Maximum value
You are given the following:
. An array A consisting of n elements
• An array B consisting of n elements
You can perform the following operations on the array:
• For each you can swap the element A[i] with A[i+1] or A[i-1]
• For each you can swap the element B[i] with B[i+1] or B[i-1]
. Each element can be swapped at most once.
Task
Determine the maximum value of for each i find A[i]xB[i]x(i+1)
Example
Assumptions
• n = 4
• A = {1,2,3,4}
• B={1,3,2,4)
Approach
You can swap A[i], with A[i+1] or A[i-1] and B[i] with B[i+1] or B[i-1] leave an element as it is.
You see that after considering all combinations of A and B. summation of A[i]xB[i]x(i+1) for each i is maximum for A={1,2,3,4},B={1,2,3,4} and the answer is 100.
i.e
(1x1x1)+(2x2x2)+(3x3x3)+(4x4x4)=100