# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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); ` `     `  `    ``// 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 `

Output:

```3
```

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

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