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

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 each other
#include <iostream>
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 each 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 each 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 each 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

<?php
// PHP code to check if arrays
// are permutations of each other

// Function to check if arrays
// are permutations of each other.
function arePermutations($a, $b, $n, $m)
{

    $sum1 = 0; $sum2 = 0;
    $mul1 = 1; $mul2 = 1;

    // Calculating sum and multiply
    // of first array
    for ($i = 0; $i < $n; $i++)
    {
        $sum1 += $a[$i];
        $mul1 *= $a[$i];
    }

    // Calculating sum and multiply
    // of second array
    for ($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
$a = array( 1, 3, 2 );
$b = array( 3, 1, 2 );

$n = sizeof($a);
$m = sizeof($b);

if (arePermutations($a, $b, $n, $m))
    echo "Yes" . "\n";
else
    echo "No" . "\n";

// This code is contributed
// by Akanksha Rai(Abby_akku)

Javascript

<script>

// JavaScript code to check if arrays
// are permutations of each other

    // Function to check if arrays
   // are permutations of each other.
    function arePermutations(a,b,n,m)
    {
        let sum1 = 0, sum2 = 0, mul1 = 1, mul2 = 1;

    // Calculating sum and multiply of first array
    for (let i = 0; i < n; i++) {
        sum1 += a[i];
        mul1 *= a[i];
    }

    // Calculating sum and multiply of second array
    for (let 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
    let a=[1, 3, 2 ];
    let b=[3, 1, 2];

    let n = a.length;
    let m = b.length;

    if (arePermutations(a, b, n, m)==true)
        document.write( "Yes");

    else
        document.write( "No");


// This code is contributed by rag2127

</script>

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