Minimum number of swaps required to sort an array of first N number
Last Updated :
16 Aug, 2021
Given an array arr[] of distinct integers from 1 to N. The task is to find the minimum number of swaps required to sort the array.
Example:
Input: arr[] = { 7, 1, 3, 2, 4, 5, 6 }
Output: 5
Explanation:
i arr swap (indices)
0 [7, 1, 3, 2, 4, 5, 6] swap (0, 3)
1 [2, 1, 3, 7, 4, 5, 6] swap (0, 1)
2 [1, 2, 3, 7, 4, 5, 6] swap (3, 4)
3 [1, 2, 3, 4, 7, 5, 6] swap (4, 5)
4 [1, 2, 3, 4, 5, 7, 6] swap (5, 6)
5 [1, 2, 3, 4, 5, 6, 7]
Therefore, total number of swaps = 5
Input: arr[] = { 2, 3, 4, 1, 5 }
Output: 3
Approach:
- For each index in arr[].
- Check if the current element is in it's right position or not. Since the array contains distinct elements from 1 to N, we can simply compare the element with it's index in array to check if it is at its right position.
- If current element is not at it's right position then swap the element with the element which has occupied its place.
- Else check for next index.
Below is the implementation of the above approach:
C++
#include <iostream>
using namespace std;
// Function to find minimum swaps
int minimumSwaps(int arr[],int n)
{
// Initialise count variable
int count = 0;
int i = 0;
while (i < n)
{
// If current element is
// not at the right position
if (arr[i] != i + 1)
{
while (arr[i] != i + 1)
{
int temp = 0;
// Swap current element
// with correct position
// of that element
temp = arr[arr[i] - 1];
arr[arr[i] - 1] = arr[i];
arr[i] = temp;
count++;
}
}
// Increment for next index
// when current element is at
// correct position
i++;
}
return count;
}
// Driver code
int main()
{
int arr[] = { 2, 3, 4, 1, 5 };
int n = sizeof(arr)/sizeof(arr[0]);
// Function to find minimum swaps
cout << minimumSwaps(arr,n) ;
}
// This code is contributed by AnkitRai01
// Java program to find the minimum
// number of swaps required to sort
// the given array
import java.io.*;
import java.util.*;
class GfG {
// Function to find minimum swaps
static int minimumSwaps(int[] arr)
{
// Initialise count variable
int count = 0;
int i = 0;
while (i < arr.length) {
// If current element is
// not at the right position
if (arr[i] != i + 1) {
while (arr[i] != i + 1) {
int temp = 0;
// Swap current element
// with correct position
// of that element
temp = arr[arr[i] - 1];
arr[arr[i] - 1] = arr[i];
arr[i] = temp;
count++;
}
}
// Increment for next index
// when current element is at
// correct position
i++;
}
return count;
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 2, 3, 4, 1, 5 };
// Function to find minimum swaps
System.out.println(minimumSwaps(arr));
}
}
# Python3 program to find the minimum
# number of swaps required to sort
# the given array
# Function to find minimum swaps
def minimumSwaps(arr):
# Initialise count variable
count = 0;
i = 0;
while (i < len(arr)):
# If current element is
# not at the right position
if (arr[i] != i + 1):
while (arr[i] != i + 1):
temp = 0;
# Swap current element
# with correct position
# of that element
temp = arr[arr[i] - 1];
arr[arr[i] - 1] = arr[i];
arr[i] = temp;
count += 1;
# Increment for next index
# when current element is at
# correct position
i += 1;
return count;
# Driver code
if __name__ == '__main__':
arr = [ 2, 3, 4, 1, 5 ];
# Function to find minimum swaps
print(minimumSwaps(arr));
# This code is contributed by 29AjayKumar
// C# program to find the minimum
// number of swaps required to sort
// the given array
using System;
class GfG
{
// Function to find minimum swaps
static int minimumSwaps(int[] arr)
{
// Initialise count variable
int count = 0;
int i = 0;
while (i < arr.Length)
{
// If current element is
// not at the right position
if (arr[i] != i + 1)
{
while (arr[i] != i + 1)
{
int temp = 0;
// Swap current element
// with correct position
// of that element
temp = arr[arr[i] - 1];
arr[arr[i] - 1] = arr[i];
arr[i] = temp;
count++;
}
}
// Increment for next index
// when current element is at
// correct position
i++;
}
return count;
}
// Driver code
public static void Main(String[] args)
{
int []arr = { 2, 3, 4, 1, 5 };
// Function to find minimum swaps
Console.WriteLine(minimumSwaps(arr));
}
}
// This code is contributed by 29AjayKumar
<script>
// javascript program to find the minimum
// number of swaps required to sort
// the given array
// Function to find minimum swaps
function minimumSwaps(arr)
{
// Initialise count variable
let count = 0;
let i = 0;
while (i < arr.length)
{
// If current element is
// not at the right position
if (arr[i] != i + 1)
{
while (arr[i] != i + 1)
{
let temp = 0;
// Swap current element
// with correct position
// of that element
temp = arr[arr[i] - 1];
arr[arr[i] - 1] = arr[i];
arr[i] = temp;
count++;
}
}
// Increment for next index
// when current element is at
// correct position
i++;
}
return count;
}
// Driver code
let arr = [2, 3, 4, 1, 5 ];
// Function to find minimum swaps
document.write(minimumSwaps(arr));
</script>
Time Complexity: O(N) where N is the size of array.
Auxiliary Space: O(1)
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