Smallest Subtree with all the Deepest Nodes

Description

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

Return 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 tree consisting of that node, plus the set of all descendants of that node.

 

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4]
Output: [2,7,4]
Explanation: We return 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 return 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].
• The values of the nodes in the tree are unique.

Solution(javascript)

// 这题其实是求公共祖先
const subtreeWithAllDeepest = function (root) {
  if (!root) {
    return null
  }
  let prev = [root]
  let current = [root]
  while (current.length > 0) {
    const next = []
    prev = current
    current.forEach((node) => {
      if (node.left) {
        node.left.parent = node
        next.push(node.left)
      }
      if (node.right) {
        node.right.parent = node
        next.push(node.right)
      }
    })
    current = next
  }
  const parentMap = {}
  for (const node of prev) {
    let parent = node
    while (parent) {
      parentMap[parent.val] = (parentMap[parent.val] || 0) + 1
      if (parentMap[parent.val] === prev.length) {
        return parent
      }
      parent = parent.parent // eslint-disable-line
    }
  }
  return null
}