Lowest Common Ancestor of a Binary Search Tree

最新推荐文章于 2022-10-04 11:47:29 发布

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本文介绍了一种在二叉搜索树(BST)中寻找两个指定节点的最低公共祖先(LCA)的方法。根据定义，最低公共祖先是指位于这两个节点路径上的最深节点。文章通过一个具体的例子进行了说明，并提供了一个C语言实现的代码片段。

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.

说明：若指针tmp所指向结点为最小祖先，则(tmp->val - p->val) * (tmp->val - q->val) <= 0。其中，小于0表示指针p,q所指结点在tmp所指结点的左右子树上；等于0表示tmp == p || tmp == q成立。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     struct TreeNode *left;
 *     struct TreeNode *right;
 * };
 */
struct TreeNode* lowestCommonAncestor(struct TreeNode* root, struct TreeNode* p, struct TreeNode* q) {
    struct TreeNode *tmp = root; 
    if((p->val - root->val) * (q->val - root->val) <= 0)    
        return root;
    else if(p->val < root->val) 
        tmp = tmp->left;
    else    
        tmp = tmp->right;

    while(NULL != tmp->left || NULL != tmp->right)
    {
        if(NULL == tmp->left)
            tmp = tmp->right;
        else if(NULL == tmp->right)
            tmp = tmp->left;

        if((p->val - tmp->val) * (q->val - tmp->val) <= 0)
            return tmp;
        else if(p->val < tmp->val) 
            tmp = tmp->left;
        else    
            tmp = tmp->right;
    }
    return NULL;
}