# Permutation of Array such that sum of adjacent elements are not divisible by 3

Given an array arr[] of positive integers, the task is to find the permutation of the array such that sum of adjacent elements is not divisible by 3.

Note: If there is no such permutation of the array print -1.
Examples:

Input: arr[] = {1, 2, 3, 4, 5}
Output: 4 1 3 5 2
Explaination:
arr[0] + arr[1] = 4 + 1 = 5 % 3 != 0
arr[1] + arr[2] = 1 + 3 = 4 % 3 != 0
arr[2] + arr[3] = 3 + 5 = 8 % 3 != 0
arr[3] + arr[4] = 5 + 2 = 7 % 3 != 0

Input: arr[] = {1, 24, 30, 42, 51}
Output: -1

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

Approach: The key observation in the problem is any that there can be only three types of the remainder for all the types of numbers That is {0, 1, 2}. Hence, we can segregate numbers into three parts and if we arrange the numbers having remainder as 0 with the numbers having remainder as 1 or 2. Then their sum is not divisible by 3. If there is no way to arrange all the numbers in this way then there is no permutation such that their sum of adjacent elements are not divisible by 3.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find the ` `// permutation of the array such that ` `// sum of adjacent elements is not ` `// divisible by 3 ` ` `  `#include ` `using` `namespace` `std; ` `#define hell 1000000007 ` `#define N 100005 ` ` `  `// Function to segregate numbers ` `// based on their remainder ` `// when divided by three ` `void` `count_k( ` `    ``vector<``int``>& arr, ``int``& c_0, ` `    ``int``& c_1, ``int``& c_2, ` `    ``stack<``int``>& ones, ` `    ``stack<``int``>& twos, ` `    ``stack<``int``>& zeros) ` `{ ` `    ``// Loop to iterate over the elements ` `    ``// of the given array ` `    ``for` `(``int` `i = 0; i < arr.size(); i++) { ` ` `  `        ``// Condition to check the ` `        ``// remainder of the number ` `        ``if` `(arr[i] % 3 == 0) { ` `            ``c_0++; ` `            ``zeros.push(arr[i]); ` `        ``} ` `        ``else` `if` `(arr[i] % 3 == 1) { ` `            ``c_1++; ` `            ``ones.push(arr[i]); ` `        ``} ` `        ``else` `{ ` `            ``c_2++; ` `            ``twos.push(arr[i]); ` `        ``} ` `    ``} ` `    ``return``; ` `} ` ` `  `// Function to find the permutation ` `// of the array such that sum of ` `// adjacent elements is not divisible by 3 ` `void` `printArrangement( ` `    ``vector<``int``>& arr, ` `    ``int``& c_0, ``int``& c_1, ``int``& c_2, ` `    ``stack<``int``>& ones, ` `    ``stack<``int``>& twos, ` `    ``stack<``int``>& zeros) ` `{ ` `    ``// Condition to check when ` `    ``// it's impossible to arrange ` `    ``if` `((c_0 == 0 && c_1 != 0 && c_2 != 0) ` `        ``or c_0 > c_1 + c_2 + 1) { ` `        ``cout << ``"-1"``; ` `        ``return``; ` `    ``} ` ` `  `    ``// Condition to check when ` `    ``// there are no zeros, and ` `    ``// only ones or only twos ` `    ``if` `(c_0 == 0) { ` `        ``for` `(``int` `i = 0; i < arr.size(); i++) { ` `            ``cout << arr[i] << ``" "``; ` `        ``} ` `        ``return``; ` `    ``} ` ` `  `    ``// Array to store the permutation ` `    ``int` `i, j, ans[N]; ` `    ``memset``(ans, -1, ``sizeof``(ans)); ` ` `  `    ``// Place the ones on alternate places ` `    ``// in the answer array, ` `    ``// leaving spaces for zeros remainder ` `    ``// elements in the array ` `    ``for` `(i = 1, j = 0; j < c_1; i += 2, j++) { ` `        ``ans[i] = ones.top(); ` `        ``ones.pop(); ` `    ``} ` ` `  `    ``// Adding a zero to ` `    ``// connect it with a two ` `    ``ans[i - 1] = zeros.top(); ` `    ``zeros.pop(); ` `    ``c_0--; ` ` `  `    ``// Place the twos on alternate places ` `    ``// in the answer array, ` `    ``// leaving spaces for zeros ` `    ``for` `(j = 0; j < c_2; j++, i += 2) { ` `        ``ans[i] = twos.top(); ` `        ``twos.pop(); ` `    ``} ` ` `  `    ``// Fill the zeros finally, ` `    ``// between the ones and the twos ` `    ``for` `(``int` `k = 0; c_0 > 0; k += 2) { ` `        ``if` `(ans[k] == -1) { ` `            ``ans[k] = zeros.top(); ` `            ``c_0--; ` `        ``} ` `    ``} ` ` `  `    ``// Print the arrangment of the array ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``if` `(ans[i] != -1) ` `            ``cout << ans[i] << ``" "``; ` `    ``} ` `    ``return``; ` `} ` ` `  `// Function to solve the problem ` `void` `solve(``int` `n, ` `           ``vector<``int``>& arr) ` `{ ` ` `  `    ``// As there can be only 3 remainders ` `    ``stack<``int``> ones, zeros, twos; ` ` `  `    ``int` `c_0 = 0, c_1 = 0, c_2 = 0; ` `    ``count_k(arr, c_0, c_1, c_2, ` `            ``ones, twos, zeros); ` ` `  `    ``// Function Call ` `    ``printArrangement( ` `        ``arr, c_0, c_1, c_2, ` `        ``ones, twos, zeros); ` `} ` ` `  `// Driver Code ` `signed` `main() ` `{ ` `    ``int` `n = 5; ` `    ``vector<``int``> arr{ 1, 2, 3, 4, 5 }; ` ` `  `    ``solve(n, arr); ` `    ``return` `0; ` `} `

Output:

```4 1 3 5 2
```

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