# Check if two arrays are permutations of each other using Mathematical Operation

• Last Updated : 02 Sep, 2022

Given two unsorted arrays of same size where arr[i] >= 0 for all i, the task is to check if two arrays are permutations of each other or not.

Examples:

```Input: arr1[] = {2, 1, 3, 5, 4, 3, 2}
arr2[] = {3, 2, 2, 4, 5, 3, 1}
Output: Yes

Input: arr1[] = {2, 1, 3, 5}
arr2[] = {3, 2, 2, 4}
Output: No```

It has been already discussed in Check if two arrays are permutations of each other using Sorting and Hashing. But in this post, a different approach is discussed.

Approach:

1. Traverse the first array A, add and multiply all the elements and store them in variables as Sum1 and Mul1 respectively.
2. Similarly, traverse the second array B, add and multiply all the elements and store them in variables as Sum2 and Mul2 respectively.
3. Now, compare both sum1, sum2 and mul1, mul2. If Sum1 == Sum2 and Mul1 == Mul2, then both arrays are permutations of each other, else not.

Implementation:

## C++

 `// CPP code to check if arrays``// are permutations of eah other``#include ``using` `namespace` `std;` `// Function to check if arrays``// are permutations of each other.``bool` `arePermutations(``int` `a[], ``int` `b[], ``int` `n, ``int` `m)``{` `    ``int` `sum1 = 0, sum2 = 0, mul1 = 1, mul2 = 1;` `    ``// Calculating sum and multiply of first array``    ``for` `(``int` `i = 0; i < n; i++) {``        ``sum1 += a[i];``        ``mul1 *= a[i];``    ``}` `    ``// Calculating sum and multiply of second array``    ``for` `(``int` `i = 0; i < m; i++) {``        ``sum2 += b[i];``        ``mul2 *= b[i];``    ``}` `    ``// If sum and mul of both arrays are equal,``    ``// return true, else return false.``    ``return` `((sum1 == sum2) && (mul1 == mul2));``}` `// Driver code``int` `main()``{` `    ``int` `a[] = { 1, 3, 2 };``    ``int` `b[] = { 3, 1, 2 };` `    ``int` `n = ``sizeof``(a) / ``sizeof``(``int``);``    ``int` `m = ``sizeof``(b) / ``sizeof``(``int``);` `    ``if` `(arePermutations(a, b, n, m))``        ``cout << ``"Yes"` `<< endl;``    ` `    ``else``        ``cout << ``"No"` `<< endl;` `    ``return` `0;``}`

## Java

 `// Java code to check if arrays``// are permutations of eah other` `import` `java.io.*;` `class` `GFG {`  `// Function to check if arrays``// are permutations of each other.``static` `boolean` `arePermutations(``int` `a[], ``int` `b[], ``int` `n, ``int` `m)``{` `    ``int` `sum1 = ``0``, sum2 = ``0``, mul1 = ``1``, mul2 = ``1``;` `    ``// Calculating sum and multiply of first array``    ``for` `(``int` `i = ``0``; i < n; i++) {``        ``sum1 += a[i];``        ``mul1 *= a[i];``    ``}` `    ``// Calculating sum and multiply of second array``    ``for` `(``int` `i = ``0``; i < m; i++) {``        ``sum2 += b[i];``        ``mul2 *= b[i];``    ``}` `    ``// If sum and mul of both arrays are equal,``    ``// return true, else return false.``    ``return` `((sum1 == sum2) && (mul1 == mul2));``}` `// Driver code` `    ``public` `static` `void` `main (String[] args) {``            ``int` `a[] = { ``1``, ``3``, ``2` `};``    ``int` `b[] = { ``3``, ``1``, ``2` `};` `    ``int` `n = a.length;``    ``int` `m = b.length;` `    ``if` `(arePermutations(a, b, n, m)==``true``)``        ``System.out.println( ``"Yes"``);``    ` `    ``else``        ``System.out.println( ``"No"``);``    ``}``}``// This code is contributed by  inder_verma..`

## Python3

 `# Python 3 program to check if arrays``# are permutations of eah other` `# Function to check if arrays``# are permutations of each other``def` `arePermutations(a, b, n, m) :` `    ``sum1, sum2, mul1, mul2 ``=` `0``, ``0``, ``1``, ``1` `    ``# Calculating sum and multiply of first array``    ``for` `i ``in` `range``(n) :``        ``sum1 ``+``=` `a[i]``        ``mul1 ``*``=` `a[i]` `    ``# Calculating sum and multiply of second array``    ``for` `i ``in` `range``(m) :``        ``sum2 ``+``=` `b[i]``        ``mul2 ``*``=` `b[i]` `    ``# If sum and mul of both arrays are equal,``    ``# return true, else return false.``    ``return``((sum1 ``=``=` `sum2) ``and` `(mul1 ``=``=` `mul2))`  `# Driver code    ``if` `__name__ ``=``=` `"__main__"` `:` `    ``a ``=` `[ ``1``, ``3``, ``2``]``    ``b ``=` `[ ``3``, ``1``, ``2``]` `    ``n ``=` `len``(a)``    ``m ``=` `len``(b)` `    ``if` `arePermutations(a, b, n, m) :``        ``print``(``"Yes"``)` `    ``else` `:``        ``print``(``"No"``)` ` ` `# This code is contributed by ANKITRAI1`

## C#

 `// C# code to check if arrays``// are permutations of eah other``using` `System;` `class` `GFG``{` `// Function to check if arrays``// are permutations of each other.``static` `bool` `arePermutations(``int``[] a, ``int``[] b,``                            ``int` `n, ``int` `m)``{` `    ``int` `sum1 = 0, sum2 = 0,``        ``mul1 = 1, mul2 = 1;` `    ``// Calculating sum and multiply``    ``// of first array``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``sum1 += a[i];``        ``mul1 *= a[i];``    ``}` `    ``// Calculating sum and multiply``    ``// of second array``    ``for` `(``int` `i = 0; i < m; i++)``    ``{``        ``sum2 += b[i];``        ``mul2 *= b[i];``    ``}` `    ``// If sum and mul of both arrays``    ``// are equal, return true, else``    ``// return false.``    ``return` `((sum1 == sum2) &&``            ``(mul1 == mul2));``}` `// Driver code``public` `static` `void` `Main ()``{``    ``int``[] a = { 1, 3, 2 };``    ``int``[] b = { 3, 1, 2 };``    ` `    ``int` `n = a.Length;``    ``int` `m = b.Length;``    ` `    ``if` `(arePermutations(a, b, n, m) == ``true``)``        ``Console.Write( ``"Yes"``);``    ` `    ``else``        ``Console.Write( ``"No"``);``}``}` `// This code is contributed``// by ChitraNayal`

## PHP

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## Javascript

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Output

`Yes`

Complexity Analysis:

• Time Complexity: O(n) where n is size of given array
• Auxiliary space: O(1) as it is using constant space

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