Check if array can be sorted with one swap

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.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


Output:

Yes

Time Complexity: O(n Log n)

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

  1. We swap adjacent elements. For example {1, 2, 3, 4, 5} becomes {1, 2, 4, 3, 5}
  2. 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 array becomes sorted or not. We check this to handle cases like {4, 1, 2, 3}

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


Output:

Yes

Time Complexity: O(n)

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



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : rituraj_jain