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Simple Sorting Algorithm (Recap)
for in range(len(A)) : k = position of min. element between A [i] and A [N-1] Swap A [i] and A [k]
A[0] A[i] A[i+1]
A[N-1]
Courtesy Prof P R Panda CSE, IIT Dellhi
Sorting Simple Sorting Algorithm (Recap) A[0] A[i] A[i+1] A[N-1] - - PowerPoint PPT Presentation
Sorting Simple Sorting Algorithm (Recap) A[0] A[i] A[i+1] A[N-1] - - PowerPoint PPT Presentation
Sorting Simple Sorting Algorithm (Recap) A[0] A[i] A[i+1] A[N-1] for in range(len(A)) : k = position of min. element between A [i] and A [N-1] Swap A [i] and A [k] Selection Sort Courtesy Prof P R Panda CSE, IIT Dellhi 2 Simple Sorting
SLIDE 2
SLIDE 3
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Simple Sorting Algorithm (Recap)
for j in range(i+1, len(A)): if A[min_index] > A[j]: min_index = j t = A [ i ] A [ i ] = A [ k ] A [ k ] = t A[0] A[i] A[i+1]
A[N-1]
Courtesy Prof P R Panda CSE, IIT Dellhi
for in range(len(A)) : k = position of min. element between A [i] and A [N-1] Swap A [i] and A [k]
Selection Sort
SLIDE 4
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Simple Sorting Algorithm (Recap)
A[0] A[i] A[i+1]
A[N-1]
Courtesy Prof P R Panda CSE, IIT Dellhi
Find Min for first time n elements: n-1 coparisons Next time : n-2 . . up to 1 Total time = (n-1)+(n-2)+….+1=(n*(n-1))/2 O(n2)
Selection Sort
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
SLIDE 6
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
SLIDE 7
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
SLIDE 8
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
SLIDE 9
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
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Merge Sort
Divide and conquer
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Merge Sort
Divide and conquer
Source:https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-0001-introduction-to-computer- science-and-programming-in-python-fall-2016/lecture-slides-code/
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Merge Sort
Running Time (Time Complexity as O) Recurrence Relation: T(1)=1 if n=1 T(n) = 2T(n/2) + cn Solution O(nlog2n)
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Quick Sort
Based on partitioing in two parts such that first part is less than equal to x and right part is greater than x. If x is an element of the array then it gets located at the right place if the seuqence is sorted.
A[0]
A[N-1]
x <=x >x pivot
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Quick Sort
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Quick Sort
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Quick Sort
Choice of pivot decides the performance of the
- algorithm. If the partitioning happens in two almost
equal parts, it is an ideal case. Time Complexity Best Case: T(1)=1 T(n)=2T(n/2)+cn where cn is the partining time Complexity O(nlog2n)
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Quick Sort
Time Complexity Worst Case: T(1)=1 T(n)=T(n-1)+T(1)+ cn where cn is the partining time Complexity O(n2) Average Case: O(nlog2n)
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Insertion Sort
Basic idea is to insert the current element at the right place. This may require shifting the elements
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Insertion Sort
https://www.geeksforgeeks.org/insertion-sort/
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Insertion Sort
Time Complexity Worst Case: O(n2) when elements are sorted in the reverse order Best Case: O(n) when elements are already sorted
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Bubble Sort
https://codingcompiler.com/bubble-sort-program-in-c-using-function/
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