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Found in: Page 203

### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

# Show all the steps used by the binary insertion sort to sort the list 3, 2, 4, 5, 1, 6.

By using the binary insertion sort, the given array 3,2,4,5,1,6 became 1,2,3,4,5,6 .

See the step by step solution

## Step 1:

1. Binary insertion sort first compares the second element with the first element and places the second element as appropriate.
2. On each subsequent pass from now on, the current element is compared with the middle of the already sorted array and determines in which subinterval does the element lie.
3. This is done repeatedly until we have obtained the position at which the element should be ideally inserted and the element inserted at the correct place.
4. The given array is 3,2,4,5,1,6 .

## Step 2:

First, compare the 2 with the first element of our array, 3 .

Since 3 > 2 so inserted 2 before 3 .

Then the array become $2,3,4,5,1,6$ .

## Step 3:

Similarly, compare 4 with the first element of our array, 2 .

Since so insert after 2.

Now, compare 4 with the second element of our array, 3 .

Since 4 > 3 so insert 4 after 3 .

Then the array become 2,3,4,5,1,6 .

## Step 4:

Now, compare 5 with the second element of our array (as this element is the half-way point), 3 .

Since 5 > 3 so insert 5 after 3 .

Again, compare 5 with the third element of our array, 4 .

Since 5 > 4 so inserted 5 after 4.

Then the array become 2,3,4,5,1,6 .

## Step 5:

Now, compare 1 with the second element of our array (as this element is the half-way point) , 3 .

Since 1 < 3 then should be inserted before 3 .

Again, compare 1 with the first element of our array 2 .

Since 1 < 2 so should be inserted before 2 .

Then the array become 1,2,3,4,5,6 .

## Step 6:

Now, compare 6 with the third element of our array (as this element is now the half-way point), 3 .

Since 6 > 3 so inserted 6 after 3 .

Again, compare 6 with the fourth element of our array, 4 .

Since 6 > 4 so inserted 6 after 4 .

Again, compare 6 with the fifth element of our array, 5 .

Since 6 > 5 so inserted 6 after 5 .

Then the array become 1,2,3,4,5,6 .

Hence, the array become 1,2,3,4,5,6 .