Linear search vs binary search: count the comparisons

This animation compares two ways to find the value 51 in a sorted list of 16 numbers. Linear search checks each element in order, needing up to 13 steps. Binary search repeatedly halves the remaining range, locating the target in just 4 steps. Side-by-side counters and a shrinking search window illustrate why binary search scales as log2 n while linear search scales as n, useful for teaching algorithm efficiency and Big O intuition.

16:9 · every frame verified for overlaps, spacing and edges before rendering

The prompt that made it

Finding 51 among 16 sorted values: linear search takes 13 steps, binary search takes 4 by halving the range each time; log2 n versus n.

Make your own version

Make the next one in this series

• Show how binary search fails on an unsorted array and why sorting matters first
• Animate Big O growth curves comparing O(log n), O(n), and O(n^2) as n increases
• Demonstrate binary search implemented recursively versus iteratively with call stack visualization

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