Searching Algorithms
Searching algorithms are indispensable tools in computer science that play a crucial role in locating specific items within a dataset efficiently. These algorithms are meticulously crafted to navigate through diverse data structures to pinpoint the required information accurately. They serve as the backbone in a wide array of applications, including databases, web search engines, and many more.
Understanding Searching
Searching involves finding a specific element within a dataset. This dataset can be in different forms like arrays, lists, trees, and other structures. The main aim of searching is to confirm if the desired element is in the dataset and, if so, to locate or retrieve it. Searching is crucial for various computational tasks and real-life situations, including information retrieval, data analysis, decision-making, and more.
Exploring Searching Algorithms in Data Structures
In the realm of data structures, a myriad of searching techniques can be employed to extract specific data efficiently. The success of a search operation hinges on its ability to locate and return the desired element accurately; otherwise, the search is deemed unsuccessful.
These searching techniques can be broadly categorized into two main groups. They include −
Sequential Searching
Interval Searching
Sequential Searching
As the name suggests, sequential searching involves looking at each piece of data one by one to find the information needed. The data doesn't need to be in a specific order for this method to work. This method is simple and checks every item in the data until it finds what is needed or until the entire dataset is searched. Sequential searching is often used when data is not sorted or when the search area is small, making it a flexible and trustworthy way to find specific elements in a dataset.
Example − Linear Search
Fig. 1: Linear Search Operation
Interval Searching
Unlike sequential searching, interval searching requires the data to be sorted. This method typically searches the data in intervals, either by dividing the data into sub-parts or by jumping through indices to find an element.
Example − Binary Search, Jump Search etc.
Searching terminologies:
Target Element:
In searching, you always have a specific target element you want to find in the data. This target could be a value, a record, a key, or any other piece of data you're interested in.
Search Space:
The search space is the entire collection of data where you're searching for the target element. The size and organization of the search space can vary depending on the data structure used.
Complexity:
Searching can be more or less complex depending on the data structure and algorithm used. Complexity is usually measured in terms of time and space requirements.
Deterministic vs. Non-deterministic:
Some searching algorithms, like binary search, are deterministic, following a clear, systematic approach. Others, such as linear search, are non-deterministic and may need to check the entire search space in the worst-case scenario.
Easy Problems on Searching:
Kth smallest element in a row-wise and column-wise sorted 2D array
Find the maximum element in an array which is first increasing and then decreasing
Given an array of of size n and a number k, find all elements that appear more than n/k times
Medium Problems on Searching:
Find the element before which all the elements are smaller than it, and after which all are greater
Maximum and minimum of an array using minimum number of comparisons
Given a sorted array and a number x, find the pair in array whose sum is closest to x
Binary Search for Rational Numbers without using floating point arithmetic