Answer to Question #294050 in Algorithms for Moon

Question

You are given an array X of floating-point numbers x1, x2, … xn. These can be rounded up or down to create a corresponding array Y of integers y1, y2, … yn

Write an algorithm that finds an appropriate Y array with the following properties:

• The rounded sums of both arrays should be equal.

• The absolute pairwise difference between elements is minimized. In other words, |x1- y1| + |x2- y2| + ... + |xn- yn| should be as small as possible.

For example, suppose your input is [1.3, 2.3, 4.4]. In this case you cannot do better than [1, 2, 5], which has an absolute difference of |1.3 - 1| + |2.3 - 2| + |4.4 - 5| = 1.

Answer 1

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