Insertion Sort by Swapping Elements
Last Updated :
22 Dec, 2022
Insertion Sort is suitable for arrays of small size. It also achieves the best-case complexity of O(n) if the arrays are already sorted. We have discussed both Iterative Insertion Sort and Recursive Insertion Sort. In this article, slightly different implementations for both iterative and recursive versions are discussed.
Iterative Insertion Sort:
Let us look at the algorithm for the iterative insertion sort
function insertionSort(V)
i, j, k
for i from 1..length(V)
k = V[i]
j = i-1
while j > 0 and k < V[j]
V[j+1] = V[j]
j -= 1
V[j] = k
return V
Inside the while loop, we shift all values larger than k by one position and then insert k into the first position where k is larger than the array value. The same effect is obtained if we swap consecutive array elements. By repeated swapping, k will travel to its correct position.
Let's take an example to illustrate this
Insert 3 in A = {1, 2, 4, 5, 6}
Put 3 at the end of list.
A = {1, 2, 4, 5, 6, 3}
3 < 6, swap 3 and 6
A = {1, 2, 4, 5, 3, 6}
3 < 5 swap 3 and 5
A = {1, 2, 4, 3, 5, 6}
3 < 4 swap 3 and 4
A = {1, 2, 3, 4, 5, 6}
3 > 2 so stop
By repeatedly swapping 3 travels to its proper position in the list
Therefore the above algorithm can be modified as
function insertionSort(V)
for i in 1...length(V)
j = i
while ( j > 0 and V[j] < V[j-1])
Swap V[j] and V[j-1]
j -= 1
return V
The CPP code for this algorithm is given below
Implementation:
C++
// Iterative CPP program to sort
// an array by swapping elements
#include <iostream>
#include <vector>
using namespace std;
using Vector = vector<int>;
// Utility function to print a Vector
void printVector(const Vector& V)
{
for (auto e : V) {
cout << e << " ";
}
cout << endl;
}
// Function performs insertion sort on
// vector V
void insertionSort(Vector& V)
{
int N = V.size();
int i, j, key;
for (i = 1; i < N; i++) {
j = i;
// Insert V[i] into list 0..i-1
while (j > 0 and V[j] < V[j - 1]) {
// Swap V[j] and V[j-1]
swap(V[j], V[j - 1]);
// Decrement j by 1
j -= 1;
}
}
}
// Driver Code
int main()
{
Vector A = { 9, 8, 7, 5, 2, 1, 2, 3 };
cout << "Array: " << endl;
printVector(A);
cout << "After Sorting :" << endl;
insertionSort(A);
printVector(A);
return 0;
}
// Iterative Java program to sort
// an array by swapping elements
import java.io.*;
import java.util.*;
class GFG
{
// Utility function to print a Vector
static void printVector( Vector<Integer> V)
{
for (int i = 0; i < V.size(); i++) {
System.out.print(V.get(i)+" ");
}
System.out.println();
}
// Function performs insertion sort on
// vector V
static void insertionSort(Vector<Integer> V)
{
int N = V.size();
int i, j, key;
for (i = 1; i < N; i++) {
j = i;
// Insert V[i] into list 0..i-1
while (j > 0 && V.get(j) < V.get(j - 1)) {
// Swap V[j] and V[j-1]
int temp= V.get(j);
V.set(j, V.get(j - 1));
V.set(j - 1, temp);
// Decrement j by 1
j -= 1;
}
}
}
public static void main (String[] args)
{
Vector<Integer> A = new Vector<Integer> ();
A.add(0, 9);
A.add(1, 8);
A.add(2, 7);
A.add(3, 5);
A.add(4, 2);
A.add(5, 1);
A.add(6, 2);
A.add(7, 3);
System.out.print("Array: ");
printVector(A);
System.out.print("After Sorting :");
insertionSort(A);
printVector(A);
}
}
//This code is contributed by Gitanjali.
# Iterative python program to sort
# an array by swapping elements
import math
# Utility function to print a Vector
def printVector( V):
for i in V:
print(i ,end= " ")
print (" ")
def insertionSort( V):
N = len(V)
for i in range(1,N):
j = i
# Insert V[i] into list 0..i-1
while (j > 0 and V[j] < V[j - 1]) :
# Swap V[j] and V[j-1]
temp = V[j];
V[j] = V[j - 1];
V[j-1] = temp;
# Decrement j
j -= 1
# Driver method
A = [ 9, 8, 7, 5, 2, 1, 2, 3 ]
n = len(A)
print("Array")
printVector(A)
print( "After Sorting :")
insertionSort(A)
printVector(A)
# This code is contributed by Gitanjali.
// Iterative C# program to sort
// an array by swapping elements
using System;
using System.Collections.Generic;
class GFG
{
// Utility function to print a Vector
static void printVector(List<int> V)
{
for (int i = 0; i < V.Count; i++)
{
Console.Write(V[i] + " ");
}
Console.WriteLine();
}
// Function performs insertion sort on
// vector V
static void insertionSort(List<int> V)
{
int N = V.Count;
int i, j;
for (i = 1; i < N; i++)
{
j = i;
// Insert V[i] into list 0..i-1
while (j > 0 && V[j] < V[j - 1])
{
// Swap V[j] and V[j-1]
int temp= V[j];
V[j] = V[j - 1];
V[j - 1] = temp;
// Decrement j by 1
j -= 1;
}
}
}
// Driver Code
public static void Main (String[] args)
{
List<int> A = new List<int> ();
A.Insert(0, 9);
A.Insert(1, 8);
A.Insert(2, 7);
A.Insert(3, 5);
A.Insert(4, 2);
A.Insert(5, 1);
A.Insert(6, 2);
A.Insert(7, 3);
Console.Write("Array: \n");
printVector(A);
Console.Write("After Sorting :\n");
insertionSort(A);
printVector(A);
}
}
// This code is contributed by 29AjayKumar
<script>
// Iterative Javascript program to sort
// an array by swapping elements
// Utility function to print a Vector
function printVector(V) {
for (let e of V) {
document.write(e + " ");
}
document.write("<br>");
}
// Function performs insertion sort on
// vector V
function insertionSort(V) {
let N = V.length;
let i, j, key;
for (i = 1; i < N; i++) {
j = i;
// Insert V[i] into list 0..i-1
while (j > 0 && V[j] < V[j - 1]) {
// Swap V[j] and V[j-1]
let temp = V[j];
V[j] = V[j - 1];
V[j - 1] = temp;
// Decrement j by 1
j -= 1;
}
}
}
// Driver Code
let A = [9, 8, 7, 5, 2, 1, 2, 3];
document.write("Array: " + "<br>");
printVector(A);
document.write("After Sorting :" + "<br>");
insertionSort(A);
printVector(A);
// This code is contributed by _saurabh_jaiswal.
</script>
OutputArray:
9 8 7 5 2 1 2 3
After Sorting :
1 2 2 3 5 7 8 9
Time Complexity: O(N*N)
Auxiliary Space: O(1)
Recursive Insertion Sort:
Consider an Array A of size N
- First recursively sort the sublist of A which is of size N-1
- Insert the last element of A into the sorted sublist.
To perform the insertion step use repeated swapping as discussed above.
Algorithm:
function insertionSortRecursive(A, N)
if N >= 1
insertionSortRecursive(A, N-1)
j = N-1
while j > 0 and A[j] < A[j-1]
Swap A[j] and A[j-1]
j = j-1
[end of while]
[end of if]
Following is the implementation of the above approach:
C++
// Recursive CPP program to sort an array
// by swapping elements
#include <iostream>
#include <vector>
using namespace std;
using Vector = vector<int>;
// Utility function to print a Vector
void printVector(const Vector& V)
{
for (auto e : V) {
cout << e << " ";
}
cout << endl;
}
// Function to perform Insertion Sort recursively
void insertionSortRecursive(Vector& V, int N)
{
if (N <= 1)
return;
// General Case
// Sort V till second last element and
// then insert last element into V
insertionSortRecursive(V, N - 1);
// Insertion step
int j = N - 1;
while (j > 0 and V[j] < V[j - 1]) {
// Swap V[j] and V[j-1]
swap(V[j], V[j - 1]);
// Decrement j
j -= 1;
}
}
// Driver Code
int main()
{
// Declare a vector of size 10
Vector A = { 9, 8, 7, 5, 2, 1, 2, 3 };
cout << "Array: " << endl;
printVector(A);
cout << "After Sorting :" << endl;
insertionSortRecursive(A, A.size());
printVector(A);
return 0;
}
// Recursive Java program to sort
// an array by swapping elements
import java.io.*;
import java.util.*;
class GFG
{
// Utility function to print a Vector
static void printVector( Vector<Integer> V)
{
for (int i = 0; i < V.size(); i++) {
System.out.print(V.get(i) + " ");
}
System.out.println();
}
// Function performs insertion sort on
// vector V
static void insertionSortRecursive(Vector<Integer> V,int N)
{
if (N <= 1)
return;
// General Case
// Sort V till second last element and
// then insert last element into V
insertionSortRecursive(V, N - 1);
// Insertion step
int j = N - 1;
// Insert V[i] into list 0..i-1
while (j > 0 && V.get(j) < V.get(j - 1))
{
// Swap V[j] and V[j-1]
int temp= V.get(j);
V.set(j, V.get(j - 1));
V.set(j - 1, temp);
// Decrement j by 1
j -= 1;
}
}
// Driver code
public static void main (String[] args)
{
Vector<Integer> A = new Vector<Integer> ();
A.add(0, 9);
A.add(1, 8);
A.add(2, 7);
A.add(3, 5);
A.add(4, 2);
A.add(5, 1);
A.add(6, 2);
A.add(7, 3);
System.out.print("Array: ");
printVector(A);
System.out.print("After Sorting :");
insertionSortRecursive(A,A.size());
printVector(A);
}
}
// This code is contributed by Gitanjali.
# Recursive python program
# to sort an array
# by swapping elements
import math
# Utility function to print
# a Vector
def printVector( V):
for i in V:
print(i, end = " ")
print (" ")
# Function to perform Insertion
# Sort recursively
def insertionSortRecursive(V, N):
if (N <= 1):
return 0
# General Case
# Sort V till second
# last element and
# then insert last element
# into V
insertionSortRecursive(V, N - 1)
# Insertion step
j = N - 1
while (j > 0 and V[j] < V[j - 1]) :
# Swap V[j] and V[j-1]
temp = V[j];
V[j] = V[j - 1];
V[j-1] = temp;
# Decrement j
j -= 1
# Driver method
A = [ 9, 8, 7, 5, 2, 1, 2, 3 ]
n=len(A)
print("Array")
printVector(A)
print( "After Sorting :")
insertionSortRecursive(A,n)
printVector(A)
# This code is contributed
# by Gitanjali.
// Recursive C# program to sort
// an array by swapping elements
using System;
using System.Collections.Generic;
class GFG
{
// Utility function to print a Vector
static void printVector(List<int> V)
{
for (int i = 0; i < V.Count; i++)
{
Console.Write(V[i] + " ");
}
Console.WriteLine();
}
// Function performs insertion sort on
// vector V
static void insertionSortRecursive(List<int> V,
int N)
{
if (N <= 1)
return;
// General Case
// Sort V till second last element and
// then insert last element into V
insertionSortRecursive(V, N - 1);
// Insertion step
int j = N - 1;
// Insert V[i] into list 0..i-1
while (j > 0 && V[j] < V[j - 1])
{
// Swap V[j] and V[j-1]
int temp = V[j];
V[j] = V[j - 1];
V[j - 1] = temp;
// Decrement j by 1
j -= 1;
}
}
// Driver code
public static void Main (String[] args)
{
List<int> A = new List<int> ();
A.Insert(0, 9);
A.Insert(1, 8);
A.Insert(2, 7);
A.Insert(3, 5);
A.Insert(4, 2);
A.Insert(5, 1);
A.Insert(6, 2);
A.Insert(7, 3);
Console.Write("Array: ");
printVector(A);
Console.Write("After Sorting :");
insertionSortRecursive(A, A.Count);
printVector(A);
}
}
// This code is contributed by Princi Singh
<script>
// Recursive Javascript program to sort an array
// by swapping elements
// Utility function to print a Vector
function printVector(V) {
for (let e of V) {
document.write(e + " ");
}
document.write("<br>");
}
// Function to perform Insertion Sort recursively
function insertionSortRecursive(V, N) {
if (N <= 1)
return;
// General Case
// Sort V till second last element and
// then insert last element into V
insertionSortRecursive(V, N - 1);
// Insertion step
let j = N - 1;
while (j > 0 && V[j] < V[j - 1]) {
// Swap V[j] and V[j-1]
let temp = V[j];
V[j] = V[j - 1];
V[j - 1] = temp;
// Decrement j
j -= 1;
}
}
// Driver Code
// Declare a vector of size 10
let A = [9, 8, 7, 5, 2, 1, 2, 3];
document.write("Array: <br>");
printVector(A);
document.write("After Sorting :<br>");
insertionSortRecursive(A, A.length);
printVector(A);
// This code is contributed by gfgking.
</script>
OutputArray:
9 8 7 5 2 1 2 3
After Sorting :
1 2 2 3 5 7 8 9
Note: The Time Complexity of the algorithm is still O(N^2) in the worst case. Moreover, these versions are potentially slower since repeated swapping requires more operations. However, these versions are discussed because of their implementation simplicity and ease of understanding.
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