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Questions and Answers
What is the time complexity of Bubble Sort in the best case?
What is the time complexity of Bubble Sort in the best case?
Which sorting algorithm is stable and has a time complexity of O(n log n) in all cases?
Which sorting algorithm is stable and has a time complexity of O(n log n) in all cases?
What is the space complexity of Quick Sort in the average case?
What is the space complexity of Quick Sort in the average case?
Which sorting algorithm uses a binary heap data structure?
Which sorting algorithm uses a binary heap data structure?
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What is the time complexity of Insertion Sort in the worst case?
What is the time complexity of Insertion Sort in the worst case?
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Which sorting algorithm is suitable for small data sets or almost-sorted data?
Which sorting algorithm is suitable for small data sets or almost-sorted data?
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What is the space complexity of Merge Sort?
What is the space complexity of Merge Sort?
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Which sorting algorithm is not stable, meaning it can swap equal elements?
Which sorting algorithm is not stable, meaning it can swap equal elements?
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Study Notes
Sorting Algorithms
Bubble Sort
- A simple sorting algorithm that works by repeatedly iterating through the data and swapping adjacent elements if they are in the wrong order.
- Time complexity: O(n^2) in worst and average cases, O(n) in best case.
- Space complexity: O(1) since it only uses a small amount of extra memory.
- Not suitable for large data sets due to its high time complexity.
Merge Sort
- A divide-and-conquer algorithm that divides the data into smaller chunks, sorts each chunk, and then merges the sorted chunks.
- Time complexity: O(n log n) in all cases.
- Space complexity: O(n) since it requires extra memory to store the temporary arrays.
- Stable sorting algorithm, meaning it maintains the relative order of equal elements.
Quick Sort
- A divide-and-conquer algorithm that selects a pivot element, partitions the data around the pivot, and then recursively sorts the sub-partitions.
- Time complexity: O(n log n) in average and best cases, O(n^2) in worst case.
- Space complexity: O(log n) in average and best cases, O(n) in worst case.
- Not stable, as it can swap equal elements.
Heap Sort
- A comparison-based sorting algorithm that uses a binary heap data structure to sort the data.
- Time complexity: O(n log n) in all cases.
- Space complexity: O(1) since it only uses a small amount of extra memory.
- Not stable, as it can swap equal elements.
Insertion Sort
- A simple sorting algorithm that works by iterating through the data one element at a time, inserting each element into its proper position in the sorted portion of the data.
- Time complexity: O(n^2) in worst and average cases, O(n) in best case.
- Space complexity: O(1) since it only uses a small amount of extra memory.
- Suitable for small data sets or almost-sorted data.
Selection Sort
- A simple sorting algorithm that works by selecting the smallest element from the unsorted portion of the data and moving it to the beginning of the sorted portion.
- Time complexity: O(n^2) in all cases.
- Space complexity: O(1) since it only uses a small amount of extra memory.
- Not suitable for large data sets due to its high time complexity.
Sorting Algorithms
Bubble Sort
- Repeatedly iterates through data, swapping adjacent elements if in wrong order
- Worst/average case time complexity: O(n^2), best case: O(n)
- Space complexity: O(1), uses minimal extra memory
- Not suitable for large data sets due to high time complexity
Merge Sort
- Divides data into smaller chunks, sorts each, and merges sorted chunks
- Time complexity: O(n log n) in all cases
- Space complexity: O(n), uses extra memory for temporary arrays
- Stable sorting algorithm, maintains relative order of equal elements
Quick Sort
- Selects pivot element, partitions data around pivot, recursively sorts sub-partitions
- Average/best case time complexity: O(n log n), worst case: O(n^2)
- Space complexity: Average/best case: O(log n), worst case: O(n)
- Not stable, can swap equal elements
Heap Sort
- Uses binary heap data structure to sort data
- Time complexity: O(n log n) in all cases
- Space complexity: O(1), uses minimal extra memory
- Not stable, can swap equal elements
Insertion Sort
- Iterates through data, inserting each element into its proper position in sorted portion
- Worst/average case time complexity: O(n^2), best case: O(n)
- Space complexity: O(1), uses minimal extra memory
- Suitable for small data sets or almost-sorted data
Selection Sort
- Selects smallest element from unsorted portion, moves it to beginning of sorted portion
- Time complexity: O(n^2) in all cases
- Space complexity: O(1), uses minimal extra memory
- Not suitable for large data sets due to high time complexity
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Description
Learn about two fundamental sorting algorithms: Bubble Sort and Merge Sort, including their time and space complexity. Understand when to use each algorithm and their limitations.
