Find Maximum Sum of Multiplied Numbers in Python

Suppose we have two lists called nums and multipliers. Now consider an operation where we can remove any number from nums and remove any number from multipliers then multiply them together. We must repeat this operation until one of the lists is empty, we have to find the maximum sum of the multiplied numbers.

So, if the input is like nums = [-4, 4, 3] multipliers = [-2, 2], then the output will be 16, as We can match -4 with -2 and 4 with 2 to get -4 * -2 + 4 * 2.

To solve this, we will follow these steps −

• sort the list nums

• sort the list multipliers

• res := 0

• if size of nums < size of multipliers, then

  • swap nums and multipliers := multipliers, nums

• n := size of nums

• m := size of multipliers

• for i in range 0 to m - 1, do

  • if multipliers[i] <= 0, then

    • res := res + nums[i] * multipliers[i]

  • otherwise,

    • res := res + multipliers[i] * nums[n -(m - i)]

• return res

Example

Let us see the following implementation to get better understanding

def solve(nums, multipliers):
   nums.sort()
   multipliers.sort()
   res = 0
   if len(nums) < len(multipliers):
      nums, multipliers = multipliers, nums

   n, m = len(nums), len(multipliers)
   for i in range(m):
      if multipliers[i] <= 0:
         res += nums[i] * multipliers[i]
      else:
         res += multipliers[i] * nums[n - (m - i)]
   return res

nums = [-4, 4, 3]
multipliers = [-2, 2]
print(solve(nums, multipliers))

Input

[-4, 4, 3], [-2, 2]

Output

16