Insertion Sort Algorithm
Insertion sort is a sorting algorithm that places an unsorted element at its suitable place in each iteration.
Insertion sort works similarly as we sort cards in our hand in a card game.
We assume that the first card is already sorted then, we select an unsorted card. If the unsorted card is greater than the card in hand, it is placed on the right otherwise, to the left. In the same way, other unsorted cards are taken and put in their right place.
- The first element in the array is assumed to be sorted. Take the second element and store it separately in temp
Compare temp with the first element. If the first element is greater than temp, then temp is placed in front of the first element.
Insertion Sort Complexity
| Time Complexity | |
|---|---|
| Best | O(n) |
| Worst | O(n2) |
| Average | O(n2) |
| Space Complexity | O(1) |
| Stability | Yes |
Time Complexities
- Worst Case Complexity:
O(n2)
Suppose, an array is in ascending order, and you want to sort it in descending order. In this case, worst case complexity occurs.
Each element has to be compared with each of the other elements so, for every nth element,(n-1)number of comparisons are made.
Thus, the total number of comparisons =n*(n-1) ~ n2 - Best Case Complexity:
O(n)
When the array is already sorted, the outer loop runs fornnumber of times whereas the inner loop does not run at all. So, there are onlynnumber of comparisons. Thus, complexity is linear. - Average Case Complexity:
O(n2)
It occurs when the elements of an array are in jumbled order (neither ascending nor descending).
Space Complexity
Space complexity is O(1) because an extra variable temp is used.
Insertion Sort Applications
The insertion sort is used when:
- the array is has a small number of elements
- there are only a few elements left to be sorted
Insertion Sort Algorithm
insertionSort(array")
mark first element as sorted
for each unsorted element X
'extract' the element X
for j <- lastSortedIndex down to 0
if current element j > X
move sorted element to the right by 1
break loop and insert X here
end insertionSort
First Program and First Approach
import java.util.Arrays;
public class insertion {
void insertionSorting(int array[]) {
int n = array.length;
for (int step = 1; step < n; step++) {
int temp = array[step];
int j = step - 1;
// Compare key with each element on the left of it until an element smaller than
// it is found.
// For descending order, change key<array[j] to key>array[j].
while (j >= 0 && temp < array[j]) {
array[j + 1] = array[j];
--j;
}
// Place key at after the element just smaller than it.
array[j + 1] = temp;
}
}
// Driver code in java language
public static void main(String args[]) {
int[] data = { 45, 5, 1, 4, 30 };
//
insertion is = new insertion();
is.insertionSorting(data);
System.out.println("Sorted Array in Ascending Order: ");
System.out.println(Arrays.toString(data));
}
}
Second Example using for loop
import java.util.Arrays;
public class insertion2 {
public static void main(String[] args) {
// this is the given array
int myArray[] = {4,12,11,20,6,44,1,3,89,63,45};
// 4 is already sorted
// sorting is start from 12 means index i =1
for (int i = 1; i<myArray.length;i++){
//run the for loop from index i =1 first round
// size of array round
// here the size of array is 11
// this temp variable will store the comparable
// value for some time when temp wil get correct position
// then it will will be fixed there
int temp = myArray[i];
// here we can use j =i-1 in for loop
// but i want to use it globaly so I used
//outside of for loop
// the benefiet of using this loop to run loop in
// shifting the array element
//In this for loop j variable will run till the
// i-1 to j =0(fist index of the array) in decreasing way
int j = i-1;
for(; j>=0; j--){
// here is the condition applied
if(myArray[j]>temp){
// if the value of temp variable will
// small
// then j will be shift one place
// and i variable will take that place
// and copied thee element
myArray[j+1]=myArray[j];
}
else {
// if the temp will big then
// there is no need to apply any condition
// because before temp variable all the
//element of the array is sorted already
// and temp is greater than those arraylist variable
// so we should break
break;
}
}
// after break the loop
// this line will be executed
// means j will be go forward one place and
//stored the temp variable
myArray[j+1]= temp;
}
// using the print of the sorted array
// we use Arrays class and util.* package
System.out.println("sorted array is "+ Arrays.toString(myArray));
}
}
// sorted array is [1, 3, 4, 6, 11, 12, 20, 44, 45, 63, 89]
Third Example using While loop Approach
import java.util.Arrays;
public class insertionWh {
public static void main(String[] args) {
// sort the array using while loop
int arr[] ={23,34,5,7,8,45,78,44,56,1,2};
// the size of array is 11
int n =11;
// this loop will run till the n size of the array
for (int i =1 ;i<n;i++){
// we will take the temp variable
// and stored the comparable value i
int temp = arr[i];
// we initialize the j=i-1
int j = i-1;
// condition in while loop
while (j>=0 && temp<arr[j]){
// here is two condition applied
// first j will run till the zero or greater than zero
//second condition is that temp will be small than
// the comparable element in the array
// after that this while loop will be executed
// niether it will be break this loop
arr[j+1] = arr[j];
// here j will be shifted one place
// and decreasing one step
j=j-1;
}
// if while loop will not executed
// means conditions will be not applied
//may be temp will be greater than the other element
// of the array so there is no need to use while loop
// and the
//we know j = i-1
// then arr[i-1+1]= temp
// then arr[i]= temp
// and I have temp variable
// the temp varible will stored in the arr[j+1]
arr[j+1] = temp;
}
System.out.println("this is sorted array"+ Arrays.toString(arr));
}
}
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