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Sum of product of each element with each element after it

Given an array arr[] of n integers. The task is to find the sum of product of each element with each element after it in the array. In other words, find sum of product of each arr[i] with each arr[j] such that j > i.

Examples :  



Input : arr[] = {9, 3, 4, 2}
Output : 107
Explanation: 
Sum of product of arr[0] with arr[1], arr[2], arr[3] is 9*3 + 9*4 + 9*2 = 81
Sum of product of arr[1] with arr[2], arr[3] is 3*4 + 3*2 = 18
Product of arr[2] with arr[3] is 4*2 = 8
Sum of all these sums is 81 + 18 + 8 = 107

Input : arr[] = {3, 5}
Output : 15



Observe to find (p*a + p*b + …..+ p*y + p*z) is equals to p*(a + b ….. y + z). 
So for each i, 0 ? i ? n – 2 we have to calculate arr[i] * (arr[j] + arr[j+1] + ….. + arr[n – 2] + arr[n – 1]), where j = i + 1 and find sum of these. 
We can reduce the complexity of finding (arr[j] + arr[j+1] + ….. + arr[n – 2] + arr[n – 1]) for each ‘i’ by precomputing the suffix sum of the array. 
Lets sum[] stores the suffix sum of the given array i.e sum[i] have arr[i] + arr[i+1] + ….. + arr[n – 2] + arr[n – 1]. 
So, after precompute sum[], we need to find the sum of arr[i]*sum[i + 1] where 0 ? i ? n – 2.

Below is the implementation of this approach: 




// C++ Program to find sum of
// product of each element
// with each element after it
#include <bits/stdc++.h>
using namespace std;
 
// Return sum of product
// of each element with
// each element after it
int findSumofProduct(int arr[], int n)
{
    int sum[n];
    sum[n - 1] = arr[n - 1];
 
    // finding suffix sum
    for (int i = n - 2; i >= 0; i--)
        sum[i] = sum[i + 1] + arr[i];
     
    // finding the sum of product of
    // each element with suffix sum.
    int res = 0;
    for (int i = 0; i < n - 1; i++)
        res += (sum[i + 1] * arr[i]);
 
    return res;
}
 
// Driver Code
int main()
{
    int arr[] = {9, 3, 4, 2};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << findSumofProduct(arr, n)
         << endl;
    return 0;
}
 





                        























                                    



                                    




                                    




                                    


                                



















// Java Program to find sum of product


// of each element with each element


// after it



class GFG {




     



    // Return sum of product of each




    // element with each element




    // after it




    static int findSumofProduct(int arr[],




                                    int n)




    {




        int sum[] = new int[n];




        sum[n - 1] = arr[n - 1];




     



        // finding suffix sum




        for (int i = n - 2; i >= 0; i--) 




            sum[i] = sum[i + 1] + arr[i];




         



        // finding the sum of product of




        // each element with suffix sum.




        int res = 0;




        for (int i = 0; i < n - 1; i++) 




            res += (sum[i + 1] * arr[i]); 




     



        return res;




    }




     



    // Driver Program




    public static void main(String[] args)




    {




         



        int arr[] = { 9, 3, 4, 2 };




        int n = arr.length;




         



        System.out.println(




                findSumofProduct(arr, n));




    }



}


 


// This code is contributed by


// Smitha Dinesh Semwal


















                        






                        























                                    



                                    




                                    




                                    


                                



















# Python3 Program to find sum of 


# product of each element with 


# each element after it 


 


# Return sum of product of each 


# element with each element after it 



def findSumofProduct(arr, n):




    sum = [None for _ in range(n)]




    sum[n-1] = arr[n - 1]



 



    # finding suffix sum 




    for i in range(n - 2, -1, -1):




        sum[i] = sum[i + 1] + arr[i]



 



    # finding the sum of product of 




    # each element with suffix sum. 




    res = 0




    for i in range(n - 1):




        res += sum[i + 1] * arr[i]




    return res



 


# Driver Code



arr = [9, 3, 4, 2]




n = len(arr)




print(findSumofProduct(arr, n))



 


# This code is contributed


# by SamyuktaSHegde


















                        






                        























                                    



                                    




                                    




                                    


                                



















// C# Program to find sum of product


// of each element with each element


// after it



using System;



 



class GFG {




     



    // Return sum of product of each




    // element with each element




    // after it




    static int findSumofProduct(int[] arr,




                                    int n)




    {




        int[] sum = new int[n];




        sum[n - 1] = arr[n - 1];




     



        // finding suffix sum




        for (int i = n - 2; i >= 0; i--) 




            sum[i] = sum[i + 1] + arr[i];




         



        // finding the sum of product of




        // each element with suffix sum.




        int res = 0;




        for (int i = 0; i < n - 1; i++) 




            res += (sum[i + 1] * arr[i]); 




     



        return res;




    }




     



    // Driver code




    static public void Main ()




    {




        int[] arr = { 9, 3, 4, 2 };




        int n = arr.Length;




         



        Console.WriteLine(findSumofProduct(arr, n));




    }



}


 


// This code is contributed by Ajit.


















                        






                        























                                    



                                    




                                    




                                    


                                



















<?php


// PHP Program to find sum of 


// product of each element


// with each element after it


 


// Return sum of product 


// of each element with 


// each element after it



function findSumofProduct($arr, $n)



{



     



    $sum = array();




    $sum[$n - 1] = $arr[$n - 1];



 



    // finding suffix sum




    for ( $i = $n - 2; $i >= 0; $i--) 




        $sum[$i] = $sum[$i + 1] + $arr[$i];




     



    // finding the sum of product of 




    // each element with suffix sum.




    $res = 0;




    for ( $i = 0; $i < $n - 1; $i++) 




        $res += ($sum[$i + 1] * $arr[$i]); 



 



    return $res;



}


 



    // Driver Code




    $arr = array(9, 3, 4, 2);




    $n = count($arr);




    echo findSumofProduct($arr, $n);




     


// This code is contributed by anuJ_67.


?>


















                        






                        























                                    



                                    




                                    




                                    


                                



















<script>


 


// Javascript Program to find sum of


// product of each element


// with each element after it


 


// Return sum of product


// of each element with


// each element after it



function findSumofProduct(arr, n)



{



    let sum = new Array(n);




    sum[n - 1] = arr[n - 1];



 



    // finding suffix sum




    for (let i = n - 2; i >= 0; i--)




        sum[i] = sum[i + 1] + arr[i];




     



    // finding the sum of product of




    // each element with suffix sum.




    let res = 0;




    for (let i = 0; i < n - 1; i++)




        res += (sum[i + 1] * arr[i]);



 



    return res;



}


 


// Driver Code


 



    let arr = [9, 3, 4, 2];




    let n = arr.length;




    document.write(findSumofProduct(arr, n)




        + "<br>");



 


// This code is contributed by Mayank Tyagi


 


</script>


















                        






                        








Output

107


Time complexity: O(n) where n is the size of the given array
Auxiliary space: O(n)
Below is Optimized Code of finding sum of product of each element with each element after it: 














                                    



                                    




                                    




                                    


                                



















// C++ Program to find sum of


// product of each element 


// with each element after it


#include <bits/stdc++.h>



using namespace std;



 


// Return sum of product 


// of each element with 


// each element after it



int findSumofProduct(int arr[], 




                     int n)



{



    int suffix_sum = arr[n - 1];



 



    // Finding product of array 




    // elements and suffix sum.




    int res = 0;




    for (int i = n - 2; i >= 0; i--) 




    {



 



        res += (suffix_sum * arr[i]);



 



        // finding suffix sum




        suffix_sum += arr[i];




    }



 



    return res;



}


 


// Driver Code



int main()



{



    int arr[] = {9, 3, 4, 2};




    int n = sizeof(arr) / sizeof(arr[0]);




    cout << findSumofProduct(arr, n) 




         << endl;




    return 0;



}


















                        






                        























                                    



                                    




                                    




                                    


                                



















// Java Program to find sum 


// of product of each 


// element with each


// element after it



import java .io.*;




class GFG {




     



    // Return sum of product of




    // each element with each




    // element after it




    static int findSumofProduct(int[] arr,




                                int n)




    {




        int suffix_sum = arr[n - 1];




     



        // Finding product of array 




        // elements and suffix sum.




        int res = 0;




        for (int i = n - 2; i >= 0; i--)




        {




            res += (suffix_sum * arr[i]);




     



            // finding suffix sum




            suffix_sum += arr[i];




        }




     



        return res;




    }



 



    // Driver code




    static public void main(String[] args)




    {




        int[] arr = {9, 3, 4, 2};




        int n = arr.length;




        System.out.println(findSumofProduct(arr, n));




    }



}


 


// This code is contributed by anuj_67.


















                        






                        























                                    



                                    




                                    




                                    


                                



















# Python 3 Program to find sum of


# product of each element 


# with each element after it


 


# Return sum of product 


# of each element with 


# each element after it



def findSumofProduct(arr, n):




    suffix_sum = arr[n - 1]



 



    # Finding product of array 




    # elements and suffix sum.




    res = 0




    for i in range(n - 2, -1, -1):



 



        res += (suffix_sum * arr[i])



 



        # finding suffix sum




        suffix_sum += arr[i]



 



    return res;



 


# Driver Code



arr = [9, 3, 4, 2];




n = len(arr);




print(findSumofProduct(arr, n))



 


# This code is contributed 


# by Akanksha Rai


















                        






                        























                                    



                                    




                                    




                                    


                                



















// C# Program to find sum 


// of product of each 


// element with each


// element after it



using System;



 



class GFG {




     



    // Return sum of product of




    // each element with each




    // element after it




    static int findSumofProduct(int[] arr,




                                int n)




    {




        int suffix_sum = arr[n - 1];




     



        // Finding product of array 




        // elements and suffix sum.




        int res = 0;




        for (int i = n - 2; i >= 0; i--)




        {




            res += (suffix_sum * arr[i]);




     



            // finding suffix sum




            suffix_sum += arr[i];




        }




     



        return res;




    }



 



    // Driver code




    static public void Main()




    {




        int[] arr = {9, 3, 4, 2};




        int n = arr.Length;




        Console.WriteLine(findSumofProduct(arr, n));




    }



}


 


// This code is contributed by Ajit.


















                        






                        























                                    



                                    




                                    




                                    


                                



















<?php


// PHP Program to find sum of


// product of each element 


// with each element after it


 


// Return sum of product 


// of each element with 


// each element after it



function findSumofProduct($arr, 




                          $n)



{



    $suffix_sum = $arr[$n - 1];



 



    // Finding product of array 




    // elements and suffix sum.




    $res = 0;




    for ( $i = $n - 2; $i >= 0; $i--) 




    {



 



        $res += ($suffix_sum * $arr[$i]);



 



        // finding suffix sum




        $suffix_sum += $arr[$i];




    }



 



    return $res;



}


 



    // Driver Code




    $arr = array(9, 3, 4, 2);




    $n = count($arr);




    echo findSumofProduct($arr, $n) 



 


 


// This code is contributed by anuJ_67.


?>


















                        






                        























                                    



                                    




                                    




                                    


                                



















<script>


 



    // Javascript Program to find sum




    // of product of each




    // element with each




    // element after it




     



    // Return sum of product of




    // each element with each




    // element after it




    function findSumofProduct(arr, n)




    {




        let suffix_sum = arr[n - 1];




      



        // Finding product of array




        // elements and suffix sum.




        let res = 0;




        for (let i = n - 2; i >= 0; i--)




        {




            res += (suffix_sum * arr[i]);




      



            // finding suffix sum




            suffix_sum += arr[i];




        }




      



        return res;




    }




     



    let arr = [9, 3, 4, 2];




    let n = arr.length;




    document.write(findSumofProduct(arr, n));




     


</script>


















                        






                        








Output

107


Time complexity: O(n) where n is the size of the given array
Auxiliary space: O(1)

	

        Article Tags : 
        

            Arrays
DSA        


		
	

	


      

      

          
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