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Let's say I have an array of floating point numbers, in sorted (let's say ascending) order, whose sum is known to be an integer N . I want to "round" these numbers to integers while leaving their sum unchanged. In other words, I'm looking for an algorithm that converts the array of floating-point numbers (call it fn ) to an array of integers (call it in ) such that: the two arrays have the same length the sum of the array of integers is N the difference between each floating-point number fn[i] and its corresponding integer in[i] is less than 1 (or equal to 1 if you really must) given that the floats are in sorted order ( fn[i] <= fn[i+1] ), the integers will also be in sorted order ( in[i] <= in[i+1] ) Given that those four conditions are satisfied, an algorithm that minimizes the rounding variance ( sum((in[i] - fn[i])^2) ) is preferable, but it's not a big deal. Examples: [0.02, 0.03, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14] => [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [0.1, 0.3, 0.4, 0.4, 0.8] => [0, 0, 0, 1, 1] [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1] => [0, 0, 0, 0, 0, 0, 0, 0, 0, 1] [0.4, 0.4, 0.4, 0.4, 9.2, 9.2] => [0, 0, 1, 1, 9, 9] is preferable => [0, 0, 0, 0, 10, 10] is acceptable [0.5, 0.5, 11] => [0, 1, 11] is fine => [0, 0, 12] is technically not allowed but I'd take it in a pinch To answer some excellent questions raised in the comments: Repeated elements are allowed in both arrays (although I would also be interested to hear about algorithms that work only if the array of floats does not include repeats) There is no single correct answer - for a given input array of floats, there are generally multiple arrays of ints that satisfy the four conditions. The application I

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