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Jump Search

Jump ahead in steps of √n to find the right block, then scan linearly within it. O(√n) — faster than linear, simpler than binary.

Visualization

Target:

Speed

Phase 1: JumpPhase 2: Linear

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Jump size = sqrt(15) = 3 | Red lines = block boundaries

Active checkFoundActive blockEliminated

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Target

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Comparisons

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Jump Size

Ready — press Play or step through manually.

Complexity

O(1)

Best Case

O(√n)

Worst / Avg

O(1)

Space

Sorted

Requires

Why √n Is Optimal

If block size = k:

•Phase 1 (block scan): at most n/k jumps
•Phase 2 (linear scan): at most k steps
•Total: n/k + k — minimised when k = √n

n=100 → block size = 10
Phase 1: ~10 jumps | Phase 2: ~10 steps

Active Recall Quiz

Question 1 of 3

What is the optimal block/jump size for jump search on an array of size n?