Lowest Common Ancestor of a Binary Search Tree
Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.
According to thedefinition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allowa node to be a descendant of itself).”
_______6______
/ \
___2__ ___8__
/ \ / \
0 _4 7 9
/ \
3 5
For example, the lowest common ancestor (LCA) of nodes2
and8
is6
. Another example is LCA of nodes2
and4
is2
, since a node can be a descendant of itself according to the LCA definition.
分析
还是分治法,左边和右边都有的话,返回根,否则哪边不空返回哪边。
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root == null)
return null;
if(root == q)
return q;
if(root == p)
return p;
TreeNode left = lowestCommonAncestor(root.left, p, q);
TreeNode right = lowestCommonAncestor(root.right, p, q);
if(left != null && right != null)
return root;
if(left != null)
return left;
else
return right;
}
一行解决,根据二叉树左右子树大小的值的性质
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
if(root == null)
return null;
if((root.val - p.val) *(root.val - q.val) < 1){
return root;
}
return lowestCommonAncestor(root.val < p.val ? root.right : root.left, p, q);
}
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