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