Ten wires are come in from the left. Ten wires leave to the right. Write a program that, given a permutation of the digits 0..9, arranges crossings on a grid that places the wires in the order designated by the permutation.
The output consists of a grid whose elements connect the left and right sides. Each cell of the grid is either empty (in that it just lets the wires through), or a crossing (in that it lets the wires trade places). Two crossings can never be placed vertically adjacent to each other. (This is equivalent to saying that the wires never split or merge, they only permute.)
Often, solutions require crossings to be spread out not just vertically but also horizontally. It is considered elegant not to make the grid wider than it has to be.
Examples:
Input: 1032547698
Output:
0 _ _ 1
\/
1 _/\_ 0
2 _ _ 3
\/
3 _/\_ 2
4 _ _ 5
\/
5 _/\_ 4
6 _ _ 7
\/
7 _/\_ 6
8 _ _ 9
\/
9 _/\_ 8
(This permutation is simply flipping wires pairwise.)
Input: 1234567890
Output:
0 _ _________________ 1
\/
1 _/\ _______________ 2
\/
2 ___/\ _____________ 3
\/
3 _____/\ ___________ 4
\/
4 _______/\ _________ 5
\/
5 _________/\ _______ 6
\/
6 ___________/\ _____ 7
\/
7 _____________/\ ___ 8
\/
8 _______________/\ _ 9
\/
9 _________________/\_ 0
(The simplest way to bubble 0 to the bottom.)
Input: 5012367894
0 _________ _ 5
\/
1 _______ /\_ 0
\/
2 _____ /\___ 1
\/
3 ___ /\_____ 2
\/
4 _ /\_______ 3
\/
5 _/\ _______ 6
\/
6 ___/\ _____ 7
\/
7 _____/\ ___ 8
\/
8 _______/\ _ 9
\/
9 _________/\_ 4
(The simplest way to bubble 4 and 5 simultaneously.)