Skip to main content

Advanced Binary Search Problems

 

Advanced Binary Search Problems

We'll apply binary search to complex data structures, such as bitonic arrays and rotated sorted arrays, to find specific elements efficiently.

Problem 1: Searching in a Bitonic Array

Consider a bitonic array as a numerical sequence simulating the trajectory of a roller coaster — first, it rises to a peak, then descends. For example, consider the array [1, 2, 3, 4, 5, 3, 1]: its first part ascends, and the last descends, making it bitonic. Your goal is to find a value in such an array. You might walk the entire path, which is exhaustive and represents our naive approach with a time complexity of O(n). Our aim today is a more efficient method.

Efficient Approach Explained

To apply binary search, we first locate the peak of the array, then perform binary search on either side of the peak: one for the increasing sub-array and one for the decreasing sub-array.

The first step is akin to finding a vantage point at the carnival for a better view:

Solution Building: Searching the Target

Now, let's perform a targeted binary search on sub-arrays:

The searching logic for the ascending part checks if the middle element is our target and updates start or end based on how the target compares. For the descending part, the logic flips since the values are now descending.

Problem 2: Searching the Minimum Element in a Rotated Sorted Array

Imagine you have a shuffled deck of cards that needs to be reordered. That could be represented with a rotated sorted array. For example, if we rotate array [1, 2, 3, 4, 5], we could get [3, 4, 5, 1, 2]. You could check each element, one by one, to find the lowest, which is our naive approach with a time complexity of O(n). Or, we could use binary search for a more efficient find.

Approach Explained

For the naive approach to finding the minimum element in a rotated sorted array, we'd sequentially traverse the array until we found the point where the current element is less than the preceding element, indicating the minimum. Instead, we adopt binary search to identify the rotation point, which harbors the smallest element. This is like deducing the first card in the shuffled deck without flipping through every card.

Solution Building: Leveraging Binary Search

Here, we apply our strategy to solve this arranged chaos:

Comments

Post a Comment

Popular posts from this blog

JavaScript Maps

Dive Into JavaScript Maps A Map stores data as key-value pairs. We'll recall how to create Maps, implement them, and delve into the details of their memory management. Understanding JavaScript Maps Maps are versatile data structures in JavaScript. They store key-value pairs and accept any data type as a key — even objects and functions! Here is how we create an empty Map: let myMap = new Map(); // creates an empty Map Here, myMap is a new JavaScript Map, eagerly awaiting to store your keys and values. Meander Through Map Methods Maps provide some essential built-in methods: set(key, value): Stores a key-value pair. get(key): Retrieves the value of a key. has(key): Checks if a key exists and returns true or false. delete(key): Erases a key-value pair. size: Returns the count of key-value pairs. To gain a better understanding, let's apply these methods: let myMap = new Map(); // Add pairs with set myMap.set('apples', 10); // Adds a new pair myMap.set('bananas', 6...
Post a Comment
Read more

How to work with Set in JavaScript

Understanding JavaScript Sets Set in JavaScript is an unordered collection of unique values. We can examine the size of the set using .size method. Notice that the set is unordered, and we can't guarantee that elements will be shown in the order we added them. Sets work similarly to JavaScript objects but are designed for uniqueness. They use hashing, a way to convert a given pearl into a unique code, which facilitates rapid storage and retrieval. When checking if an item is in a Set, JavaScript computes its hash code to locate it, much like a map leading to a treasure. Sets have numerous practical uses in database management, data analysis , and more . Problem 1: Check if Two Sets are Disjoint Let's begin by considering the function, areDisjoint which takes two arrays and determines if they are disjoint, meaning they have no elements in common. This is crucial when analysing datasets for overlapping values, similar to ensuring that two puzzle pieces from different puzzles d...
Post a Comment
Read more

The Synergy Between DevOps and Agile Methodologies

When it comes to modern software development practices, two methodologies have gained significant traction in recent years: DevOps and Agile. While they are distinct in their approaches, DevOps and Agile share common goals of improving collaboration, efficiency, and quality in software development processes. Understanding DevOps DevOps  is a set of practices that combines software development (Dev) and IT operations (Ops) to shorten the systems development life cycle and provide continuous delivery of high-quality software. It emphasizes collaboration, automation, and monitoring throughout the software delivery process. Key principles of DevOps include: Automation of processes Continuous integration and delivery Monitoring and feedback loops Collaboration between teams Exploring Agile Methodologies Agile  is an iterative approach to software development that focuses on delivering value to customers through incremental and iterative development. Agile methodologies promote adap...
Post a Comment
Read more