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Asked: 2026-05-29T04:41:32+00:00

An interview question: Given two non-ordered integer sequences a and b , their size

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An interview question:

Given two non-ordered integer sequences a and b, their size is n, all
numbers are randomly chosen: Exchange the elements of a and b, such that the sum of the elements of a minus the sum of the elements of b is minimal.

Given the example:

a = [ 5 1 3 ]
b = [ 2 4 9 ]

The result is (1 + 2 + 3) – (4 + 5 + 9) = -12.

My algorithm: Sort them together and then put the first smallest n ints in a and left in b. It is O(n lg n) in time and O(n) in space. I do not know how to improve it to an algorithm with O(n) in time and O(1) in space. O(1) means that we do not need more extra space except seq 1 and 2 themselves.

Any ideas ?

An alternative question would be: What if we need to minimize the absolute value of the differences (minimize |sum(a) - sum(b)|)?

A python or C++ thinking is preferred.

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1 Answer

  1. Editorial Team

    Revised solution:

    1. Merge both lists x = merge(a,b).

    2. Calculate median of x (complexity O(n) See http://en.wikipedia.org/wiki/Selection_algorithm )

    3. Using this median swap elements between a and b. That is, find an element in a that is less than median, find one in b that is more than median and swap them

    Final complexity: O(n)

    Minimizing absolute difference is NP complete since it is equivalent to the knapsack problem.

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