987.VerticalOrderTraversalofaBinaryTree.py

"""
    Given a binary tree, return the vertical order traversal of its nodes 
    values.
    For each node at position (X, Y), its left and right children respectively 
    will be at positions (X-1, Y-1) and (X+1, Y-1).
    Running a vertical line from X = -infinity to X = +infinity, whenever the 
    vertical line touches some nodes, we report the values of the nodes in 
    order from top to bottom (decreasing Y coordinates).
    If two nodes have the same position, then the value of the node that is 
    reported first is the value that is smaller.
    Return an list of non-empty reports in order of X coordinate. Every report 
    will have a list of values of nodes.

    Example:
            3
           / \
          9  20
            /  \
           15   7

    Input: [3,9,20,null,null,15,7]
    Output: [[9],[3,15],[20],[7]]
    Explanation: 
                Without loss of generality, we can assume the root node is at 
                position (0, 0):
                Then, the node with value 9 occurs at position (-1, -1);
                The nodes with values 3 and 15 occur at positions (0, 0) and 
                (0, -2);
                The node with value 20 occurs at position (1, -1);
                The node with value 7 occurs at position (2, -2).

    Example:
            1
           / \
          2   3
         / \ / \
        4  5 6  7

    Input: [1,2,3,4,5,6,7]
    Output: [[4],[2],[1,5,6],[3],[7]]
    Explanation: 
                The node with value 5 and the node with value 6 have the same 
                position according to the given scheme.
                However, in the report "[1,5,6]", the node value of 5 comes 
                first since 5 is smaller than 6.

    Note:
        1. The tree will have between 1 and 1000 nodes.
        2. Each node's value will be between 0 and 1000.
"""
#Difficulty:
#30 / 30 test cases passed.
#Runtime: 24 ms
#Memory Usage: 14.1 MB

#Runtime: 24 ms, faster than 99.12% of Python3 online submissions for Vertical Order Traversal of a Binary Tree.
#Memory Usage: 14.1 MB, less than 42.86% of Python3 online submissions for Vertical Order Traversal of a Binary Tree.

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right

class Solution:

    def verticalTraversal(self, root: TreeNode) -> List[List[int]]:
        x = y = 0
        result = []
        self.values = {}
        self.inorder(root, x, y)
        for x in sorted(self.values):
            temp = []
            for y in sorted(self.values[x], reverse=True):
                temp += self.values[x][y]
            result.append(temp)
        return result

    def inorder(self, root, x, y):
        if not root:
            return
        self.inorder(root.left, x-1, y-1)
        if x not in self.values:
            self.values[x] = {y : [root.val]}
        elif y not in self.values[x]:
            self.values[x].update({y : [root.val]})
        else:
            self.values[x][y].append(root.val)
            self.values[x][y].sort()
        self.inorder(root.right, x+1, y-1)