As developers, we always strive to improve the performance of our code. We want our software to run as fast as possible, while using as little resources as possible. Not only does this benefit the user experience, but it also has a positive impact on the environment. In this blog post, we will explore how binary search can help us achieve both of these goals.

## What is Binary Search?

Binary search is a classic algorithm used to find a specific value in a sorted list or array. The basic idea is to repeatedly divide the search interval in half until the target value is found, or until the interval is empty.

Let’s say we have a sorted array of integers:

`[2, 5, 8, 12, 16, 23, 38, 56, 72, 91]`

If we want to find the index of the value `23`

, we can use binary search to do it efficiently. Here’s how it works:

- We start by defining the left and right endpoints of the search interval. In this case, we set

to 0 (the first index of the array) and**left**

to 9 (the last index of the array).**right** - We calculate the middle index of the interval by taking the average of

and**left****right****:**`mid`

.`= (left + right) // 2`

- We check if the middle value of the interval is equal to our target value (
in this case). If it is, we’re done! We’ve found the index of the target value.`23`

- If the middle value is greater than our target value, we update
to be one index less than`right`

. This is because we know the target value must be in the left half of the interval**mid** - If the middle value is less than our target value, we update
to be one index greater than`left`

. This is because we know the target value must be in the right half of the interval.**mid** - We repeat steps 2-5 until we either find the target value or the interval becomes empty (i.e.,
is greater than`left`

).**right**

In this case, binary search would return the index `5`

, which is the index of the value `23`

in the array.

## Improving Performance with Binary Search

Binary search is a highly efficient algorithm, with a worst-case time complexity of O(log n), where n is the size of the search interval. This means that as the size of the interval grows, the time it takes to perform the search only grows logarithmically, rather than linearly.

To put this into perspective, let’s compare binary search to linear search, which is another algorithm for finding a value in a list. Linear search has a worst-case time complexity of O(n), where n is the size of the list. This means that as the size of the list grows, the time it takes to perform the search grows linearly. In other words, if the list doubles in size, the search time also doubles.

## Reducing Environmental Impact with Binary Search

In addition to improving performance, binary search can also have a positive impact on the environment. This is because faster algorithms generally require less energy to run, which means they produce less carbon emissions.

According to a study by the University of California, Berkeley, the energy consumption of a single Google search is equivalent to turning on a 60-watt light bulb for 17 seconds. While this may not seem like much, when you consider the billions of searches that are performed every day, it quickly adds up.

By using more efficient algorithms like binary search, we can reduce the amount of energy that is required to perform searches and other operations in our software. This not only has a positive impact on the environment, but it can also lead to cost savings for businesses that rely on large-scale computing.

## Conclusion

Binary search is a powerful algorithm that can help us improve the performance of our code while also reducing our environmental impact. By using binary search to search for values in sorted lists and arrays, we can dramatically reduce the time it takes to perform these operations, even for very large datasets.

While binary search may not be appropriate for every situation, it is a tool that every developer should be familiar with. By using more efficient algorithms in our code, we can build more sustainable software that is both faster and more environmentally friendly.

So the next time you need to search for a value in a sorted list or array, consider using binary search. Your code will be faster, and you’ll be doing your part to help reduce carbon emissions and combat climate change.