Update binary_search.md

Author: ajay-dhangar

docs/dsa/binary_search/binary_search.md

@@ -7,7 +7,7 @@ description: "In this blog post, we'll dive into the binary search algorithm, a
 tags: [dsa, algorithms, binary search]
 ---
 
-Welcome, eager learner! Today, we embark on an enlightening journey through the world of binary search. This powerful algorithm is essential for efficiently finding elements in sorted arrays, making it a staple in the toolkit of any adept programmer. Whether you're optimizing search operations or solving complex algorithmic challenges, understanding binary search is crucial. Let's delve into its mechanics, applications, and implementation.
+Binary Search algorithm is essential for efficiently finding elements in sorted arrays, making it a staple in the toolkit of any adept programmer. Whether you're optimizing search operations or solving complex algorithmic challenges, understanding binary search is crucial. Let's delve into its mechanics, applications, and implementation.
 
 ## What is Binary Search?
 
@@ -50,8 +50,9 @@ return -1;
 }
 ```
 
-How Binary Search Works
-Step-by-Step Explanation
+## How Binary Search Works
+
+### Step-by-Step Explanation
 
 1.  Initialize: Set two pointers, low at the beginning and high at the end of the array.
 2.  Middle Element: Calculate the middle element's index.
@@ -61,13 +62,14 @@ Step-by-Step Explanation
     If the middle element is greater than the target, discard the right half by setting high to mid - 1.
 4.  Repeat: Repeat steps 2 and 3 until the target is found or the low pointer exceeds the high pointer.
 
-Time Complexity
-The time complexity of binary search is
-𝑂(log𝑛)
-O(logn), where 𝑛
-n is the number of elements in the array. This logarithmic time complexity makes binary search significantly faster than linear search for large datasets.
+### Time Complexity
+
+The time complexity of binary search is $𝑂(log𝑛)$
+
+where $n$ is the number of elements in the array. This logarithmic time complexity makes binary search significantly faster than linear search for large datasets.
+
+## Practical Applications
 
-Practical Applications
 Binary search is widely used in various real-world applications and algorithmic problems:
 
 1. Searching in a Sorted Array
@@ -121,11 +123,11 @@ RETURN low
 2. Rotated Sorted Array
    Binary search can be modified to handle rotated sorted arrays, where the array is sorted but then rotated at some pivot point.
 
-Tips for Implementing Binary Search
-
+:::Tip
 Handle Edge Cases: Ensure your implementation correctly handles cases where the target element is not present or when the array is empty.
 Prevent Overflow: When calculating the middle index, use $\text{mid} = \text{low} + \frac{\text{high} - \text{low}}{2}$ instead of $\text{mid} = \frac{\text{low} + \text{high}}{2}$ to prevent potential overflow.
 Iterative vs. Recursive: Both iterative and recursive implementations are valid. Choose based on your preference and the problem constraints.
+:::
 
-In Conclusion
-Binary search is a fundamental algorithm that every programmer should master. Its efficiency and versatility make it a powerful tool for solving a wide range of problems. By understanding how binary search works and how to implement its variations, you'll be well-equipped to tackle numerous challenges in your programming journey. Happy coding!
+## Conclusion
+Binary search is a fundamental algorithm that every programmer should master. Its efficiency and versatility make it a powerful tool for solving a wide range of problems. By understanding how binary search works and how to implement its variations, you'll be well-equipped to tackle numerous challenges in your programming journey.