Bubble Sort

Compare • Swap • Bubble Up

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How bubble sort works — the compare-and-swap rule, why large values "bubble" to the end each pass, the early-exit optimization, and O(n²) / O(1) space complexity.

By the end, you can

Trace bubble sort step by step on a small array, showing the state after each pass.
Explain why each pass locks the largest unsorted element at the end of the unsorted region.
Identify how many comparisons and swaps a specific pass performs.
Explain the early-exit optimization and state its effect on best-case complexity.
State the worst-case, best-case, and space complexity of bubble sort and justify each.
Explain what "stable sort" means and why bubble sort qualifies.
Identify when bubble sort is appropriate and why insertion sort is preferred in production.

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