Insertion sort works in the similar way 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 at their right place.
A similar approach is used by insertion sort.
Insertion sort is a sorting algorithm that places an unsorted element at its suitable place in each iteration.
Suppose we need to sort the following array.
key
.key
with the first element. If the first element is greater than key
, then key is placed in front of the first elemet.
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
# Insertion sort in Python
def insertionSort(array):
for step in range(1, len(array)):
key = array[step]
j = step - 1
while j >= 0 and key < array[j]:
# For descending order, change key<array[j] to key>array[j].
array[j + 1] = array[j]
j = j - 1
array[j + 1] = key
data = [9, 5, 1, 4, 3]
insertionSort(data)
print('Sorted Array in Ascending Order:')
print(data)
// Insertion sort in Java
import java.util.Arrays;
class InsertionSort {
void insertionSort(int array[]) {
int size = array.length;
for (int step = 1; step < size; step++) {
int key = array[step];
int j = step - 1;
while (j >= 0 && key < array[j]) {
// For descending order, change key<array[j] to key>array[j].
array[j + 1] = array[j];
--j;
}
array[j + 1] = key;
}
}
public static void main(String args[]) {
int[] data = { 9, 5, 1, 4, 3 };
InsertionSort is = new InsertionSort();
is.insertionSort(data);
System.out.println("Sorted Array in Ascending Order: ");
System.out.println(Arrays.toString(data));
}
}
// Insertion sort in C
#include <stdio.h>
void printArray(int array[], int size)
{
for (int i = 0; i < size; i++)
{
printf("%d ", array[i]);
}
printf("\n");
}
void insertionSort(int array[], int size)
{
for (int step = 1; step < size; step++)
{
int key = array[step];
int j = step - 1;
while (key < array[j] && j >= 0)
{
// For descending order, change key<array[j] to key>array[j].
array[j + 1] = array[j];
--j;
}
array[j + 1] = key;
}
}
int main()
{
int data[] = {9, 5, 1, 4, 3};
int size = sizeof(data) / sizeof(data[0]);
insertionSort(data, size);
printf("Sorted array in ascending order:\n");
printArray(data, size);
}
// Insertion sort in C++
#include <iostream>
using namespace std;
void printArray(int array[], int size)
{
for (int i = 0; i < size; i++)
{
cout << array[i] << " ";
}
cout << endl;
}
void insertionSort(int array[], int size)
{
for (int step = 1; step < size; step++)
{
int key = array[step];
int j = step - 1;
while (key < array[j] && j >= 0)
{
// For descending order, change key<array[j] to key>array[j].
array[j + 1] = array[j];
--j;
}
array[j + 1] = key;
}
}
int main()
{
int data[] = {9, 5, 1, 4, 3};
int size = sizeof(data) / sizeof(data[0]);
insertionSort(data, size);
cout << "Sorted array in ascending order:\n";
printArray(data, size);
}
Time Complexities
O(n2)
(n-1)
number of comparisons are made.n*(n-1) ~ n
2
O(n)
n
number of times whereas the inner loop does not run at all. So, there is only n
number of comparison. Thus, complexity is linear.O(n2)
Space Complexity
Space complexity is O(1)
because an extra variable key
is used.
The insertion sort is used when: