Given a binary tree, print it vertically. The following example illustrates vertical order traversal.
1
/
2 3
/ /
4 5 6 7
8 9
The output of print this tree vertically will be:
4
2
1 5 6
3 8
7
9
from geeksforgeeks: http://www.geeksforgeeks.org/print-binary-tree-vertical-order/
这里垂直访问的意思是，每一列给它一个列号，左孩子比根的列号减1，右孩子比根的加1.列号相同的打印在同一行。
所以最直接的方法是，先把列数找出来。然后每一列打印，遍历树就行，只要列号等于它就打印出来。时间复杂度等于列数*树遍历，最坏情况就是O(n^2)。
If two nodes have the same Horizontal Distance (HD), then they are on same vertical line.
更简单的方法是，直接用一个hashmap，key是列号，value就是所有同一列的数，遍历一次树填好hashmap，然后就可以遍历一次hashmap把所有数按列打印出来。
变种
Print Nodes in Top View of Binary Tree
Top view of a binary tree is the set of nodes visible when the tree is viewed from the top. Given a binary tree, print the top view of it. The output nodes can be printed in any order. Expected time complexity is O(n)
A node x is there in output if x is the topmost node at its horizontal distance. Horizontal distance of a child of a node x is equal to horizontal distance of x minus 1, and that of right child is horizontal distance of x plus 1.
1
/
2 3
/ /
4 5 6 7
Top view of the above binary tree is
4 2 1 3 7
1
/
2 3
4
5
6
Top view of the above binary tree is
2 1 3 6
同样，只是把每一列第一个数打印出来。因为可以print in any order，所以用hashset来记录是否存在，如果不存在就可以打印了，并加入到hashset中。
from: http://www.geeksforgeeks.org/print-nodes-top-view-binary-tree/