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/

這里垂直訪問的意思是，每一列給它一個列號，左孩子比根的列號減1，右孩子比根的加1.列號相同的打印在同一行。

所以最直接的方法是，先把列數找出來。然后每一列打印，遍歷樹就行，只要列號等于它就打印出來。時間復雜度等于列數*樹遍歷，最壞情況就是O(n^2)。

If two nodes have the same Horizontal Distance (HD), then they are on same vertical line.

更簡單的方法是，直接用一個hashmap，key是列號，value就是所有同一列的數，遍歷一次樹填好hashmap，然后就可以遍歷一次hashmap把所有數按列打印出來。

變種

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

同樣，只是把每一列第一個數打印出來。因為可以print in any order，所以用hashset來記錄是否存在，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/

Print a Binary Tree in Vertical Order