Memorizing algorithms isn’t something that can be accomplished easily as software code can be infinite. Furthermore, there is no real benefit to doing it. What’s important for software engineers is to learn and understand algorithmic principles.
This is because programmers develop algorithms using a finite set of instructions, so it can be advantageous to understand the various constructs used to build algorithms.
Understanding algorithms is a way of thinking that will enhance your skill set. When you are equipped with this knowledge, you will be able to take a look at an algorithm and quickly understand why it’s set up in a certain manner.
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It essentially works as a filter when you’re in evaluation mode subconsciously scanning through various principles when you encounter a problem. This almost becomes second nature to most developers who repeat this process on a daily basis.
So what principles should you be aware of? Here are 10 important algorithmic concepts that every programmer should know.
1. Matrix operations
As data science grows at lightning speed, it’s important to understand that matrix multiplication is a lot faster than you would expect. Further, great minds have developed incredibly unintuitive algorithms to make matrices multiply in a way that is anticipated.
Often, these algorithms aren’t necessarily used as the MPI and BLAS libraries provide incredibly fast matrix multiplication. Whenever you’re able to do multiple calculations in terms of matrix operations, your life will be a lot easier.
When it comes to general algorithms, backtracking is a popular option to find all (or some) solutions to computational problems. These can be constraint satisfaction problems which incrementally builds candidates to the solution while at the same time abandoning each partial candidate “c” as soon as it’s determined that “c” can’t be completed to a valid solution.
Backtracking can only be applied for problems that admit the concept of a partial candidate solution followed by a comparatively quick test to ascertain if it can be completed to a valid solution. If the table is unordered, it will be totally useless for locating any given value.
Further, since backtracking can eliminate a large number of candidates with a single test, it can be a lot faster than brute force enumeration of all complete candidates.
3. Binary search
Binary search is an important concept that shows up on everything from databases to convex optimization. When you need to find a specific value buried deep inside a large set of things, you can rapidly figure out which direction you have to go by utilizing binary search.
4. Karatsuba algorithm
The Karatsuba algorithm follows a “divide and conquer” approach to fast multiplication. Fast multiplication is important and this is achieved by breaking down large numbers into smaller numbers to enable multiplication of smaller numbers.
This method can only be applied to multiply the numbers in all base systems (for example, base-10, base-2, etc.).
5. Dijkstra's algorithm
The Dijkstra's algorithm is named after the computer scientist who first conceived it in 1956 (published three years later), Edsger W. Dijkstra. It can be described as an iterative algorithm that offers the shortest path from one specific node to all other nodes on a graph.
There are many variants of Dijkstra's algorithm, but it’s the original variant that found the shortest path between two nodes. However, a variant that’s more common fixes a single node as the “source node” and then goes on to find the shortest paths to all other nodes in the graph which creates a shortest-path tree.
6. Linear least squares
Linear least square problems correspond to a specific critical form of a statistical model called linear regression (which arises from regression analysis). At its most basic, the model is an ordinary least squares model.
7. Linear regression
With the evolution of machine learning (ML), it’s vital to fully understand the principles of linear regression. This prediction method that is hundreds of years old is a great ML algorithm to implement.
This is because it requires you to estimate properties from your dataset which is simple enough for a beginner to understand.
In its simplest form, linear regression assumes a straight line relationship between the following:
- Input variables (X)
- Single output variables (y)
The output variables (y) are calculated from a linear combination of the input variables (X). This simple concept can utilize statistics on the data to estimate the coefficients required by the model to make predictions on new data.
8. Hash table
A hash table or a hash map is a data structure that can implement an associative array of abstract data types. It’s also a structure that can map keys to the values and is an efficient method to store key-value pairs.
The hash table utilizes the hash function to compute an index into an array of slots from where the desired value can be identified. Knowing when to use a hash table to solve a problem is key to deriving the most benefit from this concept.
Partition-exchange sort or quicksort is a recursive algorithm that is known to be the fastest comparison-based sorting algorithm. This approach also requires minimal extra memory and also follows the divide and conquer philosophy.
10. Knuth–Morris–Pratt (KMP) algorithm
The Knuth–Morris–Pratt algorithm (KMP algorithm) is a string search algorithm that searches for the occurrences of a word within the main text string. It does this by employing observation techniques whenever a mismatch occurs.
In this approach, the word itself exhibits enough information to determine where the next match could be. This method negates the need to re-examine previously matched characters (so you can easily see the benefit of knowing it!).
What algorithmic principles would you add to this list? Please share your thoughts in the Comments section below.