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  • Lowest Common Ancestor of Binary (Search) Tree

    Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST.

    According to the definition 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 allow a node to be a descendant of itself).”

            _______6______
           /              
        ___2__          ___8__
       /              /      
       0      _4       7       9
             /  
             3   5
    

    For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

    思路:找A与B的LCA,有两种可能  1. A或B是另一个点得祖先。比如3,2的LCA就是2。

                    2. 一个TreeNode,它的左右子树一个包含A,一个包含B。

       这种思路是对于binary tree与binary search tree都适用的,还有一种方法,利用了BST得特点,通过对数值的运算确定了,这个LCA是在root的左子树还是右子树,还是root本身。在leetcode的disscusion中有人提到了。两种的代码如下:

     1 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q){
     2         if (root == null || root == p || root == q) {
     3             return root;
     4         }
     5         TreeNode left = lowestCommonAncestor(root.left, p, q);
     6         TreeNode right = lowestCommonAncestor(root.right, p, q);
     7         
     8         if (left != null && right != null) {
     9             return root;
    10         }
    11         if (left != null) {
    12             return left;
    13         }
    14         if (right != null) {
    15             return right;
    16         }
    17         return null;
    18 }
    1 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    2         while((root.val - p.val) * (root.val - q.val) > 0) {
    3             root = (root.val - p.val) > 0 ? root.left : root.right;
    4         }
    5         return root;
    6 }
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  • 原文地址:https://www.cnblogs.com/gonuts/p/4639904.html
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