There are several distinct points located on the non-negative side of the x-axis. One of those points is at the origin (at 0). For each unique pair of points we write down the distance between them. Note that pairs (a, b) and pairs (b, a) are not unique pairs.
Given a int[] of those **distances**, return a int[] containing the locations of all points arranged in ascending order. If more than one set of locations is possible then return the set (represented as a int[]) which is lexicographically earliest (see example 1). A int[], n, comes before a int[], m, lexicographically if and only if, for the first element in which they differ, the element of n is smaller. If no set of locations is possible then return an empty int[].
For example: **distances** = {5, 2, 1, 6, 2, 3, 3, 4, 5, 6, 3, 9, 1, 4, 1}. This in order is {1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 9}. The only possible arrangement of points is the following:
0 1 2 3 4 5 6 7 8 9
--x----|----|----x----x----x----x----|----|----x--
Here 'x' represents a point. Thus the method should return {0, 3, 4, 5, 6, 9} |