# Find the maximum sum of digits of the product of two numbers

Given an array arr[] of size N( > 2). The task is to find the maximum sum of digits of the product of any two numbers of the given array.

Examples:

Input : arr[] = {8, 7}
Output : 11
The product of 8 and 7 is 56. The sum of the digits of 56 is equal to 11.

Input : arr[] = {4, 3, 5}
Output : 6
Product of 4 & 3 = 12. Sum of the digits = 3.
Product of 3 & 5 = 15. Sum of the digits = 6.
Product of 4 & 5 = 20. Sum of the digits = 2.

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

Approach: Run nested loops to select two numbers of the array and get the product. For every product check the digit sum and find the maximum digit sum.

Below is the implementation of the above approach:

## C++

 `// C++ program find the maximum sum of ` `// digits of the product of two numbers ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the sum of the digits ` `int` `sumDigits(``int` `n) ` `{ ` `    ``int` `digit_sum = 0; ` `    ``while` `(n) { ` `        ``digit_sum += n % 10; ` `        ``n /= 10; ` `    ``} ` `    ``return` `digit_sum; ` `} ` ` `  `// Function to find the maximum sum of digits of product ` `int` `productOfNumbers(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `sum = INT_MIN; ` ` `  `    ``// Run nested loops ` `    ``for` `(``int` `i = 0; i < n - 1; i++) { ` `        ``for` `(``int` `j = i + 1; j < n; j++) { ` `            ``int` `product = arr[i] * arr[j]; ` ` `  `            ``// Find the maximum sum ` `            ``sum = max(sum, sumDigits(product)); ` `        ``} ` `    ``} ` ` `  `    ``// Return the required answer ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 4, 3, 5 }; ` ` `  `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << productOfNumbers(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program find the maximum sum of ` `// digits of the product of two numbers ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to find the sum of the digits ` `static` `int` `sumDigits(``int` `n) ` `{ ` `    ``int` `digit_sum = ``0``; ` `    ``while` `(n > ``0``)  ` `    ``{ ` `        ``digit_sum += n % ``10``; ` `        ``n /= ``10``; ` `    ``} ` `    ``return` `digit_sum; ` `} ` ` `  `// Function to find the maximum sum  ` `// of digits of product ` `static` `int` `productOfNumbers(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `sum = Integer.MIN_VALUE; ` ` `  `    ``// Run nested loops ` `    ``for` `(``int` `i = ``0``; i < n - ``1``; i++)  ` `    ``{ ` `        ``for` `(``int` `j = i + ``1``; j < n; j++) ` `        ``{ ` `            ``int` `product = arr[i] * arr[j]; ` ` `  `            ``// Find the maximum sum ` `            ``sum = Math.max(sum, sumDigits(product)); ` `        ``} ` `    ``} ` ` `  `    ``// Return the required answer ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `[]arr = { ``4``, ``3``, ``5` `}; ` `     `  `    ``int` `n = arr.length; ` `     `  `    ``System.out.print( productOfNumbers(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by anuj_67.. `

## Python3

 `# Python3 program find the maximum sum of ` `# digits of the product of two numbers ` `import` `sys ` ` `  `# Function to find the sum of the digits ` `def` `sumDigits(n): ` ` `  `    ``digit_sum ``=` `0``; ` `    ``while` `(n > ``0``):  ` `        ``digit_sum ``+``=` `n ``%` `10``; ` `        ``n ``/``=` `10``; ` `     `  `    ``return` `digit_sum; ` ` `  `# Function to find the maximum sum ` `# of digits of product ` `def` `productOfNumbers(arr, n): ` ` `  `    ``sum` `=` `-``sys.maxsize ``-` `1``; ` ` `  `    ``# Run nested loops ` `    ``for` `i ``in` `range``(n ``-` `1``):  ` `        ``for` `j ``in` `range``(i ``+` `1``, n): ` `            ``product ``=` `arr[i] ``*` `arr[j]; ` ` `  `            ``# Find the maximum sum ` `            ``sum` `=` `max``(``sum``, sumDigits(product)); ` ` `  `    ``# Return the required answer ` `    ``return` `sum``; ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``arr ``=``[ ``4``, ``3``, ``5` `]; ` ` `  `    ``n ``=` `len``(arr); ` ` `  `    ``print``(``int``(productOfNumbers(arr, n))); ` ` `  `# This code contributed by PrinciRaj1992  `

## C#

 `// C# program find the maximum sum of ` `// digits of the product of two numbers ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to find the sum of the digits ` `static` `int` `sumDigits(``int` `n) ` `{ ` `    ``int` `digit_sum = 0; ` `    ``while` `(n > 0)  ` `    ``{ ` `        ``digit_sum += n % 10; ` `        ``n /= 10; ` `    ``} ` `    ``return` `digit_sum; ` `} ` ` `  `// Function to find the maximum sum  ` `// of digits of product ` `static` `int` `productOfNumbers(``int` `[]arr, ``int` `n) ` `{ ` `    ``int` `sum = ``int``.MinValue; ` ` `  `    ``// Run nested loops ` `    ``for` `(``int` `i = 0; i < n - 1; i++)  ` `    ``{ ` `        ``for` `(``int` `j = i + 1; j < n; j++) ` `        ``{ ` `            ``int` `product = arr[i] * arr[j]; ` ` `  `            ``// Find the maximum sum ` `            ``sum = Math.Max(sum, sumDigits(product)); ` `        ``} ` `    ``} ` ` `  `    ``// Return the required answer ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args) ` `{ ` `    ``int` `[]arr = { 4, 3, 5 }; ` `     `  `    ``int` `n = arr.Length; ` `     `  `    ``Console.Write(productOfNumbers(arr, n)); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```6
```

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