Podcast
Questions and Answers
Merge Sort is a sorting algorithm that follows the ______-and-conquer paradigm.
Merge Sort is a sorting algorithm that follows the ______-and-conquer paradigm.
divide
In Merge Sort, the unsorted list is divided into 'n' sub-lists, each containing ______ element.
In Merge Sort, the unsorted list is divided into 'n' sub-lists, each containing ______ element.
one
The key operation in Merge Sort is the ______ of two sorted sub-lists.
The key operation in Merge Sort is the ______ of two sorted sub-lists.
merging
Merge Sort is a ______ sorting algorithm, meaning that it maintains the relative order of equal elements.
Merge Sort is a ______ sorting algorithm, meaning that it maintains the relative order of equal elements.
Merge Sort has a consistent performance with a time complexity of $O(n log n)$ in the ______, average, and best cases.
Merge Sort has a consistent performance with a time complexity of $O(n log n)$ in the ______, average, and best cases.
Merge Sort can efficiently handle large datasets by reading and writing smaller ______ of data at a time, making it well-suited for external sorting scenarios.
Merge Sort can efficiently handle large datasets by reading and writing smaller ______ of data at a time, making it well-suited for external sorting scenarios.
Merge Sort can be easily ______, taking advantage of multiple processors or cores to enhance performance.
Merge Sort can be easily ______, taking advantage of multiple processors or cores to enhance performance.
Merge Sort has a straightforward and modular ______, making it easier to understand and maintain.
Merge Sort has a straightforward and modular ______, making it easier to understand and maintain.
The MergeSort repeatedly divides the array into two ______ until it tries to perform MergeSort on a subarray of size 1.
The MergeSort repeatedly divides the array into two ______ until it tries to perform MergeSort on a subarray of size 1.
The merge step resolves the problem of merging two sorted ______ to build one large sorted list.
The merge step resolves the problem of merging two sorted ______ to build one large sorted list.
The algorithm maintains three ______, one for each of the two arrays and one for the final sorted array.
The algorithm maintains three ______, one for each of the two arrays and one for the final sorted array.
The merge function creates ______ of the subarrays $L + A[p..q]$ and $M + A[q+1..r]$.
The merge function creates ______ of the subarrays $L + A[p..q]$ and $M + A[q+1..r]$.
Until we reach the end of either L or M, pick the ______ among the elements from L and M and place them in the correct position at $A[p..q]$.
Until we reach the end of either L or M, pick the ______ among the elements from L and M and place them in the correct position at $A[p..q]$.
Before merging, pick up the remaining elements after running out of elements in either L or M and put in ______.
Before merging, pick up the remaining elements after running out of elements in either L or M and put in ______.
In the merge function, the current index of L is maintained by i, starting at ______.
In the merge function, the current index of L is maintained by i, starting at ______.
In the Java code, n1 is calculated as qp + 1, representing the size of subarray ______.
In the Java code, n1 is calculated as qp + 1, representing the size of subarray ______.
The condition if (L[i] <= M[j]) in the merge function checks if the element in L is less than or equal to the element in ______.
The condition if (L[i] <= M[j]) in the merge function checks if the element in L is less than or equal to the element in ______.
The mergeSort function recursively calls itself with the subarrays arr, l, m and arr, m + 1, ______.
The mergeSort function recursively calls itself with the subarrays arr, l, m and arr, m + 1, ______.
The space complexity of Merge Sort is O(______).
The space complexity of Merge Sort is O(______).
Merge Sort is a ______ sorting algorithm according to the additional notes.
Merge Sort is a ______ sorting algorithm according to the additional notes.
Flashcards
What is Merge Sort?
What is Merge Sort?
A sorting algorithm that divides the unsorted list into 'n' sub-lists, each containing one element, and then repeatedly merging sub-lists to produce new sorted sub-lists until there is only one sub-list remaining, which is the sorted list.
What is a stable sorting algorithm?
What is a stable sorting algorithm?
It maintains the relative order of equal elements in the sorted output.
What is the time complexity of Merge Sort?
What is the time complexity of Merge Sort?
Merge Sort has a consistent and predictable performance with a time complexity of O(n log n) in the worst, average, and best cases.
When is Merge Sort useful for external sorting?
When is Merge Sort useful for external sorting?
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Does Merge Sort allow parallelization?
Does Merge Sort allow parallelization?
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Is Merge Sort memory-efficient?
Is Merge Sort memory-efficient?
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What is main idea of Merge Sort?
What is main idea of Merge Sort?
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How does MergeSort divide?
How does MergeSort divide?
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What does merging mean in MergeSort?
What does merging mean in MergeSort?
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What subarrays created in merge function?
What subarrays created in merge function?
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What are the three pointers used in Merge Sort?
What are the three pointers used in Merge Sort?
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Space complexity of Merge Sort
Space complexity of Merge Sort
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Study Notes
- Merge Sort is a sorting algorithm that uses the divide-and-conquer paradigm.
- It divides an unsorted list into n sub-lists, each with one element.
- It repeatedly merges sub-lists to create new sorted sub-lists until only one sorted sub-list remains.
Merge Sort Algorithm Steps
- Divide: Split the unsorted list into n sub-lists, each containing one element.
- Conquer: Repeatedly merge sub-lists into sorted sub-lists until one remains.
- Merge: Combine two sub-lists into a single sorted sub-list, repeating until the final sorted list is achieved.
- The merging of two sorted sub-lists is the key operation.
Advantages
- Stability: Merge Sort is stable, preserving the relative order of equal elements in the output.
- Predictable Performance: It has a time complexity of O(n log n) in all cases.
- External Sorting: Well-suited for external sorting where data is too large for memory.
- Parallelization: Can be easily parallelized for performance enhancement.
- Consistent Memory Usage: Uses a consistent amount of additional memory.
- Ease of Implementation: Straightforward and modular implementation.
Considerations
- Other algorithms like Quicksort, Heapsort, or insertion sort may be more appropriate depending on specific data requirements.
- Quicksort may be faster for small or pre-sorted datasets.
Decomposition
- MergeSort repeatedly divides the array into two halves until reaching a subarray of size 1.
- Achieved through recursion until it stops.
Merging Process
- The merge step involves merging two sorted lists (arrays) into one large sorted list (array).
- The algorithm uses three pointers: one for each array and one for the final sorted array.
- It compares elements from both arrays and copies the smaller element into the sorted array, moving the pointer accordingly.
- Remaining elements from the non-empty array are then copied.
Code Implementation
- Task: Merge two subarrays A[p..q] and A[q+1..r] into a sorted array A[p..r].
- Inputs: A, p, q, and r.
- Steps:
- Create copies of subarrays L (A[p..q]) and M (A[q+1..r]).
- Initialize three pointers i, j, and k for L, M, and A[p..q], respectively.
- Select larger elements from either L or M and place them in the correct position in A[p..q] until one of them runs out of elements.
- Transfer the remaining elements into A[p..q].
Time and Space Complexity
- Time Complexity:
- Best: O(n*log n)
- Worst: O(n*log n)
- Average: O(n*log n)
- Space Complexity: O(n)
- Stable: Yes
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