Program to find maximum value by inserting operators in between numbers in Python

Suppose we have a list of numbers called nums, we have to find the maximal value that can be generated by adding any binary operators like +, −, and * between the given numbers as well as insert any valid brackets.

So, if the input is like nums = [−6, −4, −10], then the output will be 100, as we can make the expression like: ((−6) + (−4)) * −10.

To solve this, we will follow these steps −

• OPS := a list of operators [+, −, *]

• N := size of A

• if all elements in A is 0, then

  • return 0

• Define a function dp() . This will take i, j

• if i is same as j, then

  • return a pair (A[i], A[i])

• low := inf, high := −inf

• for k in range i to j − 1, do

  • for each left in dp(i, k), do

    • for each right in dp(k + 1, j), do

      • for each operator op in OPS, do

        • res := left op right

        • if res < low, then

          • low := res

        • if res > high, then

          • high := res

• return pair (low, high)

• From the main method do the following −

• ans := dp(0, N − 1)

• return second value of ans

Let us see the following implementation to get better understanding −

Example

 Live Demo

import operator
class Solution:
   def solve(self, A):
      OPS = [operator.add, operator.sub, operator.mul]
      N = len(A)
      if not any(A):
         return 0
      def dp(i, j):
         if i == j:
            return [A[i], A[i]]
         low = float("inf")
         high = float("−inf")
         for k in range(i, j):
            for left in dp(i, k):
               for right in dp(k + 1, j):
                  for op in OPS:
                     res = op(left, right)
                     if res < low:
                        low = res
                     if res > high:
                        high = res
         return [low, high]
      return dp(0, N − 1)[1]
ob = Solution()
nums = [−6, −4, −10]
print(ob.solve(nums))

Input

[−6, −4, −10]

Output

100