Day 355

[vaskoz]

Good morning! Here's your coding interview problem for today.

This problem was asked by Airbnb.

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.