# Split Array into min number of subsets with difference between each pair greater than 1

Given an array arr[] of size N, the task is to split the array into a minimum number of subset such that each pair of elements in each subset have the difference strictly greater than 1.
Note: All elements in the array are distinct.

Examples:

Input: arr = {5, 10, 6, 50}
Output: 2
Explanation:
Possible partitions are: {5, 10, 50}, { 6 }

Input: arr = { 2, 4, 6 }
Output: 1
Explanation:
Possible partitions are: {2, 4, 6}

Approach: The idea is to observe that if there is no such pair i, j such that |arr[i] – arr[j]| = 1, then it is possible to put all the elements in the same partition, otherwise divide them into two partitions. So the required minimum number of partitions is always 1 or 2.

1. Sort the given array.
2. Compare the adjacent elements. If at any point their difference to be equal to 1, then print “2” as the required number of subset partition will always be 2 as we can put one of the elements from the above pair into another subset.
3. If we traversed all the array didn’t found any adjacent pair with a difference less than 2 then print “1” without splitting the array into subsets we can have all possible pairs difference at least 2.

Below is the implementation for the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to Split the array into` `// minimum number of subsets with` `// difference strictly > 1` `void` `split(``int` `arr[], ``int` `n)` `{` `    ``// Sort the array` `    ``sort(arr, arr + n);` `    ``int` `count = 1;`   `    ``// Traverse through the sorted array` `    ``for` `(``int` `i = 1; i < n; i++) {`   `        ``// Check the pairs of elements` `        ``// with difference 1` `        ``if` `(arr[i] - arr[i - 1] == 1) {`   `            ``// If we find even a single` `            ``// pair with difference equal` `            ``// to 1, then 2 partitions` `            ``// else only 1 partiton` `            ``count = 2;` `            ``break``;` `        ``}` `    ``}`   `    ``// Print the count of partitions` `    ``cout << count << endl;` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given array` `    ``int` `arr[] = { 2, 4, 6 };`   `    ``// Size of the array` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);`   `    ``// Function Call` `    ``split(arr, n);` `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.util.*;`   `class` `GFG{` `    `  `// Function to split the array into` `// minimum number of subsets with` `// difference strictly > 1` `static` `void` `split(``int` `arr[], ``int` `n)` `{` `    `  `    ``// Sort the array` `    ``Arrays.sort(arr);` `    ``int` `count = ``1``;`   `    ``// Traverse through the sorted array` `    ``for``(``int` `i = ``1``; i < n; i++) ` `    ``{` `        `  `        ``// Check the pairs of elements` `        ``// with difference 1` `        ``if` `(arr[i] - arr[i - ``1``] == ``1``)` `        ``{` `            `  `            ``// If we find even a single` `            ``// pair with difference equal` `            ``// to 1, then 2 partitions` `            ``// else only 1 partiton` `            ``count = ``2``;` `            ``break``;` `        ``}` `    ``}`   `    ``// Print the count of partitions` `    ``System.out.print(count);` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    `  `    ``// Given array` `    ``int` `arr[] = { ``2``, ``4``, ``6` `};`   `    ``// Size of the array` `    ``int` `n = arr.length;`   `    ``// Function call` `    ``split(arr, n);` `}` `}`   `// This code is contributed by jrishabh99`

## Python3

 `# Python3 implementation of` `# the above approach`   `# Function to Split the array into` `# minimum number of subsets with` `# difference strictly > 1` `def` `split(arr, n):`   `    ``# Sort the array` `    ``arr.sort()` `    ``count ``=` `1`   `    ``# Traverse through the sorted array` `    ``for` `i ``in` `range``(``1``, n):`   `        ``# Check the pairs of elements` `        ``# with difference 1` `        ``if``(arr[i] ``-` `arr[i ``-` `1``] ``=``=` `1``):`   `            ``# If we find even a single` `            ``# pair with difference equal` `            ``# to 1, then 2 partitions` `            ``# else only 1 partiton` `            ``count ``=` `2` `            ``break`   `    ``# Print the count of partitions` `    ``print``(count)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:`   `    ``# Given array` `    ``arr ``=` `[ ``2``, ``4``, ``6` `]`   `    ``# Size of the array` `    ``n ``=` `len``(arr)`   `    ``# Function call ` `    ``split(arr, n)`   `# This code is contributed by Shivam Singh`

## C#

 `// C# program for the above approach` `using` `System;` `class` `GFG{` `     `  `// Function to split the array into` `// minimum number of subsets with` `// difference strictly > 1` `static` `void` `split(``int` `[]arr, ``int` `n)` `{` `    ``// Sort the array` `    ``Array.Sort(arr); ` `    ``int` `count = 1;` ` `  `    ``// Traverse through the sorted array` `    ``for``(``int` `i = 1; i < n; i++) ` `    ``{` `         `  `        ``// Check the pairs of elements` `        ``// with difference 1` `        ``if` `(arr[i] - arr[i - 1] == 1)` `        ``{` `            ``// If we find even a single` `            ``// pair with difference equal` `            ``// to 1, then 2 partitions` `            ``// else only 1 partiton` `            ``count = 2;` `            ``break``;` `        ``}` `    ``}` ` `  `    ``// Print the count of partitions` `    ``Console.Write(count);` `}` ` `  `// Driver Code` `public` `static` `void` `Main(``string``[] args)` `{` `     `  `    ``// Given array` `    ``int``[] arr = ``new` `int``[]{ 2, 4, 6 };` ` `  `    ``// Size of the array` `    ``int` `n = arr.Length;` ` `  `    ``// Function call` `    ``split(arr, n);` `}` `}` ` `  `// This code is contributed by Ritik Bansal`

Output:

```1

```

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

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