3. CONTENTS
Introduction
Working
Algorithm and Explanation
Example with Steps
Run time Analysis of Algorithm
Implementation of Code
Output
Advantages and Disadvantage
Application
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4. Introduction
Sorting 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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5. WORKING
Insertion 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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6. WORKING
This 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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7. METHOD
Pass 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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8. ALGORITHM & EXPLANATION
Step1. Start
Step2. i=1
Step3. Check that I < a.length, if yes go to
next
step else go to Step11.
Step4. Assign ai = a[i]
Step5. j = i
Step6. 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 6
Step9. a[j] = ai
Step10. increment i by 1 and go to step 3.
Step11. Stop
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9. DEMONSTRATION
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 .
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79
47
13
74
36
21
94
56
60
10. 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.
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22
79
79
47
47
13
13
74
74
36
36
21
21
94
94
56
56
60
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14. 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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16. IMPLEMENTATION OF CODE
public 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("nnValues after the sort:n");
for(int i = 0; i <array.length; i++)
System.out.print(array[i]+" ");
System.out.println();
}
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17. 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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19. ADVANTAGES
The main advantage of the insertion sort is
its simplicity.
Advantages of insert sort
Simple to code
Very 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 intact
Very memory efficient .
Good with sequential data that is being read
in one at a time e.g. tape, hard disk.
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20. 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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21. Insertion Sort Efficiency
Sort 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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22.
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
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