Sort an almost sorted array where only two elements are swapped

Given an almost sorted array where only two elements are swapped, how to sort the array efficiently?

Examples :

Input:  arr[] = {10, 20, 60, 40, 50, 30}  
// 30 and 60 are swapped
Output: arr[] = {10, 20, 30, 40, 50, 60}

Input:  arr[] = {10, 20, 40, 30, 50, 60}  
// 30 and 40 are swapped
Output: arr[] = {10, 20, 30, 40, 50, 60}

Input:   arr[] = {1, 5, 3}
// 3 and 5 are swapped
Output:  arr[] = {1, 3, 5}

Expected time complexity is O(n) and only one swap operation to fix the array.

The idea is to traverse from rightmost side and find the first out of order element (element which is smaller than previous element). Once first element is found, find the other our of order element by traversing the array toward left side.

Below is implementation of above idea.

C++

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// C++ program to sort using one swap
#include<iostream>
#include<algorithm>
using namespace std;
  
// This function sorts an array that can be sorted
// by single swap
void sortByOneSwap(int arr[], int n)
{
    // Traverse the given array from rightmost side
    for (int i = n-1; i > 0; i--)
    {
        // Check if arr[i] is not in order
        if (arr[i] < arr[i-1])
        {
            // Find the other element to be
            // swapped with arr[i]
            int j = i-1;
            while (j>=0 && arr[i] < arr[j])
                j--;
  
            // Swap the pair
            swap(arr[i], arr[j+1]);
            break;
        }
    }
}
  
// A utility function to print an array of size n
void printArray(int arr[], int n)
{
    int i;
    for (i=0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;
}
  
/* Driver program to test insertion sort */
int main()
{
    int arr[] = {10, 30, 20, 40, 50, 60, 70};
    int n = sizeof(arr)/sizeof(arr[0]);
  
    cout << "Given array is \n";
    printArray(arr, n);
  
    sortByOneSwap(arr, n);
  
    cout << "Sorted array is \n";
    printArray(arr, n);
  
    return 0;
}

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Java

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// Java program to 
// sort using one swap
import java.io.*;
  
class GFG 
{
// This function sorts an array 
// that can be sorted by single swap
static void sortByOneSwap(int arr[], 
                          int n)
{
    // Traverse the given array
    // from rightmost side
    for (int i = n - 1; i > 0; i--)
    {
        // Check if arr[i] 
        // is not in order
        if (arr[i] < arr[i - 1])
        {
            // Find the other element 
            // to be swapped with arr[i]
            int j = i - 1;
            while (j >= 0 && arr[i] < arr[j])
                j--;
  
            // Swap the pair
            int temp = arr[i];
            arr[i] = arr[j + 1];
            arr[j + 1] = temp;
      
            break;
        }
    }
}
  
// A utility function to 
// print an array of size n
static void printArray(int arr[], int n)
{
    int i;
    for (i = 0; i < n; i++)
        System.out.print(arr[i] + " ");
    System.out.println();
}
  
// Driver Code
public static void main(String[] args) 
{
int arr[] = {10, 30, 20
             40, 50, 60, 70};
int n = arr.length;
  
System.out.println("Given array is ");
printArray(arr, n);
  
sortByOneSwap(arr, n);
  
System.out.println("Sorted array is ");
printArray(arr, n);
}
}
  
// This code is contributed by anuj_67.

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C#

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// C# program to sort using one swap 
using System;
  
class GFG 
  
// This function sorts an array 
// that can be sorted by single swap 
static void sortByOneSwap(int []arr, 
                          int n) 
    // Traverse the given array 
    // from rightmost side 
    for (int i = n - 1; i > 0; i--) 
    
        // Check if arr[i] is not in order 
        if (arr[i] < arr[i - 1]) 
        
            // Find the other element to be 
            // swapped with arr[i] 
            int j = i - 1; 
            while (j >= 0 && arr[i] < arr[j]) 
                j--; 
  
            // Swap the pair 
            int temp = arr[i]; 
            arr[i] = arr[j + 1]; 
            arr[j + 1] = temp; 
  
            break
        
    
  
// A utility function to print an 
// array of size n 
static void printArray(int []arr, int n) 
    int i; 
    for (i = 0; i < n; i++) 
        Console.Write(arr[i] + " "); 
    Console.WriteLine(); 
  
// Driver Code 
public static void Main() 
    int []arr = {10, 30, 20, 
                 40, 50, 60, 70}; 
    int n = arr.Length; 
  
    Console.WriteLine("Given array is "); 
    printArray(arr, n); 
  
    sortByOneSwap(arr, n); 
  
    Console.WriteLine("Sorted array is "); 
    printArray(arr, n); 
  
// This code is contributed by 29AjayKumar 

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PHP

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<?php
// PHP program to sort using one swap
  
// This function sorts an array 
// that can be sorted by single swap
function sortByOneSwap(&$arr, $n)
{
    // Traverse the given array
    // from rightmost side
    for ($i = $n - 1; $i > 0; $i--)
    {
        // Check if arr[i] 
        // is not in order
        if ($arr[$i] < $arr[$i - 1])
        {
            // Find the other element 
            // to be swapped with arr[i]
            $j = $i - 1;
            while ($j >= 0 && $arr[$i] < $arr[$j])
                $j--;
  
            // Swap the pair
            $temp = $arr[$i];
            $arr[$i] = $arr[$j + 1];
            $arr[$j + 1] = $temp;
      
            break;
        }
    }
}
  
// A utility function to 
// print an array of size n
function printArray(&$arr, $n)
{
    for ($i = 0; $i < $n; $i++)
        echo $arr[$i] . " ";
    echo "\n";
}
  
// Driver Code
$arr = array(10, 30, 20, 
        40, 50, 60, 70);
$n = sizeof($arr);
  
echo "Given array is " . "\n";
printArray($arr, $n);
  
sortByOneSwap($arr, $n);
  
echo "Sorted array is ". "\n";
printArray($arr, $n);
  
// This code is contributed by Akanksha Rai

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Output :

Given array is
10 30 20 40 50 60 70
Sorted array is
10 20 30 40 50 60 70

The above program works in O(n) time and swaps only one element.

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