Given two arrays A, B with size n, you could justify the positions of number in array B to maximum the sum[abs(ai-bi)], i from 0 to n or minimize the sum[abs(ai-bi)].

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Maximum: sort all numbers in A and B, Use the last n numbers to minus the first n numbers. 

Minimum: sort A and B separately. Use proof by contradiction:

Image Ai < Aj and Bi > Bj, discuss the6 situations:

Ai < Aj < Bi < Bj

Ai < Bi< Aj < Bj

Ai < Bi < Bj< Aj

Bi < Ai < Aj < Bj

Bi < Ai < Bj < Aj

Bi < Bj < Ai < Aj

In all of the situations , |Ai-Bi|+|Aj-Bj| <= |Ai-Bj|+|Aj-Bi|

数组差的绝对值