Check if array can be sorted with one swap

Last Updated : 13 Apr, 2023

Given an array containing N elements. Find if it is possible to sort it in non-decreasing order using atmost one swap.

Examples:

Input : arr[] = {1, 2, 3, 4}
Output : YES
The array is already sorted

Input : arr[] = {3, 2, 1}
Output : YES
Swap 3 and 1 to get [1, 2, 3]

Input : arr[] = {4, 1, 2, 3}
Output :NO

A simple approach is to sort the array and compare the required position of the element and the current position of the element. If there are no mismatches, the array is already sorted. If there are exactly 2 mismatches, we can swap the terms that are not in the position to get the sorted array.

Implementation:

C++

   // CPP program to check if an array can be sorted
// with at-most one swap
#include <bits/stdc++.h>
using namespace std;
 
bool checkSorted(int n, int arr[])
{
    // Create a sorted copy of original array
    int b[n];
    for (int i = 0; i < n; i++)
        b[i] = arr[i];
    sort(b, b + n);
 
    // Check if 0 or 1 swap required to
    // get the sorted array
    int ct = 0;
    for (int i = 0; i < n; i++)
        if (arr[i] != b[i])
            ct++;
    if (ct == 0 || ct == 2)
        return true;
    else
        return false;
}
 
// Driver Program to test above function
int main()
{
    int arr[] = {1, 5, 3, 4, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    if (checkSorted(n, arr))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}
 
  

Java

   // Java program to check if an array 
// can be sorted with at-most one swap
import java.util.Arrays;
 
class GFG 
{
static boolean checkSorted(int n, int arr[])
{
    // Create a sorted copy of original array
    int []b = new int[n];
    for (int i = 0; i < n; i++)
        b[i] = arr[i];
    Arrays.sort(b, 0, n);
 
    // Check if 0 or 1 swap required to
    // get the sorted array
    int ct = 0;
    for (int i = 0; i < n; i++)
        if (arr[i] != b[i])
            ct++;
    if (ct == 0 || ct == 2)
        return true;
    else
        return false;
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = {1, 5, 3, 4, 2};
    int n = arr.length;
    if (checkSorted(n, arr))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by 29AjayKumar
 
  

Python 3

   # A linear Python 3 program to check 
# if array becomes sorted after one swap
 
def checkSorted(n, arr):
     
    # Create a sorted copy of
    # original array 
    b = []
    for i in range(n):
        b.append(arr[i])
         
    b.sort()
     
    # Check if 0 or 1 swap required 
    # to get the sorted array 
    ct = 0
    for i in range(n):
        if arr[i] != b[i]:
            ct += 1
             
    if ct == 0 or ct == 2:
        return True
    else:
        return False
 
# Driver Code        
if __name__ == '__main__':
     
    arr = [1, 5, 3, 4, 2]
    n = len(arr)
     
    if checkSorted(n, arr):
        print("Yes")
         
    else:
        print("No")
 
# This code is contributed
# by Rituraj Jain
 
  

C#

   // C# program to check if an array 
// can be sorted with at-most one swap
using System;
 
class GFG 
{
static Boolean checkSorted(int n, int []arr)
{
    // Create a sorted copy of original array
    int []b = new int[n];
    for (int i = 0; i < n; i++)
        b[i] = arr[i];
    Array.Sort(b, 0, n);
 
    // Check if 0 or 1 swap required to
    // get the sorted array
    int ct = 0;
    for (int i = 0; i < n; i++)
        if (arr[i] != b[i])
            ct++;
    if (ct == 0 || ct == 2)
        return true;
    else
        return false;
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = {1, 5, 3, 4, 2};
    int n = arr.Length;
    if (checkSorted(n, arr))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by 29AjayKumar
 
  

Javascript

   <script>
// javascript program to check if an array can be sorted
// with at-most one swap
function checkSorted(n, arr)
{
 
    // Create a sorted copy of original array
    var b = Array(n).fill(0);
    for (var i = 0; i < n; i++)
        b[i] = arr[i];
    b.sort();
 
    // Check if 0 or 1 swap required to
    // get the sorted array
    var ct = 0;
    for (var i = 0; i < n; i++)
        if (arr[i] != b[i])
            ct++;
    if (ct == 0 || ct == 2)
        return true;
    else
        return false;
}
 
// Driver Program to test above function
var arr = [ 1, 5, 3, 4, 2 ];
var n = arr.length;
if (checkSorted(n, arr))
    document.write( "Yes");
else
    document.write("No");
 
// This code is contributed by noob2000.
</script>
 
  

Output

Yes

Time Complexity: O(n Log n)

Space Complexity: O(n) where n is size of input array arr. This is because array b has been created in checkSorted function.

An efficient solution is to check in linear time. Let us consider different cases that may appear after one swap.

We swap adjacent elements. For example {1, 2, 3, 4, 5} becomes {1, 2, 4, 3, 5}
We swap non-adjacent elements. For example {1, 2, 3, 4, 5} becomes {1, 5, 3, 4, 2}

We traverse the given array. For every element, we check if it is smaller than the previous element. We count such occurrences. If the count of such occurrences is more than 2, then we cannot sort the array with one swap. If the count is one, we can find elements to swap (smaller and its previous).
If the count is two, we can find elements to swap (previous of first smaller and second smaller).

After swapping, we again check if the array becomes sorted or not. We check this to handle cases like {4, 1, 2, 3}

Implementation:

C++

   // A linear CPP program to check if array becomes
// sorted after one swap
#include <bits/stdc++.h>
using namespace std;
 
int checkSorted(int n, int arr[])
{
    // Find counts and positions of 
    // elements that are out of order.
    int first = 0, second = 0;
    int count = 0;
    for (int i = 1; i < n; i++) {
        if (arr[i] < arr[i - 1]) {
            count++;
            if (first == 0)
                first = i;
            else
                second = i;
        }
    }
 
    // If there are more than two elements
    // are out of order.
    if (count > 2)
        return false;
 
    // If all elements are sorted already
    if (count == 0)
        return true;
 
    // Cases like {1, 5, 3, 4, 2}
    // We swap 5 and 2.
    if (count == 2)
        swap(arr[first - 1], arr[second]);
 
    // Cases like {1, 2, 4, 3, 5}
    else if (count == 1)
        swap(arr[first - 1], arr[first]);
 
    // Now check if array becomes sorted
    // for cases like {4, 1, 2, 3}
    for (int i = 1; i < n; i++)
        if (arr[i] < arr[i - 1])
            return false;
 
    return true;
}
 
// Driver Program to test above function
int main()
{
    int arr[] = { 1, 4, 3, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
    if (checkSorted(n, arr))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}
 
  

Java

   // A linear Java program to check if 
// array becomes sorted after one swap
class GFG
{
static boolean checkSorted(int n, int arr[])
{
    // Find counts and positions of 
    // elements that are out of order.
    int first = 0, second = 0;
    int count = 0;
    for (int i = 1; i < n; i++) 
    {
        if (arr[i] < arr[i - 1])
        {
            count++;
            if (first == 0)
                first = i;
            else
                second = i;
        }
    }
 
    // If there are more than two elements
    // are out of order.
    if (count > 2)
        return false;
 
    // If all elements are sorted already
    if (count == 0)
        return true;
 
    // Cases like {1, 5, 3, 4, 2}
    // We swap 5 and 2.
    if (count == 2)
        swap(arr, first - 1, second);
 
    // Cases like {1, 2, 4, 3, 5}
    else if (count == 1)
        swap(arr, first - 1, first);
 
    // Now check if array becomes sorted
    // for cases like {4, 1, 2, 3}
    for (int i = 1; i < n; i++)
        if (arr[i] < arr[i - 1])
            return false;
 
    return true;
}
 
static int[] swap(int []arr, int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
    return arr;
}
 
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 1, 4, 3, 2 };
    int n = arr.length;
    if (checkSorted(n, arr))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by Rajput-Ji
 
  

Python 3

   # A linear Python 3 program to check 
# if array becomes sorted after one swap
 
def checkSorted(n, arr):
     
    # Find counts and positions of 
    # elements that are out of order.
    first, second = 0, 0
    count = 0
     
    for i in range(1, n):
        if arr[i] < arr[i - 1]:
            count += 1
             
            if first == 0:
                first = i
            else:
                second = i
     
    # If there are more than two elements 
    # which are out of order.
    if count > 2: 
        return False
 
    # If all elements are sorted already 
    if count == 0: 
        return True
 
    # Cases like {1, 5, 3, 4, 2} 
    # We swap 5 and 2. 
    if count == 2: 
        (arr[first - 1], 
         arr[second]) = (arr[second],  
                         arr[first - 1]) 
 
    # Cases like {1, 2, 4, 3, 5} 
    elif count == 1: 
        (arr[first - 1],
         arr[first]) = (arr[first], 
                        arr[first - 1]) 
 
    # Now check if array becomes sorted 
    # for cases like {4, 1, 2, 3} 
    for i in range(1, n): 
        if arr[i] < arr[i - 1]:
            return False
 
    return True
 
# Driver Code
if __name__ == '__main__':
     
    arr = [1, 4, 3, 2]
    n = len(arr)
     
    if checkSorted(n, arr):
        print("Yes")
         
    else:
        print("No")
 
# This code is contributed 
# by Rituraj Jain
 
  

C#

   // A linear C# program to check if 
// array becomes sorted after one swap
using System;
 
class GFG
{
static bool checkSorted(int n, int []arr)
{
    // Find counts and positions of 
    // elements that are out of order.
    int first = 0, second = 0;
    int count = 0;
    for (int i = 1; i < n; i++) 
    {
        if (arr[i] < arr[i - 1])
        {
            count++;
            if (first == 0)
                first = i;
            else
                second = i;
        }
    }
 
    // If there are more than two elements
    // are out of order.
    if (count > 2)
        return false;
 
    // If all elements are sorted already
    if (count == 0)
        return true;
 
    // Cases like {1, 5, 3, 4, 2}
    // We swap 5 and 2.
    if (count == 2)
        swap(arr, first - 1, second);
 
    // Cases like {1, 2, 4, 3, 5}
    else if (count == 1)
        swap(arr, first - 1, first);
 
    // Now check if array becomes sorted
    // for cases like {4, 1, 2, 3}
    for (int i = 1; i < n; i++)
        if (arr[i] < arr[i - 1])
            return false;
 
    return true;
}
 
static int[] swap(int []arr, int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
    return arr;
}
 
// Driver Code
public static void Main(String[] args)
{
    int []arr = { 1, 4, 3, 2 };
    int n = arr.Length;
    if (checkSorted(n, arr))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by Rajput-Ji
 
  

Javascript

   <script>
 
// A linear Javascript program to check if array becomes
// sorted after one swap
 
function checkSorted(n, arr)
{
    // Find counts and positions of 
    // elements that are out of order.
    var first = 0, second = 0;
    var count = 0;
    for (var i = 1; i < n; i++) {
        if (arr[i] < arr[i - 1]) {
            count++;
            if (first == 0)
                first = i;
            else
                second = i;
        }
    }
 
    // If there are more than two elements
    // are out of order.
    if (count > 2)
        return false;
 
    // If all elements are sorted already
    if (count == 0)
        return true;
 
    // Cases like {1, 5, 3, 4, 2}
    // We swap 5 and 2.
    if (count == 2)
        [arr[first - 1], arr[second]] = [arr[second], arr[first - 1]];
 
    // Cases like {1, 2, 4, 3, 5}
    else if (count == 1)
        [arr[first - 1], arr[first]] = [arr[first], arr[first - 1]];
 
    // Now check if array becomes sorted
    // for cases like {4, 1, 2, 3}
    for (var i = 1; i < n; i++)
        if (arr[i] < arr[i - 1])
            return false;
 
    return true;
}
 
// Driver Program to test above function
var arr = [1, 4, 3, 2];
var n = arr.length;
if (checkSorted(n, arr))
    document.write( "Yes");
else
    document.write( "No");
 
// This code is contributed by famously.
</script>
 
  

Output

Yes

Time Complexity: O(n)

Space Complexity: O(1) as no extra space has been used.

Exercise: How to check if an array can be sorted with two swaps?

Check if an Array is Sorted

Abdullah Aslam

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Check if array can be sorted with one swap

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