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Smallest Subtree with all the Deepest Nodes

Medium

Provided the root of a binary tree, the depth of each node is the shortest distance to the root.

Produce the smallest subtree such that it contains all the deepest nodes in the original tree.

A node is called the deepest if it has the largest depth possible among any node in the entire tree.

The subtree of a node is a tree consisting of that node, plus the set of all descendants of that node.

Example 1

Original illustrative diagram 1 for Smallest Subtree with all the Deepest Nodes

Input: root = [3,5,1,6,2,0,8,null,null,7,4]

Output: [2,7,4]

Explanation: We produce the node with value 2, colored in yellow in the diagram.

The nodes coloured in blue are the deepest nodes of the tree.

Notice that nodes 5, 3 and 2 contain the deepest nodes in the tree but node 2 is the smallest subtree among them, so we produce it.

Example 2

Input: root = [1]

Output: [1]

Explanation: The root is the deepest node in the tree.

Example 3

Input: root = [0,1,3,null,2]

Output: [2]

Explanation: The deepest node in the tree is 2, the valid subtrees are the subtrees of nodes 2, 1 and 0 but the subtree of node 2 is the smallest.

Constraints

  • The number of nodes in the tree will be in the range [1, 500].
  • 0 <= Node.val <= 500
  • The values of the nodes in the tree are unique.

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