Given the sequence 9 2 3 8 7 4 5 6 List all the element comp

Given the sequence 9, 2, 3, 8, 7, 4, 5, 6 List all the element comparisons made by insertion sort in the corresponding order. Use to denote a comparison of a and b. If the algorithm compares A[i] with A[j], you should write , rather than . For example, if the algorithms compares the first element with the fourth element, you should write , rather than .

Solution

In Insertion Sort, let A[i] is current element and A[j] is the next element in the array.

For each element A[i], if A[i]>A[j], swap the elements until A[i]<=A[j].

Solution:

Given Array of Elements: [ 9,2,3,8,7,4,5,6]

Step 1: A[i]=9, A[j]=2, As A[i]>A[j], so swap the elements, so new updated array is: [2,9,3,8,7,4,5,6]

Step 2: A[i]=9, A[j]=3, As A[i]>A[j], so swap the elements, so new updated array is: [2,3,9,8,7,4,5,6]

Step 3: A[i]=9, A[j]=8, As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,9,7,4,5,6]

Step 4: A[i]=9, A[j]=7, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,9,4,5,6]

Step 5: A[i]=9, A[j]=4, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,4,9,5,6]

Step 6: A[i]=9, A[j]=5, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,4,5,9,6]

Step 7: A[i]=9, A[j]=6, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,4,5,6,9]

NOTE: As per insertion sort logi 2 and 3 are at the correct position, so there is no need to compare them with other elements, so next element to be compared is 8.

Step 8: A[i]=8, A[j]7=, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,7,8,4,5,6,9]

Step 9: A[i]=8, A[j]=4, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,7,4,8,9,5,6]

Step 10: A[i]=8, A[j]=9, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,7,4,8,9,5,6]

Step 11: A[i]=9, A[j]=5, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,4,5,9,6]

Step 12: A[i]=9, A[j]=6, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,8,7,4,5,6,9]

Step 13: A[i]=8, A[j]=7, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,7,8,4,9,5,6]

Step 14: A[i]=8, A[j]=4, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,7,4,8,9,5,6]

Step 15: A[i]=7, A[j]=4, as As A[i]>A[j], so swap the elements, so new updated array is: [2,3,4,7,8,9,5,6]

Now we have to place 5, 6 as per the sorted element list so performing the comparision of element 5 and 6 with the 7,8,9, we get the answer as follow:

So the sorted array is : [2,3,4,5,6,7,8,9]