While data structures serve as the foundation of a software application, algorithms denote the sequence of operations needed to handle these data structures. In short, an algorithm is a sequence of operations required to solve a particular problem or conduct some calculations.

Although inefficient algorithms may not cause any harm to the application while dealing with small amounts of data, as soon as we reach terabytes of data being processed per second by our applications, millions of cloud requests being handled and machine learning operations, the algorithms’ efficiency become vital for the business. Every software engineer should learn about algorithms to write scalable software and pass technical interviews.

1. Sorting Algorithms:

Arranging Data LayerSorting is a very common problem in Computer Science. Sorting data into a specific order (numerically, alphabetically, chronologically) becomes a prerequisite for optimizing other operations (searching).

Divide and Conquer: Merge Sort & Quick SortSimple algorithms such as Bubble Sort or Insertion Sort have the quadratic time complexity of $O(n^2)$ making them unsuitable for large arrays of data. Nowadays, the divide and conquer approach is widely used.

Merge Sort is an algorithm that recursively splits an array into two parts till elements become independent. Then it sorts the split elements and combines them into a single sorted array. Merge Sort guarantees the time complexity of $O(n \log n)$ in any case (best/worst/average). Nevertheless, Merge Sort requires additional $O(n)$ space to store temporary results of splitting.

2. Searching Algorithms:

Searching for a Needle in a HaystackNow that your data tier is sorted, the next thing you want to do is searching for a particular element in the array.

Linear Search vs Binary Search: The Power of LogarithmsIn case you need to find an element in an unsorted array, the only way out is to check every element from the 0 index till $n$, this approach is called Linear Search. It takes $O(n)$ time. But what happens when the data tier is sorted? You may use Binary Search.

Binary Search starts by comparing your element to the middle element of the array:

If the element equals the middle element, you stop the search here.

If the element is less than the middle element, the right half of the array becomes irrelevant.

If the element is greater than the middle element, the left half of the array becomes irrelevant.

The efficiency of Binary Search may be shown in the following way: searching for a user among 4 billion records using Linear Search will take up to 4 billion operations. Binary Search will find that user in just 32 operations.

3. Graph Traversal Algorithms:

Analyzing ConnectionsA graph is a non-linear data structure describing connections between multiple vertices. Traversal algorithms describe the way of exploring vertices of the graph.

Breadth-First Search (BFS): Exploring Layers by LayersBFS starts with exploring the root node and its neighbors. Next, it expands nodes in the second layer of depth and so on. Internally, BFS relies on the Queue data structure (First-In, First-Out).

Having a uniformly expanding nature, BFS is the algorithm of choice to find the shortest path in an unweighted graph. It is used to drive routing algorithms in GPS mapping software, social networks, and peer-to-peer networks.

Depth-First Search (DFS): Expanding as Deep as PossibleConversely to BFS, DFS starts with exploring a root node and exploring its branch as far as possible. After that, it backs up to the root and explores another path. DFS uses the Stack data structure internally (or the call stack of the programming language in case of recursive implementation).

4. Pathfinding Algorithms:

Finding a Shortest RouteWhile BFS is able to find the shortest route on an unweighted grid, most real-life problems involve more complicated situations where the cost of moving depends on every edge.

Dijkstra’s AlgorithmDijkstra’s algorithm finds the shortest path from the source node to all other nodes of the graph. Dijkstra’s algorithm keeps the list of shortest distances to all vertices of the graph from the starting node. Then it extracts the minimum-distance vertex from a priority queue (heap) and updates distances accordingly. This algorithm drives all network routing protocols (e.g., OSPF), and routing software.

5. Hashing and Cryptographic Algorithms:

Securely Handling DataIn addition to the operations with data structures, algorithms are used to validate integrity and confidentiality of information.

Hashing Algorithms (MD5, SHA-256)A hashing algorithm accepts an input string of arbitrary length (from a password to multi-gigabyte files) and produces a string of fixed length. Hashing functions are irreversible and deterministic, which means that it is impossible to get the input from a hash and the same input will always produce the same hash.

Moreover, a good hashing function produces different hashes with even minimal changes in the input. Hashing functions are widely used for password storage, indexing keys in databases, and ensuring file integrity.

6. Dynamic Programming:

Avoiding Unnecessary CalculationsSometimes to solve a particular problem, you will have to decompose it into smaller subproblems. However, in case of a naive recursive approach, the same subproblem may be calculated several times. Dynamic Programming (DP) is a technique aimed at avoiding redundant calculations.

Frequently Asked Questions (FAQ)

1. What is the difference between Space Complexity and Time Complexity?

Time Complexity describes the relation between the time of execution of an algorithm and the size of the input data ($n$). Space Complexity describes the additional amount of memory required for execution. A production-ready software engineer has to balance these two properties, as decreasing execution time often leads to allocating more memory.

2. Why Quick Sort is preferred over Merge ?

Sort if its worst-case performance is $O(n^2)$?While Merge Sort provides the guaranteed worst-case time complexity of $O(n \log n)$, it requires an additional array of size $O(n)$ to be allocated, which is undesirable in the case of huge arrays. Quick Sort is an in-place sorting algorithm which sorts the data in place with the $O(\log n)$ space consumption. Moreover, in practice Quick Sort is faster due to CPU cache optimizations.

3. What is a “Greedy Algorithm”?

How does it differ from Dynamic Programming?Greedy algorithm tries to choose the optimal option in every step hoping to get the overall optimal solution. Although efficient, greedy algorithm may not work correctly in certain cases. Dynamic Programming finds a globally optimal solution calculating all possible options after decomposing the problem into overlapping subproblems.