Interactive Binary Search Visualization
Standard Binary Search
Watch how binary search efficiently finds a target value in a sorted array by repeatedly dividing the search space in half.
Interactive Visualization:
Step 0 of 4: Initial state
Finding First Occurrence
See how binary search can be modified to find the first occurrence of a target value in a sorted array with duplicates.
Interactive Visualization:
Step 0 of 18: Initial state
Rotated Sorted Array
Explore how binary search can be adapted to search in a rotated sorted array.
Interactive Visualization:
Note: The array is rotated at index 0 (value 38). This means the original sorted array was split at this point and the second part was moved to the beginning.
Step 0 of 14: Initial state
Learning Objective
Visualize how binary search algorithms work through interactive examples of different variations.
Visualizing Binary Search
Binary search can be challenging to understand without seeing it in action. These visualizations will help you grasp how binary search efficiently narrows down the search space.
Standard Binary Search
Find a target value in a sorted array by repeatedly dividing the search space in half.
Finding First Occurrence
Find the first occurrence of a target value in a sorted array with duplicates.
Rotated Sorted Array
Search in a sorted array that has been rotated at some pivot point.
Standard Binary Search
Watch how binary search efficiently finds a target value in a sorted array by repeatedly dividing the search space in half.
Interactive Visualization:
Step 0 of 4: Initial state
How it works: The algorithm compares the target value to the middle element of the array. If they match, the search is complete. If the target is less than the middle element, the search continues in the left half. If the target is greater, the search continues in the right half.
Binary Search Properties
Binary search is a highly efficient algorithm with several key properties:
- Time Complexity: O(log n) - Each step eliminates half of the remaining elements.
- Space Complexity: O(1) for iterative implementation, O(log n) for recursive due to call stack.
- Prerequisite: The array must be sorted for binary search to work correctly.
- Efficiency: Binary search is much faster than linear search for large arrays.
The visualization shows how binary search efficiently narrows down the search space by half in each step, making it extremely fast even for large datasets.
Notice how the algorithm adjusts the left and right pointers to focus on the relevant portion of the array in each step.