# Print the two possible permutations from a given sequence

Given an array arr containing N positive integers, the task is to check if the given array can be dissociated into two permutations or not and print the permutations if possible. A sequence of M integers is called a permutation if it contains all integers from 1 to M exactly once.
Examples:

Input: arr[] = { 1, 2, 5, 3, 4, 1, 2 }, N = 7
Output: {1 2 5 3 4}, {1 2}

Input: arr[] = {2, 1, 1, 3}, N = 4
Output: Not possible

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

Approach:

• First of all, we need to check if the array is the concatenation of two permutations.It is explained in this article.
• If so, find the largest element of the array, say x.
• If the elements at indices [0, x-1] and [x, n-1] form two valid permutations, print them.
• Otherwise, print the elements at indices [0, n -1 – x] and [n – x, n – 1] as the two valid permutations.

Below is the implementation of the above approach:

## C++

 `// C++ program to print two ` `// permutations from a given sequence ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to check if the sequence is ` `// concatenation of two permutations or not ` `bool` `checkPermutation(``int` `arr[], ``int` `n) ` `{ ` `    ``// Computing the sum of all the ` `    ``// elements in the array ` `    ``long` `long` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``sum += arr[i]; ` ` `  `    ``// Computing the prefix sum ` `    ``// for all the elements in the array ` `    ``long` `long` `prefix[n + 1] = { 0 }; ` `    ``prefix = arr; ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``prefix[i] = prefix[i - 1] + arr[i]; ` ` `  `    ``// Iterating through the i ` `    ``// from lengths 1 to n-1 ` `    ``for` `(``int` `i = 0; i < n - 1; i++) { ` ` `  `        ``// Sum of first i+1 elements ` `        ``long` `long` `lsum = prefix[i]; ` ` `  `        ``// Sum of remaining n-i-1 elements ` `        ``long` `long` `rsum = sum - prefix[i]; ` ` `  `        ``// Lengths of the 2 permutations ` `        ``long` `long` `l_len = i + 1, ` `                  ``r_len = n - i - 1; ` ` `  `        ``// Checking if the sums ` `        ``// satisfy the formula or not ` `        ``if` `(((2 * lsum) ` `             ``== (l_len * (l_len + 1))) ` `            ``&& ((2 * rsum) ` `                ``== (r_len * (r_len + 1)))) ` `            ``return` `true``; ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// Function to print the ` `// two permutations ` `void` `printPermutations(``int` `arr[], ``int` `n, ` `                       ``int` `l1, ``int` `l2) ` `{ ` `    ``// Print the first permutation ` `    ``for` `(``int` `i = 0; i < l1; i++) { ` `        ``cout << arr[i] << ``" "``; ` `    ``} ` `    ``cout << endl; ` ` `  `    ``// Print the second permutation ` `    ``for` `(``int` `i = l1; i < n; i++) { ` `        ``cout << arr[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Function to find the two permutations ` `// from the given sequence ` `void` `findPermutations(``int` `arr[], ``int` `n) ` `{ ` `    ``// If the sequence is not a ` `    ``// concatenation of two permutations ` `    ``if` `(!checkPermutation(arr, n)) { ` `        ``cout << ``"Not Possible"``; ` `        ``return``; ` `    ``} ` ` `  `    ``int` `l1 = 0, l2 = 0; ` ` `  `    ``// Find the largest element in the ` `    ``// array and set the lengths of the ` `    ``// permutations accordingly ` `    ``l1 = *max_element(arr, arr + n); ` `    ``l2 = n - l1; ` ` `  `    ``set<``int``> s1, s2; ` `    ``for` `(``int` `i = 0; i < l1; i++) ` `        ``s1.insert(arr[i]); ` ` `  `    ``for` `(``int` `i = l1; i < n; i++) ` `        ``s2.insert(arr[i]); ` ` `  `    ``if` `(s1.size() == l1 && s2.size() == l2) ` `        ``printPermutations(arr, n, l1, l2); ` `    ``else` `{ ` `        ``swap(l1, l2); ` `        ``printPermutations(arr, n, l1, l2); ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 2, 1, 3, 4, 5, ` `                  ``6, 7, 8, 9, 1, ` `                  ``10, 2 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` ` `  `    ``findPermutations(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java program to print two ` `// permutations from a given sequence ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `  `  `// Function to check if the sequence is ` `// concatenation of two permutations or not ` `static` `boolean` `checkPermutation(``int` `arr[], ``int` `n) ` `{ ` `    ``// Computing the sum of all the ` `    ``// elements in the array ` `    ``long` `sum = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``sum += arr[i]; ` `  `  `    ``// Computing the prefix sum ` `    ``// for all the elements in the array ` `    ``int` `[]prefix = ``new` `int``[n + ``1``]; ` `    ``prefix[``0``] = arr[``0``]; ` `    ``for` `(``int` `i = ``1``; i < n; i++) ` `        ``prefix[i] = prefix[i - ``1``] + arr[i]; ` `  `  `    ``// Iterating through the i ` `    ``// from lengths 1 to n-1 ` `    ``for` `(``int` `i = ``0``; i < n - ``1``; i++) { ` `  `  `        ``// Sum of first i+1 elements ` `        ``long` `lsum = prefix[i]; ` `  `  `        ``// Sum of remaining n-i-1 elements ` `        ``long` `rsum = sum - prefix[i]; ` `  `  `        ``// Lengths of the 2 permutations ` `        ``long` `l_len = i + ``1``, ` `                  ``r_len = n - i - ``1``; ` `  `  `        ``// Checking if the sums ` `        ``// satisfy the formula or not ` `        ``if` `(((``2` `* lsum) ` `             ``== (l_len * (l_len + ``1``))) ` `            ``&& ((``2` `* rsum) ` `                ``== (r_len * (r_len + ``1``)))) ` `            ``return` `true``; ` `    ``} ` `  `  `    ``return` `false``; ` `} ` `  `  `// Function to print the ` `// two permutations ` `static` `void` `printPermutations(``int` `arr[], ``int` `n, ` `                       ``int` `l1, ``int` `l2) ` `{ ` `    ``// Print the first permutation ` `    ``for` `(``int` `i = ``0``; i < l1; i++) { ` `        ``System.out.print(arr[i]+ ``" "``); ` `    ``} ` `    ``System.out.println(); ` `  `  `    ``// Print the second permutation ` `    ``for` `(``int` `i = l1; i < n; i++) { ` `        ``System.out.print(arr[i]+ ``" "``); ` `    ``} ` `} ` `  `  `// Function to find the two permutations ` `// from the given sequence ` `static` `void` `findPermutations(``int` `arr[], ``int` `n) ` `{ ` `    ``// If the sequence is not a ` `    ``// concatenation of two permutations ` `    ``if` `(!checkPermutation(arr, n)) { ` `        ``System.out.print(``"Not Possible"``); ` `        ``return``; ` `    ``} ` `  `  `    ``int` `l1 = ``0``, l2 = ``0``; ` `  `  `    ``// Find the largest element in the ` `    ``// array and set the lengths of the ` `    ``// permutations accordingly ` `    ``l1 = Arrays.stream(arr).max().getAsInt(); ` `    ``l2 = n - l1; ` `  `  `    ``HashSet s1 = ``new` `HashSet(), ` `            ``s2 = ``new` `HashSet(); ` `    ``for` `(``int` `i = ``0``; i < l1; i++) ` `        ``s1.add(arr[i]); ` `  `  `    ``for` `(``int` `i = l1; i < n; i++) ` `        ``s2.add(arr[i]); ` `  `  `    ``if` `(s1.size() == l1 && s2.size() == l2) ` `        ``printPermutations(arr, n, l1, l2); ` `    ``else` `{ ` `        ``l1 = l1+l2; ` `        ``l2 = l1-l2; ` `        ``l1 = l1-l2; ` `        ``printPermutations(arr, n, l1, l2); ` `    ``} ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``2``, ``1``, ``3``, ``4``, ``5``, ` `                  ``6``, ``7``, ``8``, ``9``, ``1``, ` `                  ``10``, ``2` `}; ` `    ``int` `n = arr.length; ` `  `  `    ``findPermutations(arr, n); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 program to print two ` `# permutations from a given sequence ` ` `  `# Function to check if the sequence is ` `# concatenation of two permutations or not ` `def` `checkPermutation(arr, n): ` `    ``# Computing the sum of all the ` `    ``# elements in the array ` `    ``sum` `=` `0` `    ``for` `i ``in` `range``(n): ` `        ``sum` `+``=` `arr[i] ` ` `  `    ``# Computing the prefix sum ` `    ``# for all the elements in the array ` `    ``prefix ``=` `[``0` `for` `i ``in` `range``(n``+``1``)] ` `    ``prefix[``0``] ``=` `arr[``0``] ` `    ``for` `i ``in` `range``(``1``,n): ` `        ``prefix[i] ``=` `prefix[i ``-` `1``] ``+` `arr[i] ` ` `  `    ``# Iterating through the i ` `    ``# from lengths 1 to n-1 ` `    ``for` `i ``in` `range``(n ``-` `1``): ` `         `  `        ``# Sum of first i+1 elements ` `        ``lsum ``=` `prefix[i] ` ` `  `        ``# Sum of remaining n-i-1 elements ` `        ``rsum ``=` `sum` `-` `prefix[i] ` ` `  `        ``# Lengths of the 2 permutations ` `        ``l_len ``=` `i ``+` `1` `        ``r_len ``=` `n ``-` `i ``-` `1` ` `  `        ``# Checking if the sums ` `        ``# satisfy the formula or not ` `        ``if` `(((``2` `*` `lsum) ``=``=` `(l_len ``*` `(l_len ``+` `1``))) ``and`  `                ``((``2` `*` `rsum) ``=``=` `(r_len ``*` `(r_len ``+` `1``)))): ` `            ``return` `True` ` `  `    ``return` `False` ` `  `# Function to print the ` `# two permutations ` `def` `printPermutations(arr,n,l1,l2): ` `    ``# Print the first permutation ` `    ``for` `i ``in` `range``(l1): ` `        ``print``(arr[i],end ``=` `" "``) ` ` `  `    ``print``(``"\n"``,end ``=` `""); ` ` `  `    ``# Print the second permutation ` `    ``for` `i ``in` `range``(l1, n, ``1``): ` `        ``print``(arr[i], end ``=` `" "``) ` ` `  `# Function to find the two permutations ` `# from the given sequence ` `def` `findPermutations(arr,n): ` `     `  `    ``# If the sequence is not a ` `    ``# concatenation of two permutations ` `    ``if` `(checkPermutation(arr, n) ``=``=` `False``): ` `        ``print``(``"Not Possible"``) ` `        ``return` ` `  `    ``l1 ``=` `0` `    ``l2 ``=` `0` ` `  `    ``# Find the largest element in the ` `    ``# array and set the lengths of the ` `    ``# permutations accordingly ` `    ``l1 ``=` `max``(arr) ` `    ``l2 ``=` `n ``-` `l1 ` ` `  `    ``s1 ``=` `set``() ` `    ``s2 ``=` `set``() ` `    ``for` `i ``in` `range``(l1): ` `        ``s1.add(arr[i]) ` ` `  `    ``for` `i ``in` `range``(l1,n): ` `        ``s2.add(arr[i]) ` ` `  `    ``if` `(``len``(s1) ``=``=` `l1 ``and` `len``(s2) ``=``=` `l2): ` `        ``printPermutations(arr, n, l1, l2) ` `    ``else``: ` `        ``temp ``=` `l1 ` `        ``l1 ``=` `l2 ` `        ``l2 ``=` `temp ` `        ``printPermutations(arr, n, l1, l2) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``2``, ``1``, ``3``, ``4``, ``5``,``6``, ``7``, ``8``, ``9``, ``1``,``10``, ``2``] ` `    ``n ``=` `len``(arr) ` ` `  `    ``findPermutations(arr, n) ` ` `  `# This code is contributed by Surendra_Gangwar `

## C#

 `     `  `// C# program to print two ` `// permutations from a given sequence ` `using` `System; ` `using` `System.Linq; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` `   `  `// Function to check if the sequence is ` `// concatenation of two permutations or not ` `static` `bool` `checkPermutation(``int` `[]arr, ``int` `n) ` `{ ` `    ``// Computing the sum of all the ` `    ``// elements in the array ` `    ``long` `sum = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``sum += arr[i]; ` `   `  `    ``// Computing the prefix sum ` `    ``// for all the elements in the array ` `    ``int` `[]prefix = ``new` `int``[n + 1]; ` `    ``prefix = arr; ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``prefix[i] = prefix[i - 1] + arr[i]; ` `   `  `    ``// Iterating through the i ` `    ``// from lengths 1 to n-1 ` `    ``for` `(``int` `i = 0; i < n - 1; i++) { ` `   `  `        ``// Sum of first i+1 elements ` `        ``long` `lsum = prefix[i]; ` `   `  `        ``// Sum of remaining n-i-1 elements ` `        ``long` `rsum = sum - prefix[i]; ` `   `  `        ``// Lengths of the 2 permutations ` `        ``long` `l_len = i + 1, ` `                  ``r_len = n - i - 1; ` `   `  `        ``// Checking if the sums ` `        ``// satisfy the formula or not ` `        ``if` `(((2 * lsum) ` `             ``== (l_len * (l_len + 1))) ` `            ``&& ((2 * rsum) ` `                ``== (r_len * (r_len + 1)))) ` `            ``return` `true``; ` `    ``} ` `   `  `    ``return` `false``; ` `} ` `   `  `// Function to print the ` `// two permutations ` `static` `void` `printPermutations(``int` `[]arr, ``int` `n, ` `                       ``int` `l1, ``int` `l2) ` `{ ` `    ``// Print the first permutation ` `    ``for` `(``int` `i = 0; i < l1; i++) { ` `        ``Console.Write(arr[i]+ ``" "``); ` `    ``} ` `    ``Console.WriteLine(); ` `   `  `    ``// Print the second permutation ` `    ``for` `(``int` `i = l1; i < n; i++) { ` `        ``Console.Write(arr[i]+ ``" "``); ` `    ``} ` `} ` `   `  `// Function to find the two permutations ` `// from the given sequence ` `static` `void` `findPermutations(``int` `[]arr, ``int` `n) ` `{ ` `    ``// If the sequence is not a ` `    ``// concatenation of two permutations ` `    ``if` `(!checkPermutation(arr, n)) { ` `        ``Console.Write(``"Not Possible"``); ` `        ``return``; ` `    ``} ` `   `  `    ``int` `l1 = 0, l2 = 0; ` `   `  `    ``// Find the largest element in the ` `    ``// array and set the lengths of the ` `    ``// permutations accordingly ` `    ``l1 = arr.Max(); ` `    ``l2 = n - l1; ` `   `  `    ``HashSet<``int``> s1 = ``new` `HashSet<``int``>(), ` `            ``s2 = ``new` `HashSet<``int``>(); ` `    ``for` `(``int` `i = 0; i < l1; i++) ` `        ``s1.Add(arr[i]); ` `   `  `    ``for` `(``int` `i = l1; i < n; i++) ` `        ``s2.Add(arr[i]); ` `   `  `    ``if` `(s1.Count == l1 && s2.Count == l2) ` `        ``printPermutations(arr, n, l1, l2); ` `    ``else` `{ ` `        ``l1 = l1+l2; ` `        ``l2 = l1-l2; ` `        ``l1 = l1-l2; ` `        ``printPermutations(arr, n, l1, l2); ` `    ``} ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]arr = { 2, 1, 3, 4, 5, ` `                  ``6, 7, 8, 9, 1, ` `                  ``10, 2 }; ` `    ``int` `n = arr.Length; ` `   `  `    ``findPermutations(arr, n); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```2 1
3 4 5 6 7 8 9 1 10 2
```

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