Algorithms

8 min readAug 14, 2024

Algorithms are the foundation of problem-solving in computer science, guiding how computers perform tasks efficiently. This blog will explore four fundamental algorithms: Linear Search, Binary Search, Bubble Sort, and Selection Sort. These algorithms are essential for searching and sorting data, which are vital operations in many software applications. Whether you’re a beginner or an experienced programmer, understanding these basic algorithms is crucial for mastering efficient coding. We’ll cover the differences between Linear and Binary Search, followed by the basics of Bubble Sort and Selection Sort, providing a solid foundation for more advanced techniques.

Liner Search

The linear search algorithm is another alternative name for the sequential search algorithm. It is the most straightforward type of search algorithm. In the linear search method, we just cross the list completely check for every element in the list, and compare it with the data for which location is to be found. If it’s found, it returns the item's location, or it results in a ‘NULL’ return by the algorithm.

Advantages of Liner Search

Simplicity — Linear search can be easily comprehended and implemented. It’s a simple algorithm with very simple logic and simple loops, making it very fitting for anyone just starting in the field of algorithms about searching.
No Pre-Processing Required — Linear search can be applied to data structures that are unsorted or have no specific order as a prerequisite.
Versatility — This algorithm is applied to all data structures, whether arrays, linked lists, or even collections when random access isn’t possible.
Low Memory Usage — Linear search has a constant space complexity of O(1) since it requires only a small number of variables to maintain the current position and the target.
Works with Small Dataset — Sometimes, the simplicity of linear search can overcome the additional benefits that are brought in by the complex algorithms of search, especially when dealing with small datasets.
No Assumptions — Another merit of linear search is that it does not make any assumptions about the distribution or properties of the dataset.

Disadvantages of Liner Search

Inefficiency for Large Datasets — Linear search has a time complexity of O(n), where n is the number of elements in the dataset to be searched. As such, it can prove inefficient over large datasets because it may end up examining every element.
Poor Performance — The performance of linear search is poor compared to other advanced search algorithms like binary search, especially when the size of the dataset becomes large.
Not Suitable for Sorted Data — Linear search does not use the fact that the dataset is sorted, unlike binary search, which is much faster on sorted data.
Searches Are Inefficient if Done Frequently — As a result of the linearity in its time complexity, linear search can turn into a bottleneck in case many search operations are needed.
High Time Complexity — Each of the search operations, it probably goes through all the elements; this could be time-consuming, especially where there are large numbers of elements to be dealt with in the dataset.
Poor Scalability — Linear search has very poor performance for large data sizes; it is not appropriate for applications requiring fast queries on big datasets.

Binary Search

Binary search is a searching technique that works efficiently on ordered lists. Therefore, we need to ensure the list is sorted to perform the binary search for an element in some list. Binary search is a divide-and-conquer approach where the list is divided into two halves and the required element is compared with its middle element. In the case of a match, it returns the location of the middle element; otherwise, it searches into either half depending upon the result produced through the match.

Advantages of Binary Search

Efficiency — Time Complexity: Binary search runs in O(log n), making it much faster compared to linear search’s O(n) for large data sets. It manages this by reducing the size of the search space by half with each step.
Performance on Large Datasets — Binary Search, due to its logarithmic time complexity, is viable for very large data sets on which a linear search would be impractically slow.
Predictable Performance — One of the important properties of binary search is that it is predictable its performance does not vary with the size of data beyond its logarithmic growth. Predictability is a desirable property in several performance-sensitive applications.
Fewer Comparisons — Binary search has fewer comparisons compared to linear search; thus, it brings about performance benefits, mostly where comparisons are dear operations.
Immutable Data — Binary Search is very good at searching datasets that do not change frequently since the overhead of maintaining sorted data is justified by its fast search times.

Disadvantages Of Binary Search

Requires Sorted Data — The biggest disadvantage of binary search is that it requires the data to be sorted previously. The process of sorting can be fairly computationally expensive O(nlogn)), which is counterproductive when applying binary search for frequently changing datasets.
Implementation Complexity — The implementation of binary search in its recursive form, in particular, is complex due to the careful handling of index calculations and boundary conditions when compared to linear search.
Inefficient over Small Dataset — For small datasets, binary search does not bring much benefit in performance over linear search because added overhead from sorting and extra logic associated with binary search may not be justifiable.
Not Suitable for Linked Lists — Binary search is also inappropriate for data structures where random access is forbidden, like linked lists, because elements in these structures cannot be efficiently accessed by their index.
Overhead of Maintaining Sorted Data — In the case of frequently updated dynamic data, maintaining the list in a sorted fashion may be too expensive to gain the advantages of binary search on search.
Non-Trivial Index Calculations — Care should be taken that no overflow occurs during the midpoint calculation. This is especially true for languages that do not handle integer overflows gracefully.

Bubble Sort

The mechanism of bubble sort works based on repeated swapping of the adjacent elements until they are not in the intended order. It is so named because the movement of array elements is just like the movement of air bubbles in the water. Bubbles in water rise up to the surface similarly, the array elements in bubble sort move to the end in each iteration. Though it is easy to use, it is primarily used as an educational tool because the performance of bubble sort is poor in the real world. It is not suitable for large data sets. The average and worst-case complexity of Bubble sort is O(n2), where n is many items.

Advantages of Bubble Sort

Simplicity — It is easy to understand, thus making it a very good algorithm for educational purposes and beginners in algorithms. The logic behind the algorithm includes only simple comparisons and swaps, which are pretty easy to implement and trace.
In-place Sorting — Bubble sort is an in-place sorting algorithm that means it requires only a small constant amount of additional memory space for its execution. There is no need for additional space for any extra data structures like arrays or lists to hold the intermediate data.
Stability — Another important property of Bubble Sort is that it is a stable sorting algorithm; that is, it produces the same result as any other stable sorting algorithm. This means relative order between equal elements is maintained in the sorted array. This point often becomes quite significant when the key to be used for sorting is a subset of the data.
Early Termination — This algorithm can be optimized by adding a condition to stop early if no swaps are made in a pass through the array, which means it is already sorted. This optimization will enhance the performance for nearly sorted arrays.

Disadvantages of Bubble Sort

Inefficiency — Among the algorithms for sorting huge data sets, the Bubble sort is highly inefficient. This will be with an average and worst-case time complexity of O(n2)O(n2). Therefore, it is unfit to sort a huge list or array.
Performance — Even in the best case, when the array is already sorted, the amount of comparisons that Bubble Sort does is (n−1)(n−1). Hence, in any case, for the best-case time complexity, it is O(n)O(n). Under these circumstances, a more efficient algorithm will be able to do better.
Non-Essential Operations — The algorithm wastes comparisons and swaps, even when the elements are in order, thus inserting additional operations that lower performance.
Low Practical Value — Due to its inefficiency, bubble sort is rarely used in real applications, except perhaps in education or very small dataset sorting.

Selection Sort

In selection sort, on every pass, the smallest value is selected from the unsorted elements of the array and inserted into its proper position in the array. It is also one of the easiest algorithms. It is an internal comparison sorting algorithm. This algorithm divides the array into two parts: one is a sorted part, and another is an unsorted part. First of all, the sorted part is empty and the unsorted part is the array given. The part that is sorted is placed on the left, while the one that is not is on the right. In selection sort, the first smallest element is selected from the unsorted array and placed at the first position. Then, the second smallest element is selected and placed in the second position. The process continues till the array is completely sorted.

Advantages of Selection Sort

Simplicity — The selection sort algorithm is straightforward, and it is easy to learn and implement because it derives from a straightforward idea: selecting elements in an increasing or decreasing manner.
In-place Sorting — This sorting algorithm is done in-place, meaning that it uses only a constant amount of additional memory space, O(1)O(1), beyond the input array itself.
Good Performance on Small Lists — For small arrays or lists, simplicity, and low overhead can be the significant advantages of Selection Sort.
Predictable Pattern — The number of swaps performed by this algorithm is always exactly n−1n−1 which may be useful if writing to memory is significantly more expensive than comparisons (although the same number of swaps can be achieved by better algorithms like Heap Sort).

Disadvantages of Selection Sort

Inefficiency — The average and worst-case time complexity of Selection Sort is O(n2)O(n2), where denotes the number of elements in the array. This makes it inefficient for large datasets compared to more advanced sorting algorithms like Quick Sort, Merge Sort, or Heap Sort.
Unstable — The fact that Selection Sort is not a stable sorting algorithm means that it can change the relative order of equal elements, which might be considered as one of the negative sides when sorting data structures with complex fields.
Bad Performance on Already Sorted Arrays — Unlike other simple sorting algorithms, including Bubble Sort with its early termination optimization, Selection Sort does not benefit from the partial ordering of the input array; it makes the same number of comparisons regardless of the initial order of the array.
Redundant Comparisons — This algorithm makes a large number of redundant comparisons since it keeps on comparing the elements with each other even when the minimum element is found at the early part of a pass through the array

Conclusion

Understanding algorithms like Linear Search, Binary Search, Bubble Sort, and Selection Sort is essential for building a solid foundation in computer science. Each has its strengths and weaknesses: Linear Search is simple for small datasets, while Binary Search is efficient with sorted data. Bubble Sort is easy to implement but slow, whereas Selection Sort is more systematic but not ideal for large datasets. By exploring these, you’ve strengthened your grasp of key concepts in searching and sorting. Thank you for reading, and I hope this knowledge aids you in your programming journey. Happy coding!