二叉查找树(4) - 中序查找一个给定值的前驱以及后继

标签：二叉排序树   二叉查找树   二叉查找树的前驱和后继   bst的前驱和后继   

下面是实现此操作的算法，采用递归：

输入: 根节点, 键值
输出: 前驱节点，后继节点
1. If root is NULL
      then return
2. if key is found then
    a. If its left subtree is not null
        Then predecessor will be the right most 
        child of left subtree or left child itself.
    b. If its right subtree is not null
        The successor will be the left most child 
        of right subtree or right child itself.
    return
3. If key is smaller then root node
        set the successor as root
        search recursively into left subtree
    else
        set the predecessor as root
        search recursively into right subtree

下面是基于上面算法的C++代码实现：

// BST中查找前驱和后继的C++程序
#include <iostream>

struct Node
{
	int key;
	Node *left;
	Node *right;
};

//在BST中查找指定值的前驱和后继，分别保存在pre和suc中。
void findPreSuc(Node* root, int key, Node*& pre, Node*& suc)
{
	// 空树
	if (root == NULL)
		return;

	// 找到匹配的节点
	if (root->key == key)
	{
		// 左子树中最大值为前驱
		if (root->left != NULL)
		{
			Node* tmp = root->left;
			while (tmp->right)
				tmp = tmp->right;
			pre = tmp;
		}

		// 右子树中最小值为后继
		if (root->right != NULL)
		{
			Node* tmp = root->right;
			while (tmp->left)
				tmp = tmp->left;
			suc = tmp;
		}
		return;
	}

	// 指定值小于根节点值，继续查找左子树
	if (root->key > key)
	{
		suc = root;
		findPreSuc(root->left, key, pre, suc);
	}
	else //查找右子树
	{
		pre = root;
		findPreSuc(root->right, key, pre, suc);
	}
}

// 创建一个新的BST节点
Node *createNewNode(int item)
{
	Node *temp = new Node;
	temp->key = item;
	temp->left = temp->right = NULL;
	return temp;
}

//插入新节点至二叉搜索树中
Node* insert(Node* node, int key)
{
	//空树
	if (node == NULL)
		return createNewNode(key);

	//递归插入。如果已存在指定值，则不插入
	if (key < node->key)
		node->left = insert(node->left, key);
	else if (key > node->key)
		node->right = insert(node->right, key);

	//返回未修改的node指针
	return node;
}

// 中序遍历二叉搜索树
void inorder(Node *root)
{
	if (root != NULL)
	{
		inorder(root->left);
		std::cout << " " << root->key << " ";
		inorder(root->right);
	}
}

int main()
{
	/* 构建一颗如下所示的BST
	     55
 	   /          	  33      77
         /  \    /         22   44  66   88
	*/
	Node *root = NULL;
	root = insert(root, 55);
	insert(root, 33);
	insert(root, 22);
	insert(root, 44);
	insert(root, 77);
	insert(root, 66);
	insert(root, 88);

	Node* pre = NULL, *suc = NULL;
	int key = 59;

	findPreSuc(root, key, pre, suc);
	if (pre != NULL)
		std::cout << "Predecessor is " << pre->key << std::endl;
	else
		std::cout << "No Predecessor\n";

	if (suc != NULL)
		std::cout << "Successor is " << suc->key << std::endl;
	else
		std::cout << "No Successor\n";

	return 0;
}

二叉查找树(4) - 中序查找一个给定值的前驱以及后继

标签：二叉排序树   二叉查找树   二叉查找树的前驱和后继   bst的前驱和后继   

原文地址：http://blog.csdn.net/shltsh/article/details/46510453