【算法与数据结构】235、LeetCode二叉搜索树的最近公共祖先

所有的LeetCode题解索引，可以看这篇文章——【算法和数据结构】LeetCode题解。

一、题目

二、解法

  思路分析：本题和这道题类似【算法与数据结构】236、LeetCode二叉树的最近公共祖先，相同的算法也能解这道题，但是没有充分利用到二叉搜索树的性质，二叉搜索树的性质为中间节点的键值大于所有左子树节点的键值，大于所有右子树的键值。因此要找到两个节点的最近祖先节点，只需要确定节点位于[p,q]（或者是[q,p]大小未知，左闭右闭的区间）区间内。那么当节点键值比两个节点的键值都小时，说明公共最先节点在右子树内，遍历右子树即可，反之亦然，最终剩下的就是最近公共祖先节点。
  程序如下：

class Solution {
public:
    // 后序遍历: 左右中
    // 1、输入参数
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        // 2、终止条件
        if (root == NULL) return root;    // 如果节点相等或者是空节点返回

        // 3、单层递归逻辑
        if ((root->val > q->val && root->val > p->val)) {
            TreeNode* left = lowestCommonAncestor(root->left, p, q);    // 左
            if (left != NULL) return left;
        }
        if ((root->val < q->val && root->val < p->val)) {
            TreeNode* right = lowestCommonAncestor(root->right, p, q);    // 右
            if (right != NULL) return right;
        }   
        return root;
    }
};

三、完整代码

# include 
# include 
# include 
# include 
using namespace std;

// 树节点定义
struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode() : val(0), left(nullptr), right(nullptr) {}
    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
    TreeNode(int x, TreeNode* left, TreeNode* right) : val(x), left(left), right(right) {}
};

class Solution {
public:
    // 后序遍历: 左右中
    // 1、输入参数
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        // 2、终止条件
        if (root == NULL) return root;    // 如果节点相等或者是空节点返回

        // 3、单层递归逻辑
        if ((root->val > q->val && root->val > p->val)) {
            TreeNode* left = lowestCommonAncestor(root->left, p, q);    // 左
            if (left != NULL) return left;
        }
        if ((root->val < q->val && root->val < p->val)) {
            TreeNode* right = lowestCommonAncestor(root->right, p, q);    // 右
            if (right != NULL) return right;
        }   
        return root;
    }
};

// 前序遍历迭代法创建二叉树，每次迭代将容器首元素弹出（弹出代码还可以再优化）
void Tree_Generator(vector<string>& t, TreeNode*& node) {
    if (!t.size() || t[0] == "NULL") return;    // 退出条件
    else {
        node = new TreeNode(stoi(t[0].c_str()));    // 中
        if (t.size()) {
            t.assign(t.begin() + 1, t.end());
            Tree_Generator(t, node->left);              // 左
        }
        if (t.size()) {
            t.assign(t.begin() + 1, t.end());
            Tree_Generator(t, node->right);             // 右
        }
    }
}

template<typename T>
void my_print(T& v, const string msg)
{
    cout << msg << endl;
    for (class T::iterator it = v.begin(); it != v.end(); it++) {
        cout << *it << ' ';
    }
    cout << endl;
}

template<class T1, class T2>
void my_print2(T1& v, const string str) {
    cout << str << endl;
    for (class T1::iterator vit = v.begin(); vit < v.end(); ++vit) {
        for (class T2::iterator it = (*vit).begin(); it < (*vit).end(); ++it) {
            cout << *it << ' ';
        }
        cout << endl;
    }
}

// 层序遍历
vector<vector<int>> levelOrder(TreeNode* root) {
    queue<TreeNode*> que;
    if (root != NULL) que.push(root);
    vector<vector<int>> result;
    while (!que.empty()) {
        int size = que.size();  // size必须固定, que.size()是不断变化的
        vector<int> vec;
        for (int i = 0; i < size; ++i) {
            TreeNode* node = que.front();
            que.pop();
            vec.push_back(node->val);
            if (node->left) que.push(node->left);
            if (node->right) que.push(node->right);
        }
        result.push_back(vec);
    }
    return result;
}

// 前序遍历,找二叉树中指定的键值
TreeNode* traversal_preOrder(TreeNode* cur, int val) {
    if (cur == NULL) return NULL;
    if (cur->val == val) return cur;        // 中
    if (traversal_preOrder(cur->left, val) != NULL) return traversal_preOrder(cur->left, val);        // 左   
    if (traversal_preOrder(cur->right, val) != NULL) return traversal_preOrder(cur->right, val);     // 右  
    return NULL;
}

int main()
{
    // 构建二叉树
    vector<string> t = { "6", "2", "0", "NULL", "NULL", "4", "3", "NULL", "NULL", "5", "NULL", "NULL", "8", "7", "NULL", "NULL", "9", "NULL", "NULL" };   // 前序遍历
    my_print(t, "目标树");
    TreeNode* root = new TreeNode();
    Tree_Generator(t, root);
    vector<vector<int>> tree = levelOrder(root);
    my_print2<vector<vector<int>>, vector<int>>(tree, "目标树:");

    // 构建p, q节点
    int p = 2, q = 8;
    TreeNode* P_node = traversal_preOrder(root, p);
    TreeNode* Q_node = traversal_preOrder(root, q);

    // 找最近公共祖先节点
    Solution s;
    TreeNode* result = s.lowestCommonAncestor(root, P_node, Q_node);
    cout << "节点 " << P_node->val << " 和节点 " << Q_node->val << " 的最近公共祖先节点为 " << result->val << endl;

    system("pause");
    return 0;
}

end