Suppose we are given two increasing arrays A and B , we need to find max((a[j]-a[i-1] )- (b[j]-b[i-1])) , where j>=i .
Can we solve it in better than O(n^2) time complexity . If so , please give me any Hint .
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You are basically asking for $$$max((a[j] - b[j]) - (a[i] - b[i]))$$$ where
i < jholds. Let $$$c_i = a_i - b_i$$$. Then it becomes: $$$max(c[j] - pref[j - 1])$$$ where $$$pref[i]$$$ is minimum element of $$$c[0...i]$$$. This can be solved in linear time.