Exponential Search

Exponential Search

First expand the search boundary exponentially, then perform binary search inside the discovered range.

How to use

• Enter a target and press Search to animate the whole search, or press Step to advance one comparison at a time.
• Reset clears the run; New Array draws a new sorted array of 20 distinct values.
• Red labels above the cells mark the probed bounds 1, 2, 4, 8, 16; the blue bar shows the current binary-search interval [lo, hi].

Algorithm

1. If A[0] equals the target, stop.
2. Start with bound = 1 and double it while bound < n and A[bound] < target.
3. The target, if present, lies in A[bound/2 … min(bound, n − 1)]; run binary search there.

Complexity

If the target is at position i, the doubling phase takes about log₂ i steps and the binary search works on a range of size about i, so the total time is O(log i) ≤ O(log n) with O(1) extra space. It is useful for unbounded or very large sorted lists, where the target is near the beginning.