Data structures and algorithms - sorting algorithms

Jun 21, 20152 likes1,733 views

This document discusses different sorting algorithms and their complexities. It covers slow sorts like bubble sort and insertion sort which have quadratic time complexity, as well as medium sorts like merge sort which has linearithmic time complexity. Merge sort works by dividing the array into sublists of one element and then merging the sublists together until the entire list is sorted. The document provides pseudocode examples and analyses the time complexities of various sorting algorithms.

Data Structures and Algorithms -
Sorting algorithms
Abimbola Idowu
The Andela Institute

Why sorting algorithms
3
• Efficient sorting is important for the use of other
algorithms such as search
• The way data is sorted affects how fast it can be
traversed or searched for
• Poor choice of algorithms affect the runtime of our
code

Classifications
• Computation complexity
• Memory Usage
• Stability
• Comparison sort...
4

Bubble Sort
• Loop through the array
• Compares each pair of adjacent elements
• Swaps if they are in wrong order
• Repeat until no swap is done
• Array is sorted
6

Pseudocode
7
procedure bubbleSort( A : list of sortable items )
n = length(A)
repeat
swapped = false
for i = 1 to n-1 inclusive do
/* if this pair is out of order */
if A[i-1] > A[i] then
/* swap them and remember something changed */
swap( A[i-1], A[i] )
swapped = true
end if
end for
until not swapped
end procedure

Bubble sort complexity
8
Best Average Worst
n n2
n2

Insertion sort
• Loop through the array
• Pick an element in the array
• Find the location where it belongs in the array
• Continue till loops ends
• Array is sorted
9

Pseudocode
10
for i ← 1 to length(A) - 1
j ← i
while j > 0 and A[j-1] > A[j]
swap A[j] and A[j-1]
j ← j - 1
end while
end for

Insertion sort complexity
11
Best Average Worst
n n2
n2

Why is slow slow
12
• Comparison is local
• Guarantee to always make a lot of
comparison

Merge Sort
• Divide the array in sublist until each sublist
contains one elements
• Merge sublists until there are one
• Array is sorted
14

Pseudocode
15
function merge(left, right)
var list result
while notempty(left) and notempty(right)
if first(left) <= first(right)
append first(left) to result
left = rest(left)
else
append first(right) to result
right = rest(right)
// either left or right may have elements left
while notempty(left)
append first(left) to result
left = rest(left)
while notempty(right)
append first(right) to result
right = rest(right)
return result

Merge sort complexity
16
Best Average Worst
n n logn n logn

Next time
• Other types of medium sorts
• Fast sorts
17

The document discusses several sorting algorithms: insertion sort, selection sort, bubble sort, and merge sort. It provides descriptions of how each algorithm works and comparisons of their time complexities. For insertion sort, it notes its advantage for nearly sorted data but quadratic worst-case time. Selection sort runs in quadratic time with little advantage for ordered data. Bubble sort is easy to implement but slower than insertion sort. Merge sort works by recursively dividing the array into halves and then merging the sorted halves.

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The document discusses different types of searching algorithms. It describes sequential search which searches an unsorted list sequentially until the target item is found or the entire list is searched. The average runtime is O(n) as the item could be anywhere in the list. Binary search is described as more efficient for sorted lists, repeatedly dividing the search space in half and comparing the target to the middle element. Indexes are also summarized, including clustered vs unclustered indexes and different approaches to storing data entries.

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The document discusses various sorting algorithms. It describes how sorting algorithms arrange elements of a list in a certain order. Efficient sorting is important as a subroutine for algorithms that require sorted input, such as search and merge algorithms. Common sorting algorithms covered include insertion sort, selection sort, bubble sort, merge sort, and quicksort. Quicksort is highlighted as an efficient divide and conquer algorithm that recursively partitions elements around a pivot point.

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This document discusses different sorting algorithms including bubble sort, insertion sort, and selection sort. It provides details on each algorithm, including time complexity, code examples, and graphical examples. Bubble sort is an O(n2) algorithm that works by repeatedly comparing and swapping adjacent elements. Insertion sort also has O(n2) time complexity but is more efficient than bubble sort for small or partially sorted lists. Selection sort finds the minimum value and swaps it into place at each step.

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This presentation discusses several sorting algorithms: insertion sort, merge sort, quick sort, and counting sort. Insertion sort iterates through a list and inserts each element into the sorted position. Merge sort and quick sort are divide-and-conquer algorithms that split the list into halves, sort the halves, and merge the results. Counting sort works by counting the number of objects that have each distinct key value. The algorithms are analyzed and their time and space complexities are compared.

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The document presents information on insertion sort, including: - Insertion sort works by partitioning an array into sorted and unsorted portions, iteratively finding the correct insertion point for elements in the unsorted portion and shifting other elements over to make space. - The insertion sort algorithm uses a nested loop structure to iterate through the array, comparing elements and shifting them if needed to insert the current element in the proper sorted position. - The time complexity of insertion sort is O(n^2) in the worst case when the array is reverse sorted, requiring up to n(n-1)/2 comparisons and shifts, but it is O(n) in the best case of a presorted array. On average,

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The document discusses sorting algorithms and randomized quicksort. It explains that quicksort is an efficient sorting algorithm that was developed by Tony Hoare in 1960. The quicksort algorithm works by picking a pivot element and reordering the array so that all smaller elements come before the pivot and larger elements come after. It then recursively applies this process to the subarrays. Randomized quicksort improves upon quicksort by choosing the pivot element randomly, making the expected performance of the algorithm good for any input.

Insertion sortLovely Professional University

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The document discusses the quicksort algorithm. It begins by stating the learning goals which are to explain how quicksort works, compare it to other sorting algorithms, and discuss its advantages and disadvantages. It then provides an introduction and overview of quicksort, describing how it uses a divide and conquer approach. The document goes on to explain the details of how quicksort partitions arrays and provides examples. It analyzes the best, average, and worst case complexities of quicksort and discusses its strengths and limitations.

Insertion sortDorina Isaj

Insertion sort is an algorithm that iterates through an array, comparing each element to its predecessor and swapping the two if out of order, until the entire array is sorted from lowest to highest value. It is more efficient than bubble sort because it requires fewer element comparisons. While slower than quick sort, heap sort, or merge sort for large arrays, insertion sort performs well for small or nearly-sorted data sets due to its simple implementation requiring only O(n) time at best case. Pseudocode and Java code are provided as examples.

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Insertion sortalmaqboli

Insertion sort works by iterating through an array, inserting each element into its sorted position by shifting other elements over. It finds the location where each element should be inserted into the sorted portion using a linear search, moving larger elements out of the way to make room. This sorting algorithm is most effective for small data sets and can be implemented recursively or iteratively through comparisons and shifts.

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Quicksort is a sorting algorithm developed by Tony Hoare in 1960 that uses a divide-and-conquer approach. It works by first selecting a pivot element and partitioning the array around it, such that all elements with values less than the pivot come before elements with values greater than the pivot. It then recursively applies the same approach to the sub-arrays until the entire list is sorted. Radix sort is a non-comparative integer sorting algorithm that sorts data by grouping keys based on their individual digit values at each significant position. It makes multiple passes over the data, sorting by one digit on each pass in order of significant value.

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This document provides a summary of a lecture on sorting algorithms: 1) It introduces sorting concepts and sorting problems. Common sorting algorithms discussed include selection sort, insertion sort, merge sort, and quick sort. 2) Selection sort and insertion sort algorithms are explained in detail with examples. Selection sort has a running time of O(n^2) in all cases. 3) Insertion sort's running time depends on how sorted the input array is - it is O(n) for a presorted array but O(n^2) for a reverse sorted array. 4) The time complexity of both algorithms is analyzed mathematically. Selection sort is always O(n^2) while

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Data structures and algorithms - sorting algorithms

1. Data Structures and Algorithms - Sorting algorithms Abimbola Idowu The Andela Institute

2. Introduction to Sorting Algorithms

3. Why sorting algorithms 3 • Efficient sorting is important for the use of other algorithms such as search • The way data is sorted affects how fast it can be traversed or searched for • Poor choice of algorithms affect the runtime of our code

4. Classifications • Computation complexity • Memory Usage • Stability • Comparison sort... 4

5. Part 1 - Slow sort

6. Bubble Sort • Loop through the array • Compares each pair of adjacent elements • Swaps if they are in wrong order • Repeat until no swap is done • Array is sorted 6

7. Pseudocode 7 procedure bubbleSort( A : list of sortable items ) n = length(A) repeat swapped = false for i = 1 to n-1 inclusive do /* if this pair is out of order */ if A[i-1] > A[i] then /* swap them and remember something changed */ swap( A[i-1], A[i] ) swapped = true end if end for until not swapped end procedure

8. Bubble sort complexity 8 Best Average Worst n n2 n2

9. Insertion sort • Loop through the array • Pick an element in the array • Find the location where it belongs in the array • Continue till loops ends • Array is sorted 9

10. Pseudocode 10 for i ← 1 to length(A) - 1 j ← i while j > 0 and A[j-1] > A[j] swap A[j] and A[j-1] j ← j - 1 end while end for

11. Insertion sort complexity 11 Best Average Worst n n2 n2

12. Why is slow slow 12 • Comparison is local • Guarantee to always make a lot of comparison

13. Part 2 - Medium Sort

14. Merge Sort • Divide the array in sublist until each sublist contains one elements • Merge sublists until there are one • Array is sorted 14

15. Pseudocode 15 function merge(left, right) var list result while notempty(left) and notempty(right) if first(left) <= first(right) append first(left) to result left = rest(left) else append first(right) to result right = rest(right) // either left or right may have elements left while notempty(left) append first(left) to result left = rest(left) while notempty(right) append first(right) to result right = rest(right) return result

16. Merge sort complexity 16 Best Average Worst n n logn n logn

17. Next time • Other types of medium sorts • Fast sorts 17

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