1123. Lowest Common Ancestor of Deepest Leaves

1123. Lowest Common Ancestor of Deepest Leaves #

题目 #

Given a rooted binary tree, return the lowest common ancestor of its deepest leaves.

Recall that:

  • The node of a binary tree is a leaf if and only if it has no children
  • The depth of the root of the tree is 0, and if the depth of a node is d, the depth of each of its children is d+1.
  • The lowest common ancestor of a set S of nodes is the node A with the largest depth such that every node in S is in the subtree with root A.

Example 1:

Input: root = [1,2,3]
Output: [1,2,3]
Explanation: 
The deepest leaves are the nodes with values 2 and 3.
The lowest common ancestor of these leaves is the node with value 1.
The answer returned is a TreeNode object (not an array) with serialization "[1,2,3]".

Example 2:

Input: root = [1,2,3,4]
Output: [4]

Example 3:

Input: root = [1,2,3,4,5]
Output: [2,4,5]

Constraints:

  • The given tree will have between 1 and 1000 nodes.
  • Each node of the tree will have a distinct value between 1 and 1000.

题目大意 #

给你一个有根节点的二叉树,找到它最深的叶节点的最近公共祖先。

回想一下:

  • 叶节点 是二叉树中没有子节点的节点
  • 树的根节点的 深度 为 0,如果某一节点的深度为 d,那它的子节点的深度就是 d+1
  • 如果我们假定 A 是一组节点 S 的 最近公共祖先,S 中的每个节点都在以 A 为根节点的子树中,且 A 的深度达到此条件下可能的最大值。  

提示:

  • 给你的树中将有 1 到 1000 个节点。
  • 树中每个节点的值都在 1 到 1000 之间。

解题思路 #

  • 给出一颗树,找出最深的叶子节点的最近公共祖先 LCA。
  • 这一题思路比较直接。先遍历找到最深的叶子节点,如果左右子树的最深的叶子节点深度相同,那么当前节点就是它们的最近公共祖先。如果左右子树的最深的深度不等,那么需要继续递归往下找符合题意的 LCA。如果最深的叶子节点没有兄弟,那么公共父节点就是叶子本身,否则返回它的 LCA。
  • 有几个特殊的测试用例,见测试文件。特殊的点就是最深的叶子节点没有兄弟节点的情况。

代码 #


package leetcode

/**
 * Definition for a binary tree node.
 * type TreeNode struct {
 *     Val int
 *     Left *TreeNode
 *     Right *TreeNode
 * }
 */
func lcaDeepestLeaves(root *TreeNode) *TreeNode {
	if root == nil {
		return nil
	}
	lca, maxLevel := &TreeNode{}, 0
	lcaDeepestLeavesDFS(&lca, &maxLevel, 0, root)
	return lca
}

func lcaDeepestLeavesDFS(lca **TreeNode, maxLevel *int, depth int, root *TreeNode) int {
	*maxLevel = max(*maxLevel, depth)
	if root == nil {
		return depth
	}
	depthLeft := lcaDeepestLeavesDFS(lca, maxLevel, depth+1, root.Left)
	depthRight := lcaDeepestLeavesDFS(lca, maxLevel, depth+1, root.Right)
	if depthLeft == *maxLevel && depthRight == *maxLevel {
		*lca = root
	}
	return max(depthLeft, depthRight)
}


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