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

Given two unsorted arrays of same size, 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

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

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:

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

Below is the implementation of above approach:

C++

// CPP code to check if arrays 
// are permutations of eah other 
#include <iostream> 
using namespace std; 
  
// Function to check if arrays 
// are permutaitons 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 permutaitons 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.. 

Python 3

# Python 3 program to check if arrays  
# are permutations of eah other  
  
# Function to check if arrays  
# are permutaitons 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 permutaitons 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 