# Maximize the Value of an Expression

Given an array A, maximize value of the expression (A[s] – A[r] + A[q] – A[p]) where p, q, r and s are indices of the input array and s > r > q > p.

For example,

Input:  A[] = [3, 9, 10, 1, 30, 40]

Output: 46

(40 – 1 + 10 – 3) will result in maximum value

Naive solution would be to generate all combinations of such numbers. The time complexity of this solution would be O(n4).

We can use Dynamic Programming to solve this problem. The idea is to create four lookup tables L1[], L2[], L3[] and L4[] where –

• L1[] stores the maximum value of A[s]
• L2[] stores the maximum value of A[s] – A[r]
• L3[] stores the maximum value of A[s] – A[r] + A[q]
• L4[] stores the maximum value of A[s] – A[r] + A[q] – A[p]

Then the maximum value would be present in index 0 of L4[], which is our required answer.

Below is its C++/Java implementation:

Output:

46

## Java

Output:

46

The time complexity of above solution is O(n) and auxiliary space used by the program is O(n).

Please use ideone or C++ Shell or any other online compiler link to post code in comments.
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