksort work!
In its simplest form, a selection sort algorithm sorts the data by searching through a list for the smallest element then placing this in the first index position. Once this is complete, it then repeats itself moving up in elements until the whole list has been sorted. As others have noted, the time complexity for this algorithm is O(n2). Having a time complexity of O(n2) makes it a potentially very slow algorithm, especially if the data set is large (James, 2015).
Quicksort will sort an array by dividing it into two parts, it uses a pivot element to compare and divide the array into higher/lower indexes of the pivot value. Quicksort is implemented in a recursive manner until the whole array is sorted. Typically in ascending order. The worst case performance scenario O(n2), the same as selection sort, but on average will perform at O(n log n) (James,2015).
Graphs are nonlinear data structures that consist of a set number of nodes(vertices) and a set of edges that connect the nodes.
In graphs, a pair (x,y) is called an edge. an edge tells us that the x node connects to the y node.
When viewing a graph, the dots are the vertecies/nodes and the lines are the edges.
When it comes to questions that graphs can solve.
Anything with connected nodes is by definition a part of the graph theory domain. Any tree or network and more. Social networks, semantic networks, dependency trees, etc.
These can be used to map out chains of events, and connections. This can be used to also find the shortest possible route between nodes as well as determine root causes of issues within routes/chains/relationships.