Lowest Common Ancestor of a Binary Search Tree(树中两个结点的最低公共祖先)

题目描述：

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.

　　利用二叉排序树的性质，可以很好地解决这道题。

solution：

TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
if (root == NULL || p == NULL || q == NULL)
return NULL;

if (root->val > p->val && root->val > q->val)
return lowestCommonAncestor(root->left, p, q);
else if (root->val < p->val && root->val < q->val)
return lowestCommonAncestor(root->right, p, q);
else
return root;
}

　　如果只是一颗普通的二叉树呢？

solution：

TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
if (!root)
return NULL;
if (root == p || root == q)
return root;
TreeNode *L = lowestCommonAncestor(root->left, p, q);
TreeNode *R = lowestCommonAncestor(root->right, p, q);
if (L && R)
return root;
return L ? L : R;
}

来源：Lowest Common Ancestor of a Binary Tree Part I

如果二叉树的结点存在指向父结点的指针，问题可以转化为求两个单链表的相交结点。

solution：

struct TreeNode {
int val;
TreeNode *left;
TreeNode *right;
TreeNode *parent;
};

int getHeight(TreeNode *p)
{
int height = 0;
while (p)
{
height++;
p = p->parent;
}
return height;
}

TreeNode* lowestCommonAncestor(TreeNode *p, TreeNode *q)
{
int h1 = getHeight(p);
int h2 = getHeight(q);

if (h1 > h2)
{
swap(h1, h2);
swap(p, q);
}

int dh = h2 - h1;
for (int h = 0; h < dh; ++h)
q = q->parent;
while (p && q)
{
if (p == q)
return p;
p = p->parent;
q = q->parent;
}
return NULL;
}

来源：Lowest Common Ancestor of a Binary Tree Part II