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

Python Server Side Programming Programming

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

Arnab Chakraborty

Updated on: 2020-12-15T12:49:50+05:30

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