What is the time and space complexity of bubble sort?
This question assesses your ability to explain the time and space complexity of bubble sort by understanding how the algorithm operates.
Answer 1: Full explanation in spoken form
English
Bubble sort has a time complexity of O(n) in the best case, when the array is already sorted and the implementation includes a check to detect no swaps. In the average and worst cases, its time complexity is O(n²), as it repeatedly compares and swaps adjacent elements in nested loops.
Its space complexity is O(1) because it’s an in-place algorithm that doesn’t use extra memory apart from a few temporary variables.
While bubble sort is simple and easy to understand, it’s inefficient for large datasets and is mainly used for teaching purposes.
Key Expressions
- O(1): Constant space complexity
- in-place algorithm: Algorithm that modifies the input directly
- detect no swaps: Optimization that stops early if no swaps occur
- compare and swap: Basic operation in bubble sort
- nested loops: Loops inside loops, contributing to O(n²) time
Answer 2: Concise and natural explanation
English
In the best case, when the array is already sorted, bubble sort runs in O(n) time — if the implementation checks for no swaps. But in most real-world cases, including the average and worst, the time complexity is O(n²) due to repeated comparisons and swaps.
The space complexity is O(1) because the algorithm sorts the array in place, without using extra memory.
Key Expressions
- best case / average case / worst case: Types of input scenarios
- check for no swaps: Early-exit optimization
- sort in place: Sort directly in the original array
- compare and swap: Core operation of bubble sort
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