What Is A Binary Search Algorithm?

binary search algorithm

Binary Search Algorithm (BSA) is a search algorithm where we start at the middle of the list and work our way outwards until we find what we’re looking for.

In computer science, the binary search algorithm is a data-searching technique that searches for an item in sorted arrays using a divide-and-conquer strategy. 

In its simplest form, the algorithm starts with an initial guess at the desired value; if the collection contains the target value, the result is returned immediately. 

Otherwise, the guessed value is divided into two halves, and the process is repeated recursively on each half. 

If either subarray does not contain the target value, the algorithm returns to the top level and tries again with the smaller subarray.

The complexity of the binary search algorithm is O(log n), where n is the length of the input array. That means that the number of comparisons performed grows logarithmically with the size of the input array.

What is Binary Search?

Binary search is a method used to find items within a sorted set. When searching for something specific, binary search is faster than linear search.

Binary search is an efficient finding of things within a sorted set, like a list or array.

Binary search is a method for finding an item in an array using only two comparisons instead of linear searches through the entire list.

The algorithm works like this: start at the beginning of the collection and compare the first element with the target. If they match, stop searching.

Otherwise, move one place to the right and repeat the process. This continues until either the first element matches or all elements have been checked.

It is also known as a binary chop, half-interval, midpoint, bisection, or stepwise search.

What is linear search?

Another popular way to find things in a list is called linear search. A linear search algorithm looks at each element in the list sequentially until it finds the target.

This is inefficient because it requires O(n) time to complete.

What is quickselect?

There is a third way to find things in lists. This is called quickselect. Quickselect starts by picking the smallest element in the list.

Then, it picks the second-smallest element in the list, and so on, until it reaches the end of the list. At this point, it returns the index of the picked first element.

What is a graph search algorithm?

A graph Search Algorithm is a mathematical technique used to find paths between nodes in a graph.

A node represents something, while edges represent connections between them. These algorithms allow us to find these paths efficiently.

For example, if we have a social network where people are connected based on their friendship, then we could use graph search algorithms to find out who our friends are.

We would start at some person’s profile page (node) and follow the links until we reach someone else’s profile page (another node). In this way, we could find out who our friends were.

There are many different types of graphs, including directed, undirected, weighted, etc. Each type of graph has its unique characteristics.

What is a star search algorithm?

A star search algorithm is a type of search algorithm that uses a set of points (stars) to represent each possible location where the target could be located.

Each point is connected to a number called its weight, representing how likely the target is at that particular point. The algorithm aims to find the best path between two stars.

The first step in any star search algorithm is to create a graph representation of the problem space. This means that we need to decide what information we want to use to determine whether something is present or not.

We then have to figure out how to store that data efficiently. Once we have our graph, we can start looking for the target using a heuristic function.

Heuristics are rules of thumb that help us make decisions about problems without calculating everything precisely.

What is a Binary Search tree?

A binary search tree (BST) is a self-balancing binary search tree data structure where each node contains two pointers to its children, rather than just one pointer to its left child, as in a normal tree search algorithm. 

A binary search tree algorithm is a balanced tree in which the height of any subtree rooted at some node never exceeds log n, where n is the number of nodes in the subtree. 

In addition, no matter how deep the root is, the maximum depth of the entire tree is O(log n).

now we talk about the type of sort:

1. Binary Search Tree

A binary search tree (BST) is a type of self-balancing binary search tree data structure where each node contains a value and two pointers, left and right.

A binary tree search algorithm is a balanced tree if, after any rotation operation, the tree’s height does not change.

2. Insertion Sort

Insertion sort is a comparison-based sorting algorithm. Given an array of n distinct items, insertion sort repeatedly performs the following steps until done:

a. Compare the current item being processed to its correct position in sorted order;

b. If the current item’s position is less than the correct position, insert the recent article at the proper place and update the indices accordingly;

c. Otherwise, do nothing and move to step 2.

3. Bubble Sort

Bubble sort is a simple yet effective sorting algorithm. It works by comparing adjacent pairs of values and swapping them if they are out of order.

4. Selection Sort

Selection sort is a basic sorting algorithm. It starts by selecting the first element of the list to be sorted and then compares it with each successive piece until all have been reached.

Once complete, it swaps the selected part with the last remaining component and repeats the process.

5. Merge Sort

Merge Sort is a divide-and-conquer sorting algorithm. It recursively breaks down more extensive lists into smaller sublists until only one element remains.

6. Heap Sort

Heap sort is a sorting technique where items are placed onto a heap and sorted based on their size.

How does Binary Search work?

Binary search is a method used to find items within a sorted array. It is also known as a binary search algorithm.

In this article, we will discuss how binary search works.

1. Divide Array Into Two Equal Parts

Let’s say we’re looking for the number 12 in an unsorted array of numbers. We’d divide the array into two equal parts, like so:

0 1 2 3 4 5 6 7 8 9 10 11 12

We’d end up with two arrays:

0 1 2 3 4 5… 6 7 8 9 10…

2. Look For Item Within Left Half

Now let’s assume that we found the value 12 in the left half of the array. How would we go about finding it in the right half?

We’d compare the values until we found the correct match. Let’s say we found the value 12 on the left side. 

Here’s how we’d proceed:

0 1 2 3…

4 5 6 7…

So now we’ve narrowed down the possible locations for the value 12 to just four positions:

0 1 2…

Since we didn’t find the value 12 in the first part of the array, we moved on to the next position.

0 1 2…

1. What Is Sorting?

Sorting is a process of arranging elements in order based on some criteria. For example, sorting alphabetically arranges all the letters of the English alphabet in ascending order.

2. How Does Sorting Arrange Elements?

Sorting uses a comparison operator to compare the values of the elements being compared. For example, suppose we are comparing apples and oranges.

We can arrange them according to size, color, etc., but when we are done, we may end up with apples first, followed by oranges.

3. Why Do We Sort?

We sort things so that we can quickly identify the desired element.

For example, if we were looking for a specific letter, we wouldn’t randomly look through every letter until we found it. Instead, we’d sort them alphabetically and look only at the first letter of each word.

4. What Are Arrays?

An array is a collection of objects arranged in a particular sequence. For example, an array containing numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is called an array of integers.

5. What Is a List?

A list is another name for an array. Lists commonly store information like phone numbers, addresses, names, dates, times, etc.

6. What Is a Linked List?

A linked list is similar to a list except that instead of storing the elements sequentially, it stores them next to each other. 

Why Do We Need Binary Search?

Binary search is a method of finding an item in an ordered list. To find something in a list, we need to start at the beginning and work our way toward the end.

If we know where the item is located, we must look at each item until we find it. However, we need to do a binary search if we don’t know where the item is.

In an algorithms binary search, we divide the list into two halves. Then we check the middle half first. If the item isn’t there, we move onto the left side.

We move to the right side if it’s still not there. Once we’ve checked both sides, we’re done!

The algorithm for binary search is simple enough. You take the midpoint of the list and compare it to what you want to find. If they match, then you’re done. Otherwise, split the list into two equal parts and repeat the process.

Here’s an example of how binary search works. Let’s say you wanted to find the number 5 in a list of numbers.

First, you would make sure that the list starts with 0. Next, you’d split the list into two halves, ensuring that the length of each half is 1/2 the size of the original list. So, in this case, the first half would consist of and the second half would consist of.

Now, let’s say that the number you were looking for was 6. Since the number you’re searching for is smaller than the average value in the list (the midpoint), you’ll go to the left side of the list.

Since the number you want to find is larger than the average value in each half, you’ll go to the right side of the list. Therefore, the final result would be, since the number you’re looking for is between 0 and 2.

searching algorithms time complexity cheat sheet:

Why Binary Search algorithm is best?

Binary search is the simplest way to find a specific value in an array. To do this, we need to know where our target number lies.

We then start at the beginning of the list and work towards the end until we reach the point where our target value resides. If our target value does not reside near the array’s beginning or end, we have no choice but to move back to the middle of the array.

Once we’ve reached the middle, we repeat the same steps. By doing this repeatedly, we eventually arrive at the location of our target value.

What are the steps of Binary Search?

An algorithm for binary search is a method used to find items within a sorted array. John Venn first introduced it in 1823.

We’ll discuss the steps involved in binary search. 

Step 1: Determine the location of the item being searched for.

Step 2: Choose a starting point.

Step 3: Compare the value of the item being searched with the value of the starting point.

Step 4: Continue comparing until the starting position’s value matches the item’s value.

Step 5: Return the index of the starting position.

Where is Binary Search used?

1. Data Structures

The binary search algorithms are used in data structures where we need to find something in an array/list. We use binary search to determine whether an item exists in an array/list.

If yes, we return its index; otherwise, we must go further down the list until we reach the end.

2. Algorithms

We use binary search to solve problems like finding the minimum value in an array/list, finding the maximum value in an array/ list, etc.

3. Applications

the algorithm of binary search is widely used in sorting, searching, and other applications.

What is bubble sorting in C?

Bubble sort is a simple algorithm for sorting data. In computer science, a bubble sort is a type of quick sort where each pass over the array compares two adjacent elements (elements closer together) and swaps them if they are out of order. Bubble sort works well for small arrays but becomes slow for larger ones.

What is bubble sorting? 

A bubble sort is a method of sorting data using a series of passes over the data. Each pass goes through the entire list once, comparing pairs of items simultaneously.

If the first pair is not sorted, the second pair is compared, etc., until all pairs are checked. At the end of the last pass, the list is returned to its original state.

How does bubble sorting work?

The basic idea behind bubble sort is to compare adjacent items in the list, swapping them if necessary. To do this, we need some way of identifying adjacent items.

One approach uses pointers to identify the item before and after each comparison. We start with the first item in the list and move forward one step at a time.

When we reach the current position, we check whether the value stored there matches the value stored at the previous pointer. If they match, we swap the values; otherwise, we skip the rest of the loop.

Once we’ve finished going through the whole list, we return the original list to its original state. Since we’re only checking adjacent items, we don’t need to keep track of any intermediate states.

Which sorting algorithm is best?

QuickSort is a divide-and-conquer algorithm that divides the array into two arrays (or subarrays) based on some criteria (in our case, we’re going to sort numbers ascending).

Then each subarray gets sorted recursively until only one item remains.

Which is the best algorithm for searching?

Types of search algorithms for searching:

1. BFS (Breadth-First Search)

The Breadth-First Search (BFS) algorithm is a searching algorithm that starts at the root node and expands outward until all nodes have been visited.

This algorithm helps find solutions to problems that are unique and not repeated. In computer science, breadth-first search is a graph traversal technique that begins at a vertex and explores adjacent vertices before moving onto nonadjacent ones.

2. DFS (Depth-First Search)

A Depth-First Search (DFS) algorithm is similar to a Breadth-First Search except that instead of exploring all neighbors of a given node, it only explores the closest neighbor.

A depth-first search is often used to find a path between two points in a graph.

3. Greedy Algorithm

Greedy search algorithms are greedy. These algorithms always choose the option that gives them the highest benefit without considering any other options.

Greedy searching algorithms are often used in combinatorial optimization problems.

4. Best Fit Algorithm

Best fit algorithms work by minimizing some cost functions. Cost functions are mathematical expressions that describe how much we want something to change.

The best-fit algorithm finds the minimum value of a cost function.

5. Heuristic Algorithms

Heuristics are algorithms that do not guarantee optimal results. Instead, they try to minimize the time taken to reach an answer.

Heuristic algorithms are commonly used in artificial intelligence applications.

6. Hill Climbing Algorithm

Hill climbing algorithms start with an initial guess and then improve upon it.

Each iteration takes a guess and moves it uphill towards the optimum solution. Hill climbing algorithms are often used in optimization problems.

7. Local Search Algorithms

Local search algorithms use local information to guide their search.

Local search algorithms make decisions based on what’s already known about the problem rather than blindly making guesses.

What are the limitations of the Binary Search algorithm?

1. Time Complexity

The time complexity of the algorithm binary search is O(log n), where n is the number of elements in the array.

2. Space Complexity

The space complexity of the binary search is logarithmic since we need only two pointers (one for the leftmost position and one for the rightmost position).

3. Worst Case Performance

In case of worst-case performance, the running time of binary search is proportional to the square root of the size of the input data set.

In other words, if the input data set contains N items, then the running time of binary searching is O(N^0.5).

4. Average Case Performance

Average case performance means that the average value of running time of the binary search algorithm is O(log n), where n is the number of elements in the array.

In other words, the running time of the binary search algorithm is proportional to the logarithm of the number of elements in a given array.

5. Best Case Performance

Best case performance means that binary search algorithms’ best possible running time is linear, i.e., O(n).

6. Memory Usage

Memory usage of the binary search algorithm is constant, i.e., O (1) bytes.

7. Input Size

The input size of the binary search algorithm is not bounded.


The binary search algorithm is the best search algorithm a method of searching for a specific item in a sorted list. In this case, we have a sorted array containing numbers 1-100.

We want to find out if the number 50 exists in the array. To do this, we start at index 0 (the first position) and compare each value until we find the correct one.

If we cannot find the number, we move on to the second index and repeat the same process. Once we reach the array’s end, we know our target does not exist.

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