PYTHON - INSERTION SORT CODE

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Example :


def insertion_sort(arr):
    n = len(arr)
    for i in range(1, n):
        key = arr[i]
        j = i-1

        #Insert arr[i] or key into the sorted sequence arr[0...i-1]

        while j>=0 and arr[j] > key :

            arr[j+1] = arr[j]
            j-=1

        arr[j+1] = key


arr = [5, 3, 6, 2, 1, 4]
insertion_sort(arr)
for i in range(len(arr)):
    print(arr[i])

Output :

1
2
3
4
5
6

We are just bothered about the def insertion_sort(arr) method, where the sorting logicis defined.

We have the array

arr = [5, 3, 6, 2, 1, 4]

Which we have passed to the insertion_sort(..) method.

In the insertion_sort(..) method, we have taken the count of the elements of the array.

n = len(arr)

Then, we are running a for loop which will iterate the array starting from the secondelement till the last element.

for i in range(1, n):

And we are setting the 2nd element of the array as the key.

key = arr[i]

i.e. Content of arr[1] is the key initially. So, the value of key is 3.

Then we make the value of j as i-1.

j = i-1

That's because we need to compare the key (i.e. arr[1]) with the left hand side elements(i.e. arr[0], where the value of j is 0) of the key.

And that is where the while loop comes into picture. Which takes care of the comparisonof the key with the left hand side of the array.

while j>=0 and arr[j] > key :
	arr[j+1] = arr[j]
	j-=1

Note : Refer to the above diagram.

The above while loop is quite self explanatory. Where, we are getting into the whileloop if the key(i.e. value of arr[1] that is 3) is less than arr[j] (i.e. value ofarr[0] that is 5).

And we are replacing the value of arr[j+1](i.e. arr[1]) with arr[j] (i.e. arr[0]).

arr[j+1] = arr[j]

Now, arr[1] contains 5. Also arr[0] contains 5, but arr[0] should be 3.

So, how the value of arr[0] is replaced by 3.

That happens when we get out of the loop, when the condition j>=0 is met by while loop.

Note : Remember the control comes out of while loop when j is less than 0. Which means whenthe value of j becomes -1.

And set the value of arr[0] with the key (i.e. 3).

arr[j+1] = key

Since, -1+1 is 0. So the above is arr[0] = key.

And finally, arr[0] is set to 3.

Similar, process follows for the entire loop.

Efficiency / Running time of Insertion Sort

If we consider the Insertion Sort Algorithm, there are two loops. First is the for loop.And inside the for loop there is a while loop.

The for loop executes n times(Assuming the array contains n elements).

Now, for each iteration of for loop, the while loop also executes n times in worstcase.

Which means for 1st iteration of for loop,

while loop runs 1 time.

Similarly, for 2nd iteration of for loop,

while loop runs 2 times.

Similarly, for nth iteration of for loop,

while loop runs n times.

So, the running time is close to n*n or n^2.

So, in worst case the running time is O(n^2).

Note : Worst case is the scenario where the array elements are all sorted in descendingorder. i.e. 6, 5, 4, 3, 2, 1.

And in best case the running time is O(n).

Note : Best case is the scenario where the array elements are all sorted in ascending order.

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