# Minimum number of swaps required to sort an array of first N number

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 ` `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

 `// 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

 `# 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#

 `// 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`

## Javascript

 ``

Output:

`3`

Time Complexity: O(N) where N is the size of array.
Auxiliary Space: O(1)

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