What is Product of all Subarrays of an Array?

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Q: How to use Product of all Subarrays of an Array in Data Structures and Algorithms?

Given an array of integers arr of size N, the task is to print products of all subarrays of the array

Given an array of integers arr of size N, the task is to print products of all subarrays of the array.

Examples:

Input: arr[] = {2, 4}
Output: 64
Here, subarrays are [2], [2, 4], [4]
Products are 2, 8, 4
Product of all Subarrays = 64

Input : arr[] = {10, 3, 7}
Output : 27783000
Here, subarrays are [10], [10, 3], [10, 3, 7], [3], [3, 7], [7]
Products are 10, 30, 210, 3, 21, 7
Product of all Subarrays = 27783000

Naive Approach: A simple solution is to generate all sub-array and compute their product.

C++

// C++ program to find product
// of all subarray of an array
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find product of all subarrays
void product_subarrays(int arr[], int n)
{
    // Variable to store the product
    int product = 1;
 
    // Compute the product while
    // traversing for subarrays
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            for (int k = i; k <= j; k++)
                product *= arr[k];
        }
    }
 
    // Printing product of all subarray
    cout << product << "\n";
}
 
// Driver code
int main()
{
    int arr[] = { 10, 3, 7 };
 
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function call
    product_subarrays(arr, n);
 
    return 0;
}

Java

// Java program to find product
// of all subarray of an array
import java.util.*;
 
class GFG {
 
    // Function to find product of all subarrays
    static void product_subarrays(int arr[], int n)
    {
 
        // Variable to store the product
        int product = 1;
 
        // Compute the product while
        // traversing for subarrays
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                for (int k = i; k <= j; k++)
                    product *= arr[k];
            }
        }
 
        // Printing product of all subarray
        System.out.print(product + "\n");
    }
 
    // Driver code
    public static void main(String args[])
    {
        int arr[] = { 10, 3, 7 };
        int n = arr.length;
 
        // Function call
        product_subarrays(arr, n);
    }
}
 
// This code is contributed by shivanisinghss2110

Python3

# Python3 program to find product
# of all subarray of an array
 
# Function to find product of all subarrays
def product_subarrays(arr, n):
 
    # Variable to store the product
    product = 1;
 
    # Compute the product while
    # traversing for subarrays
    for i in range(0, n):
        for j in range(i, n):
            for k in range(i, j + 1):
                product *= arr[k];
         
    # Printing product of all subarray
    print(product, "\n");
 
# Driver code
arr = [ 10, 3, 7 ];
 
n = len(arr);
 
# Function call
product_subarrays(arr, n);
 
# This code is contributed by Code_Mech

C#

// C# program to find product
// of all subarray of an array
using System;
 
class GFG {
 
    // Function to find product of all subarrays
    static void product_subarrays(int[] arr, int n)
    {
 
        // Variable to store the product
        int product = 1;
 
        // Compute the product while
        // traversing for subarrays
        for (int i = 0; i < n; i++) {
            for (int j = i; j < n; j++) {
                for (int k = i; k <= j; k++)
                    product *= arr[k];
            }
        }
 
        // Printing product of all subarray
        Console.Write(product + "\n");
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        int[] arr = { 10, 3, 7 };
        int n = arr.Length;
 
        // Function call
        product_subarrays(arr, n);
    }
}
 
// This code is contributed by shivanisinghss2110

Javascript

<script>
  // Javascript program to find product 
  // of all subarray of an array 
   
  // Function to find product of all subarrays 
  function product_subarrays(arr, n) 
  { 
   
      // Variable to store the product 
      let product = 1; 
 
      // Compute the product while 
      // traversing for subarrays 
      for (let i = 0; i < n; i++) { 
          for (let j = i; j < n; j++) { 
              for (let k = i; k <= j; k++) 
                  product *= arr[k]; 
          } 
      } 
 
      // Printing product of all subarray 
      document.write(product + "</br>"); 
  } 
   
  let arr = [ 10, 3, 7 ]; 
  let n = arr.length; 
 
  // Function call 
  product_subarrays(arr, n); 
 
// This code is contributed by divyeshrabadiya07.
</script>

Output:

27783000

Time Complexity: O(n³)

Auxiliary Space: O(1)

Efficient Approach: An efficient approach is to use two loops and calculate the products while traversing the subarrays.
Below is the implementation of the above approach:

C++

// C++ program to find product
// of all subarray of an array
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find product of all subarrays
void product_subarrays(long long int arr[], int n)
{
    // Variable to store the product
    long long int res = 1;
 
    // Compute the product while
    // traversing for subarrays
    for (int i = 0; i < n; i++) {
        long long int product = 1;
        for (int j = i; j < n; j++) {
            product = product * arr[j];
            res *= product;
        }
    }
    // Printing product of all subarray
    cout << res << "\n";
}
 
// Driver code
int main()
{
    long long int arr[] = { 10, 3, 7 };
 
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function call
    product_subarrays(arr, n);
 
    return 0;
}

Java

// Java program to find product
// of all subarray of an array
import java.util.*;
 
class GFG {
 
    // Function to find product of all subarrays
    static void product_subarrays(int arr[], int n)
    {
        // Variable to store the product
        int res = 1;
 
        // Compute the product while
        // traversing for subarrays
        for (int i = 0; i < n; i++) {
            int product = 1;
            for (int j = i; j < n; j++) {
                product = product * arr[j];
                res *= product;
            }
        }
 
        // Printing product of all subarray
        System.out.println(res + "\n");
    }
 
    // Driver code
    public static void main(String args[])
    {
        int arr[] = { 10, 3, 7 };
 
        int n = arr.length;
 
        // Function call
        product_subarrays(arr, n);
    }
}
 
// This code is contributed by AbhiThakur

Python3

# Python3 program to find product
# of all subarray of an array
 
# Function to find product of all subarrays
def product_subarrays(arr, n):
 
    # Variable to store the product
    res = 1;
 
    # Compute the product while
    # traversing for subarrays
    for i in range(n):
        product = 1
        for j in range(i, n):
            product *= arr[j];
            res = res * product
 
    # Printing product of all subarray
    print(res);
 
# Driver code
if __name__ == '__main__':
    arr = [ 10, 3, 7 ];
 
    n = len(arr);
 
    # Function call
    product_subarrays(arr, n);
 
# This code is contributed by Princi Singh

C#

// C# program to find product
// of all subarray of an array
using System;
 
class GFG {
 
    // Function to find product of all subarrays
    static void product_subarrays(int[] arr, int n)
    {
        // Variable to store the product
        int res = 1;
 
        // Compute the product while
        // traversing for subarrays
        for (int i = 0; i < n; i++) {
            int product = 1;
            for (int j = i; j < n; j++) {
                product *= arr[j];
                res = res * product;
            }
        }
 
        // Printing product of all subarray
        Console.WriteLine(res + "\n");
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        int[] arr = { 10, 3, 7 };
 
        int n = arr.Length;
 
        // Function call
        product_subarrays(arr, n);
    }
}
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
// Javascript program to find product
// of all subarray of an array
 
// Function to find product of all subarrays
function product_subarrays(arr, n)
{
    // Variable to store the product
    var res = 1;
 
    // Compute the product while
    // traversing for subarrays
    for (var i = 0; i < n; i++) {
        var product = 1;
        for (var j = i; j < n; j++) {
            product = product * arr[j];
            res *= product;
        }
    }
    // Printing product of all subarray
    document.write( res );
}
 
// Driver code
var arr = [10, 3, 7];
var n = arr.length;
// Function call
product_subarrays(arr, n);
 
 
</script>

Output:

27783000

Time Complexity: O(n²)

Auxiliary Space: O(1)