public class Sort {
void insertionSort(int[] arr) {
int n = arr.Length;
for (int i=1; i < n; i++) {
int key = arr[i];
int j = i-1;
/* Insert arr[i] or key into the sorted sequence arr[0...i-1] */
while(j>=0 && arr[j] > key) {
arr[j+1] = arr[j];
j--;
}
arr[j+1] = key;
}
}
public static void Main(string[] args) {
int[] arr = {5, 3, 6, 2, 1, 4};
Sort sort = new Sort();
sort.insertionSort(arr);
for(int i=0; i < arr.Length; i++) {
System.Console.Write( arr[i]+", ");
}
}
}
We are just bothered about the void insertionSort(int[] arr) method, where the sortinglogic is defined.
We have the array
int[] arr = {5, 3, 6, 2, 1, 4};Which we have passed to the insertionSort(..) method.
In the insertionSort(..) method, we have taken the count of the elements of the array.
int n = arr.Length;
Then, we are running a for loop which will iterate the array starting from the secondelement till the last element.
for (int i=1; i < n; i++)
And we are setting the 2nd element of the array as the key.
int 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.
int 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 && arr[j] > key) {
arr[j+1] = arr[j];
j--;
}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.
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.
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).
And in best case the running time is O(n).