Introduction
Algorithms are what enable these fields to operate i.e. what runs a computer program. Concerning this, computer algorithms are just another name for the sequence of the steps a computer has to follow to solve the problem or perform the tasks. The quantity of algorithms is immense each being the most powerful or more menial in their own right. While most of these algorithms are similar in the way they operate, certain algorithms rise above others due to efficiency, versatility, or new new-oriented approach. Through this personal blog post, we will delve into some of the top algorithms of our time.
Table of Contents
QuickSort
QuickSort is a base of a faster and more structured sorting method that divides an array of data into smaller arrays. A dimension is split into two parts; in the first one will be put all the elements that are less than the specified value, the so-called pivot, and in the other all the elements more than the pivot.
The other.QuickSort algorithm separates the array, and it is called until the two subarrays have been already sorted. It has the average and worst-case complexity of O(nlogn), which implies that it is optimal for large-sized data sets.
Dijkstra’s Algorithm
Dijkstra’s algorithm is a widely known algorithm for designing the shortest path between various input nodes in a graph. Dijkstra is known to be the pioneering computer scientist who provided the idea in 1956.
A block of nodes which is the minimum distance from the source is what the Algorithm is used for. It is a greedy algorithm, and hence, at each step, it will always make the best possible choice (out of the multiple choices available) and keep searching for the ultimate best solution. The AI algorithm employs a priority queue to determine the order of the next nodes in the queue. The priority queue reformulates nodes placed sequentially in their distance from the source node.
Binary Search
The Binary Search is a simple as well as efficient algorithm that is helpful when looking for an element of a list that is sorted. This is an efficient algorithm with two cases: the worst one is O(logn) and the average case is O(logn).
So, decreases the execution time by speeding itself up when dealing with large datasets compared to a linear search.
The binary search algorithm divides the search interval into two parts and repeats the process which is halving until reaching the desired result. If the value of the search key is less than the number that is in the middle of the interval, the algorithm proceeds to the lower half. Only then, it should be the other way round. Iteration of this algorithm continues until it finds the value or the interval is empty.
Merge Sort
Merge Sort is a highly adaptable sorting algorithm that recursively divides the array into two halves, sorts those halves, and then merges them. The merging sort finds this application and its time complexity is O(nlogn). At any given time rather it consumes extra space hence it is less complex.
Breadth-First Search (BFS)
BFS (Breadth-first Search) stands for a tree or graph data structure searching or traversing algorithm. It starts with the root tree (or a random node on a graph) and explores all nodes on the same level before shifting to the ones on the next level. It seems especially important for the shortest route in the unweighted graphs.
Depth-First Search (DFS)
Another algorithm, viz. Depth-First Search (DFS), also works for traversal or search of tree or graph data structures. The algorithm begins the exploration at the root node, and it proceeds with exploring all the branches up to the level possible, before backtracking. DFS is a versatile algorithm and in many cases, it is used for cycle detection, pathfinding, and topological sorting.
Floyd-Warshall Algorithm
Floyd-Warshall algorithm is an algorithm that is used for solving the problem of finding shortest paths in a graph with weighted edges (positive or negative). In graphs with such weights, the negative cycle can be met. The algorithm deals with the path traversal between all vertex pairs by using all possible path acts through the graph. With this O(V3) complexity, it ensures that the algorithm has polynomial space and time comparisons in a graph.
These heuristic techniques combined with some others mentioned above serve as the basis for the solving of issues in computer science. They are all very different in what capacities they can be used and learning when to use which would lead to becoming an algorithmic thinker.
Bellman-Ford Algorithm
The role of the Bellman-Ford Algorithm is to be able to find a path that is the shortest distance from a source vertex to all other vertices in the graph. This algorithm can handle some cases of graphs, where some of the edges are negative.
The Bellman-Ford algorithm begins its operation by setting the distances from the source to all nodes to infinite and the distance to the source itself to 0 which is the initial value. It, finally can relax all the edges ∣V∣−1 times where ∣V∣ is the being the number of vertices. Taking a required pass happens through the procedure in which we scan all edges and update the distances. For edge (u, v), the weight value will be changed to u-v if the current distance of v is more than then the sum of u-v and u’s distance.
The order of complexity of Bellman-Ford is O(∣V∣∣E∣) and it shows the time required for running it proportional to ∣V∣∣E∣ where ∣V∣ is the number of scales and several vertices are the number of nodes because the fewer neighbors the person has the fewer likely it is that they catch some disease. It is slower than Dijkstra’s, but also more flexible – it will work with weights of any sign.
Knapsack Algorithm
One of the many optimization problems found in combinatorics is the Knapsack algorithm. Once given a list of the items coupled with the weight and the value, it rates the amount of each item to assemble a collection in which its total weight is lower or equal to a given finish line and the total value as large as possible.
The knapsack problem can be solved with a dynamic programming way, where we first solve the simplest case of the knapsack problem and further use the obtained solution to solve the whole knapsack problem. We use the table’s rows as items and the weight of each as columns. Then, for the wxthth row of the table, we put the weight needed to collect the n items that their total weight would be w. The encoding complexity of the Knapsack algorithm is O(nW) – the convention is to place these things in the form of f(n) = W.
K-Means Clustering
K-means clustering is one type of unsupervised learning algorithm that places components in a relevant cluster based on characteristics. There is one thing that you should know about this. It is called “K-Means” because it forms k clusters from the data, where k is a variable that is given by the user.
The algorithm consequently starts the loop to assign each data point to one of the K groups based on the feature attributes. Data objects are positioned according to their closeness, which is determined by feature similarity via Euclidean and/or Manhattan distances.
The K-Means algorithm’s time complexity is given by O(n). Which is n corresponding to the number of data points. Nevertheless, it is highly scalable and its efficiency is evident in the large data processing operations that it can handle.
These particular algorithms, along with the ones that already have been mentioned, are the essential elements not only of the various specialties within computer science but also of solving efficient problems. Those differ with the type of scenarios they can be applied and a general understanding of its use can your algorithmic thinking skills.
Conclusion
Let me show you only one from each area of computing; algorithms that represent the best thinking that we have so far. The efficiency of QuickSort, Dijkstra’s Algorithm, and Binary Search in solving existing problems of computing should not be looked down upon. Learning algorithmic thinking is a critical aspect of becoming a qualitative software professional. Now, keep in mind that the most suitable algorithm for you depends on each situation. Of course, each case has its specific algorithm with it!
