987 Vertical Order Traversal of a Binary Tree.py

Author: rajeevranjancom

987 Vertical Order Traversal of a Binary Tree.py

@@ -0,0 +1,76 @@
+#!/usr/bin/python3
+"""
+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 1:
+
+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 2:
+
+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:
+
+The tree will have between 1 and 1000 nodes.
+Each node's value will be between 0 and 1000.
+"""
+
+
+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, x):
+        self.val = x
+        self.left = None
+        self.right = None
+
+
+from collections import defaultdict
+
+
+class Solution:
+    def __init__(self):
+        self.mp = defaultdict(list)  # element (-Y, val)  # from left to right, top to bottom
+
+    def verticalTraversal(self, root: TreeNode) -> List[List[int]]:
+        self.dfs(root, 0, 0)
+        ret = []
+        mn = min(self.mp)
+        mx = max(self.mp)
+        for i in range(mn, mx+1):
+            ret.append([
+                val
+                for _, val in sorted(self.mp[i])
+            ])
+        return ret
+
+    def dfs(self, node, x, y):
+        if not node:
+            return
+        self.mp[x].append((-y, node.val))
+        self.dfs(node.left, x-1, y-1)
+        self.dfs(node.right, x+1, y-1)