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Analysis and Design of Algorithms Sorting Algorithms I

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Analysis and Design of Algorithms Sorting Algorithms Bubble Sort Selection Sort Insertion Sort

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Analysis and Design of Algorithms  Sorting Algorithm is an algorithm made up of a series of instructions that takes an array as input, and outputs a sorted array.  There are many sorting algorithms, such as:  Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Comb Sort, Pigeonhole Sort, Cycle Sort

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Analysis and Design of Algorithms Bubble Sort

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Analysis and Design of Algorithms Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.

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Analysis and Design of Algorithms Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Swap two element if necessary  Step3: Repeat this process for all the elements until the entire array is sorted

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Analysis and Design of Algorithms  Example 1 Assume the following Array: 5 1 4 2

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Analysis and Design of Algorithms  First Iteration:  Compare 5 1 4 2  j  j+1

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Analysis and Design of Algorithms  First Iteration:  Swap 1 5 4 2  j  j+1

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Analysis and Design of Algorithms  First Iteration:  Compare 1 5 4 2  j  j+1

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Analysis and Design of Algorithms  First Iteration:  Swap 1 4 5 2  j  j+1

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Analysis and Design of Algorithms  First Iteration:  Compare 1 4 5 2  j  j+1

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Analysis and Design of Algorithms  First Iteration:  Swap 1 4 2 5  j  j+1

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Analysis and Design of Algorithms 1 4 2 5

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Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1

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Analysis and Design of Algorithms  Second Iteration:  Compare 1 4 2 5  j  j+1

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Analysis and Design of Algorithms  Second Iteration:  Swap 1 2 4 5  j  j+1

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Analysis and Design of Algorithms 1 2 4 5

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Analysis and Design of Algorithms  Third Iteration:  Compare 1 2 4 5  j  j+1

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Analysis and Design of Algorithms 1 2 4 5

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Analysis and Design of Algorithms  Array is now sorted 1 2 3 4

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Analysis and Design of Algorithms 5 4 2 1 3 4 5 2 1 3 4 2 5 1 3 4 2 1 5 3 4 2 1 3 5 4 2 1 3 5 2 4 1 3 5 2 1 4 3 5 2 1 3 4 5 2 1 3 4 5 1 2 3 4 5 1 2 3 4 5  Example 2:

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Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63

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Analysis and Design of Algorithms  What is the output of bubble sort after the 1st iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63

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Analysis and Design of Algorithms  Python Code

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Analysis and Design of Algorithms

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Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 5 4 3 2 1

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Analysis and Design of Algorithms Selection Sort

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Analysis and Design of Algorithms The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from unsorted part and putting it at the beginning.

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Analysis and Design of Algorithms Algorithm:  Step1: Find the minimum value in the list  Step2: Swap it with the value in the current position  Step3: Repeat this process for all the elements until the entire array is sorted

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Analysis and Design of Algorithms  Example 1 Assume the following Array: 8 12 5 9 2

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Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min

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Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  j  min

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Analysis and Design of Algorithms  Move 8 12 5 9 2  j  i  min

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Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j

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Analysis and Design of Algorithms  Compare 8 12 5 9 2  i  min  j

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Analysis and Design of Algorithms  Move 8 12 5 9 2  i  j  min

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Analysis and Design of Algorithms  Smallest 8 12 5 9 2  i  min

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Analysis and Design of Algorithms  Swap 8 12 5 9 2  min  i

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Analysis and Design of Algorithms  Sorted  Un Sorted 2 12 5 9 8  Sorted  Un Sorted

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Analysis and Design of Algorithms  Compare 2 12 5 9 8  i  min  j  Sorted

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Analysis and Design of Algorithms  Move 2 12 5 9 8  i  min  j  Sorted

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Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min

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Analysis and Design of Algorithms  Compare 2 12 5 9 8  Sorted  i  j  min

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Analysis and Design of Algorithms  Smallest 2 12 5 9 8  Sorted  i  min

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Analysis and Design of Algorithms  Swap 2 12 5 9 8  Sorted  i  min

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Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 12 9 8  Sorted  Un Sorted

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Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  j  min

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Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  j  min

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Analysis and Design of Algorithms  Compare 2 5 12 9 8  Sorted  i  min  j

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Analysis and Design of Algorithms  Move 2 5 12 9 8  Sorted  i  min  j

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Analysis and Design of Algorithms  Smallest 2 5 12 9 8  Sorted  i  min

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Analysis and Design of Algorithms  Swap 2 5 12 9 8  Sorted  i  min

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Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted

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Analysis and Design of Algorithms  Compare 2 5 8 9 12  Sorted  i  min  j

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Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  Un Sorted

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Analysis and Design of Algorithms  Sorted  Un Sorted 2 5 8 9 12  Sorted  i  min

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Analysis and Design of Algorithms  Array is now sorted 2 5 8 9 12  Sorted

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Analysis and Design of Algorithms 12 10 16 11 9 7  Example 2: 7 10 16 11 9 12 7 9 16 11 10 12 7 9 10 11 16 12 7 9 10 11 16 12 7 9 10 11 12 16 12 10 16 11 9 7

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Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63

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Analysis and Design of Algorithms  What is the output of selection sort after the 2nd iteration given the following sequence of numbers: 13 2 9 4 18 45 37 63 a) 2 4 9 13 18 37 45 63 b) 2 9 4 13 18 37 45 63 c) 13 2 4 9 18 45 37 63 d) 2 4 9 13 18 45 37 63

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Analysis and Design of Algorithms  Python Code

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Analysis and Design of Algorithms

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Analysis and Design of Algorithms  Time Complexity: O(n2) as there are two nested loops  Example of worst case 2 3 4 5 1

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Analysis and Design of Algorithms Insertion Sort

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Analysis and Design of Algorithms Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands.

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Analysis and Design of Algorithms  Algorithm:  Step1: Compare each pair of adjacent elements in the list  Step2: Insert element into the sorted list, until it occupies correct position.  Step3: Swap two element if necessary  Step4: Repeat this process for all the elements until the entire array is sorted

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Analysis and Design of Algorithms  Assume the following Array: 5 1 4 2

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Analysis and Design of Algorithms  Compare  Store= 5 1 4 2  i  j  j+1 1

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Analysis and Design of Algorithms  Move  Store= 5 4 2  i  j  j+1 1

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Analysis and Design of Algorithms  Move  Store= 1 5 4 2  i  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 5 4 2  i  j 4  j+1

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Analysis and Design of Algorithms  Move  Store= 1 5 2  i  j 4  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 5 2  i  j 4  j+1

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Analysis and Design of Algorithms  Move  Store= 1 4 5 2  i  j  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 4 5 2  i  j 2  j+1

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Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1

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Analysis and Design of Algorithms  Move  Store= 1 4 5  i  j 2  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 4 5  i  j 2  j+1

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Analysis and Design of Algorithms  Compare  Store= 1 2 4 5  i  j  j+1

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Analysis and Design of Algorithms  Array is now sorted 1 2 4 5

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Analysis and Design of Algorithms 5 1 8 3 9 2  Example 2: 1 5 8 3 9 2 1 5 8 3 9 2 1 3 5 8 9 2 1 3 5 8 9 2 1 2 3 5 8 9 5 1 8 3 9 2

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Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9

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Analysis and Design of Algorithms  What is the output of insertion sort after the 1st iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 7 5 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9

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Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9

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Analysis and Design of Algorithms  What is the output of insertion sort after the 2nd iteration given the following sequence of numbers: 7 3 5 1 9 8 4 6 a) 3 5 7 1 9 8 4 6 b) 1 3 7 5 9 8 4 6 c) 3 4 1 5 6 8 7 9 d) 1 3 4 5 6 7 8 9

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Analysis and Design of Algorithms  Python Code

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Analysis and Design of Algorithms

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Analysis and Design of Algorithms  Time Complexity: O(n2)  Example of worst case 5 4 3 2 1

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Analysis and Design of Algorithms facebook.com/mloey [email protected] twitter.com/mloey linkedin.com/in/mloey [email protected] mloey.github.io

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