Minimum and Maximum values of an expression with * and +
Given an expression which contains numbers and two operators ‘+’ and ‘*’, we need to find maximum and minimum value which can be obtained by evaluating this expression by different parenthesization.
Input : expr = “1+2*3+4*5” Output : Minimum Value = 27, Maximum Value = 105 Explanation: Minimum evaluated value = 1 + (2*3) + (4*5) = 27 Maximum evaluated value = (1 + 2)*(3 + 4)*5 = 105
We can solve this problem by dynamic programming method, we can see that this problem is similar to matrix chain multiplication, here we are trying different parenthesization to maximize and minimize expression value instead of number of matrix multiplication.
In below code first we have separated the operators and numbers from given expression then two 2D arrays are taken for storing the intermediate result which are updated similar to matrix chain multiplication and different parenthesization are tried among the numbers but according to operators occurring in between them. At the end last cell of first row will store the final result in both the 2D arrays.
Minimum value : 27, Maximum value : 105
Time Complexity: O(n^3), as we have three nested loops in the function.
Space Complexity: O(n^2), since we are using a 2D matrix to store the values of all the subproblems.
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