Java presentation on

INSERTION SORT

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Presentation by

Faisal Shaikh (+919664710953)

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CONTENTSIntroductionWorkingAlgorithm and ExplanationExample with StepsRun time Analysis of AlgorithmImplementation of CodeOutputAdvantages and DisadvantageApplication

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IntroductionSorting data is one of the most

important computing applications.Insertion sort is one of the techniques

used for sorting data. Inserting a new item into a sorted

part of a sub array at each pass through the array is insertion sort.

Insertion sort performs different number of comparisons depending on the initial ordering of the elements.

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WORKINGInsertion sort algorithm divides the list

into two parts sorted and unsorted.

Sorted part contains only one element, one element from the unsorted list is inserted at its correct position in the sorted list.

As a result, sorted list grows by one element and the unsorted list shrinks by one element in each pass.

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WORKINGThis sorting algorithm is

frequently used when n is small. The insertion sort algorithm

scans A from A[1] to A[N], inserting each element A[K] into its proper position in the previously sorted sub array A[1], A[2], …., A[K-1]. That is…

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METHODPass 1. A[1] by itself is trivially sorted.

Pass 2. A[2] is inserted either before or after A[1] so that: A[1], A[2] is sorted.

Pass 3. A[3] is inserted into its proper place in A[1], A[2], that is, before A[1], between A[1] & A[2], or after A[2], so that: A[1], A[2], A[3] is sorted.

Pass 4. A[4] is inserted into its proper place in A[1], A[2], A[3] so that:

A[1], A[2], A[3], A[4] is sorted.

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ALGORITHM & EXPLANATIONStep1. StartStep2. i=1Step3. Check that I < a.length, if yes go to

next step else go to Step11. Step4. Assign ai = a[i]Step5. j = iStep6. Check that j > 0 & a[j-1] > ai, if yes

go to next else go to Step9.Step7. a[j] = a[j-1]Step8. j = j-1 & go to Step 6Step9. a[j] = aiStep10. increment i by 1 and go to step 3.Step11. Stop

1. Insertion sort algorithm divides the list into parts, sorted and unsorted

2. Initially sorted list contain only one element.

3. In each pass, one element from the unsorted list is inserted at its correct position in sorted list.

4. Consider an unsorted list in an array .

DEMONSTRATION

22 79 47 13 74 36 21 94 56 60

22 79 47 13 74 36 21 94 56 60

22 79 47 13 74 36 21 94 56 60

22 79 47 13 74 36 21 94 56 60

To sort this list we need to divide the list into two sub-list sorted and unsorted, initially sorted list contain only one element. As shown in the figure below.

22 47 79 13 74 36 21 94 56 60

13 22 37 79 74 36 21 94 56 60

13 22 37 74 79 36 21 94 56 60

13 22 36 37 74 79 21 94 56 60

13 21 22 36 37 74 79 94 56 60

13 21 22 36 37 74 79 94 56 60

13 21 22 36 37 56 74 79 94 60

13 21 22 36 37 56 60 74 79 94

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RUNTIME ANALYSIS

In Insertion sort the worst case occurs when the array A is in reverse order and the inner loop must use the maximum number K-1 of comparisons. Hence

f(n) = 1 + 2 + … + (n-1) = n(n-1)/2 = O(n^2)

• The Average case, f(n) = ½ + 2/2 + … + n-1/2 = n(n-1)/4 = O(n^2)

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Summarized result Table:

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IMPLEMENTATION OF CODEpublic class InsertionSort{

public static void main(String a[]){

int array[] = {12,9,4,99,120,1,3,10};System.out.println("\nValues Before the sort:\n");

for(i = 0; i < array.length; i++)System.out.print( array[i]+" ");

insertion_srt(array, array.length); System.out.println("\n\nValues after the sort:\n");

for(int i = 0; i <array.length; i++)System.out.print(array[i]+" ");

System.out.println(); }

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public static void insertion_srt(int array[], int n){for (int i = 1; i < n; i++){

int j = i;int B = array[i];

while ((j > 0) && (array[j-1] > B)){ array[j] = array[j-1]; j--;}array[j] = B; } }}

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SNAPSHOT

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ADVANTAGES

The main advantage of the insertion sort is its simplicity.

Advantages of insert sortSimple to codeVery good performance with small lists.Very good when the list is almost sorted.Sort-stable which means it keeps the relative

positions of the elements intactVery memory efficient .Good with sequential data that is being read

in one at a time e.g. tape, hard disk.

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DISADVANTAGES

Disadvantages include the great inefficiency for large arrays.

The disadvantage of the insertion sort is that it does not perform as well as other, better sorting algorithms. 

Disadvantage of insertion sort compared to alternatives

Poor performance with large lists.Not as quick as merge sort or

quicksort

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Insertion Sort EfficiencySort algorithm determine the sort

effort for a given sort.Sort effort is defined as the relative

efficiency of a sort.It can be determined in several

ways, but we use the number of loops in the sort.

Another common measure is the number of moves and comparisons needed to sort the list

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Of course, the best measure is the time it takes to actually run the sort.

For analyzing different sorts, therefore he first two measure are more meaningful.

Let’s now analyze the straight insertion sort and the shell sort algorithm to determine their relative efficiency.

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THANK YOU!!