# What Is Binary Search Algorithm in Data Structure?

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Angela Bailey

What Is Binary Search Algorithm in Data Structure?

When it comes to efficiently searching for an element in a sorted list, the binary search algorithm is a popular and efficient choice. This algorithm follows a divide-and-conquer approach to find the desired element by repeatedly dividing the search space in half.

## How Does Binary Search Work?

The binary search algorithm works by comparing the Target element with the middle element of the sorted list. If they match, the search is successful.

If the Target element is smaller than the middle element, the algorithm narrows down the search space to the lower half of the list. Similarly, if the Target element is greater than the middle element, it focuses on the upper half of the list.

This process continues until either the Target element is found or there are no more elements left to search.

## Binary Search Algorithm Steps:

1. Step 1: Start with a sorted list and define variables for low and high indexes.
2. Step 2: Calculate mid index as (low + high) / 2.
3. Step 3: Compare if Target equals list[mid].
• If true, return mid as the index where Target is found.
• If false, move to step 4 or step 5 based on whether Target is smaller or greater than list[mid].
4. Step 4: If Target is smaller than list[mid], update high = mid – 1 and go back to step 2.
5. Step 5: If Target is greater than list[mid], update low = mid + 1 and go back to step 2.

## Time Complexity of Binary Search:

The binary search algorithm has a time complexity of O(log n), where n is the number of elements in the sorted list. This logarithmic time complexity makes it highly efficient, especially for large datasets. It outperforms linear search algorithms, which have a time complexity of O(n).

## Benefits of Using Binary Search Algorithm:

• Efficiency: The binary search algorithm is efficient and performs well, even with large datasets.
• Versatility: It can be applied to any sorted list, regardless of its size or data type.
• Optimization: Binary search minimizes the number of comparisons needed to find the Target element, reducing the overall search time.

### Conclusion

The binary search algorithm is a powerful tool in data structures for efficient searching. By dividing the search space in half at each step, it quickly narrows down the possibilities until it finds the desired element. With its logarithmic time complexity and versatility, the binary search algorithm is widely used in various applications that require fast and reliable searching capabilities.