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
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