In the turnpike reconstruction problem, you are given n(n - 1)/2 distances in sorted order. The problem is to find the positions of n points on the line that give rise to these distances. For example, the distances {1, 2, 3, 4, 5, 6} can be determined by placing the second point 1 unit from the first, the third point 3 from the second, and the fourth point 2 from the third. Design and implement an efficient algorithm to report all solutions to the turnpike reconstruction problem. Exploit additive constraints when possible to minimize the search. With proper pruning, problems with hundreds of points can be solved reliably.