Merge Sort
Introduction to Merge Sort
Merge Sort is a popular sorting algorithm that follows the divide and conquer approach. The algorithm works by breaking down the list into smaller sub-lists and sorting them individually.
These sorted sub-lists are then merged back together to obtain the final sorted list.
Time & Space Complexity
- Merge sort is a divide and conquer algorithm, it has a logarithmic time complexity of O(n log n)
- Merge sort's space complexity is O(n)
What is a merge sort?
{"answers": {"A": "C - A sorting algorithm that finds the smallest element and puts it first", "B": "A - A sorting algorithm that repeatedly swaps adjacent elements", "C": "D - A sorting algorithm that divides the data in half and sorts each half", "D": "B - A sorting algorithm that puts elements into buckets"}, "question_text": "What is a merge sort?", "correct_answer": "C"}
Steps of Merge Sort
- Divide the unsorted list into smaller sub-lists until each sub-list contains only one element.
- Repeatedly merge adjacent sub-lists to produce new sorted sub-lists until there is only one sub-list remaining. This is done by comparing the elements of the sub-lists and merging them in the correct order.
- The final sorted list is obtained when all sub-lists are merged.
Merge Sort in Python
def merge_sort(arr):
if len(arr) <= 1: return arr
mid = len(arr) // 2
left = merge_sort(arr[:mid])
right = merge_sort(arr[mid:])
return merge(left, right)
def merge(left, right):
result, i, j = [], 0, 0
while i < len(left) and j < len(right):
result.append(left[i] if left[i] < right[j] else right[j])
if left[i] < right[j]: i += 1
else: j += 1
return result + left[i:] + right[j:]
# Example
print(merge_sort([38, 27, 43, 3, 9, 82, 10]))Advantages of Merge Sort
- Merge Sort guarantees a stable sort, which means that the order of equal elements is preserved.
- It performs well on large lists and has a time complexity of O(n log n), where n is the number of elements in the list.
Merge Sort is a stable sorting algorithm. What does it mean?
{"answers": {"A": "It guarantees the worst-case time complexity of O(n log n).", "B": "It maintains the relative order of elements with equal keys.", "C": "It always sorts the array in ascending order.", "D": "It performs well for already partially sorted arrays."}, "question_text": "Merge Sort is a stable sorting algorithm. What does it mean?", "correct_answer": "B"}
Disadvantages of Merge Sort:
- It is not an in-place sorting algorithm, meaning it needs extra storage proportional to the size of the input list.
- Because it is usually implemented using recursion it can be difficult for beginner programmers to implement and understand.
- Due to the extra setup it's not efficient for very small lists ( < 40 items)
What is a disadvantage of Merge Sort?
{"answers": {"A": "The worst-case time complexity is O(n^2).", "B": "Inefficient for small-sized arrays.", "C": "Requires additional memory space.", "D": "Not suitable for sorting numbers."}, "question_text": "What is a disadvantage of Merge Sort?", "correct_answer": "C"}
Review: Fill in the Blanks
sort is a widely used ing algorithm that has a of Ο(n logn). It is a algorithm that follows the approach. The key step in is the , which combines two sorted sub-arrays into a single sorted array.
The merge function is crucial for the , an implementation of Merge sort that aims to minimize the use of additional memory. ing algorithms are advantageous in terms of as they do not require extra space proportional to the input size. However, in-place merge sort achieves this at the cost of additional and .
The time complexity of Merge sort is linearithmic, which means it grows in a non-linear, but not quadratic, fashion. The is commonly used to express the time complexity of algorithms and Merge sort has a Ο(n logn) time complexity in both average and worst-case scenarios.
Merge sort is a , meaning that it maintains the relative order of equal elements in the input sequence. This stability is preserved through the recursive nature of the algorithm.
plays a significant role in Merge sort, as the algorithm divides the input array into smaller sub-arrays until each sub-array consists of a single element. Then, the algorithm recursively merges these sub-arrays back together until the entire array is sorted.
The space complexity of Merge sort is dependent on the implementation. In the in-place merge sort, since the merging happens in-place, the space complexity is Ο(n). However, in the , where extra memory is allocated for merging, the space complexity is Ο(n logn).
To better understand the steps involved in Merge sort, let's take a look at the :
In summary, Merge sort is an efficient and stable sorting algorithm with a . Its recursive nature, along with the merge function, allows it to divide the input array, sort the smaller sub-arrays, and merge them back together to obtain the final sorted array.
The merge function is crucial for the , an implementation of Merge sort that aims to minimize the use of additional memory. ing algorithms are advantageous in terms of as they do not require extra space proportional to the input size. However, in-place merge sort achieves this at the cost of additional and .
The time complexity of Merge sort is linearithmic, which means it grows in a non-linear, but not quadratic, fashion. The is commonly used to express the time complexity of algorithms and Merge sort has a Ο(n logn) time complexity in both average and worst-case scenarios.
Merge sort is a , meaning that it maintains the relative order of equal elements in the input sequence. This stability is preserved through the recursive nature of the algorithm.
plays a significant role in Merge sort, as the algorithm divides the input array into smaller sub-arrays until each sub-array consists of a single element. Then, the algorithm recursively merges these sub-arrays back together until the entire array is sorted.
The space complexity of Merge sort is dependent on the implementation. In the in-place merge sort, since the merging happens in-place, the space complexity is Ο(n). However, in the , where extra memory is allocated for merging, the space complexity is Ο(n logn).
To better understand the steps involved in Merge sort, let's take a look at the :
In summary, Merge sort is an efficient and stable sorting algorithm with a . Its recursive nature, along with the merge function, allows it to divide the input array, sort the smaller sub-arrays, and merge them back together to obtain the final sorted array.
Click the keywords below to fill in the blanks:
Out-Of-Place Sort
Recursive
Merge Sort
Space Complexity
Merge
Time Complexity
Comparison-Based Sort
Linearithmic Time Complexity
In-Place Merge Sort
Average Case
Stable Sort
In-Place Sort
Merge Function
Pseudocode
Recursion
Big-O Notation
Divide And Conquer
Swaps
Comparisons
✓ All blanks filled correctly! Great job!
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Introduction to Merge Sort
- Introduction to Merge Sort
- Steps of Merge Sort
- Merge Sort in Python
- Advantages of Merge Sort
- Disadvantages of Merge Sort:
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