Bottom View of Binary Tree

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 https://workat.tech/problem-solving/practice/bottom-view-binary-tree


There are different ways to look at a binary tree. The bottom view of a binary tree contains the set of nodes that will be visible if you look at the binary tree from the bottom.

Note: If there are multiple bottom-most nodes for a horizontal distance from root, use the later one in level-order traversal.

Given the root node of a binary tree, return an array containing the node elements in the bottom view, from left to right.

bottom-view-binary-tree

Testing

Input Format

The first line contains an integer T denoting the number of test cases.

For each test case, the input has 2 lines:

  • The first line contains an integer n denoting the number of nodes in the tree (including the NULL nodes).
  • The second line contains n space-separated integers that will form the binary tree. The integers follow level order traversal of the tree where -1 indicates a NULL node.

Output Format

For each test case, the output contains a line with space-separated integers representing the bottom view of the binary tree.

Sample Input

5
7
1 2 -1 4 -1 5 6
3
6 -1 4
7
8 -1 9 -1 10 11 12
5
28 14 11 -1 48
1
6

Expected Output

5 4 6 1
6 4
8 11 10 12
14 48 11
6

1 <= T <= 10
1 <= n <= 105
1 <= node value <= 106

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Intuition
Level Order  Q based BFS
Pair (Node, col)

Map<Integer, Integer> - col to node.val

At each col, the last node.val is visible from bottom
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Time Complexity - O(N)
Space Complexity - O(N)
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