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import java.util.ArrayList; |
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import java.util.List; |
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public class BinarySearchTree { |
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// 树的根结点 |
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private TreeNode root = null; |
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// 遍历结点列表 |
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private List<TreeNode> nodelist = new ArrayList<>(); |
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// 当前结点 |
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private class TreeNode { |
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private int key; |
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private TreeNode leftChild; |
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private TreeNode rightChild; |
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private TreeNode parent; |
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public TreeNode(int key, TreeNode leftChild, TreeNode rightChild, |
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TreeNode parent) { |
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this.key = key; |
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this.leftChild = leftChild; |
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this.rightChild = rightChild; |
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this.parent = parent; |
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} |
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public int getKey() { |
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return key; |
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} |
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public String toString() { |
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String leftkey = (leftChild == null ? "" : String |
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.valueOf(leftChild.key)); |
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String rightkey = (rightChild == null ? "" : String |
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.valueOf(rightChild.key)); |
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return "(" + leftkey + " , " + key + " , " + rightkey + ")"; |
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} |
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} |
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/** |
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* isEmpty: 判断二叉查找树是否为空;若为空,返回 true ,否则返回 false . |
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* |
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*/ |
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public boolean isEmpty() { |
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if (root == null) { |
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return true; |
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} else { |
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return false; |
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} |
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} |
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/** |
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* TreeEmpty: 对于某些二叉查找树操作(比如删除关键字)来说,若树为空,则抛出异常。 |
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*/ |
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public void TreeEmpty() throws Exception { |
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if (isEmpty()) { |
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throw new Exception("树为空!"); |
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} |
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} |
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/** |
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* search: 在二叉查找树中查询给定关键字 |
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* |
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* @param key |
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* 给定关键字 |
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* @return 匹配给定关键字的树结点 |
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*/ |
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public TreeNode search(int key) { |
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TreeNode pNode = root; |
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while (pNode != null && pNode.key != key) { |
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if (key < pNode.key) { |
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pNode = pNode.leftChild; |
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} else { |
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pNode = pNode.rightChild; |
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} |
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} |
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return pNode; |
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} |
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/** |
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* minElemNode: 获取二叉查找树中的最小关键字结点 |
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* |
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* @return 二叉查找树的最小关键字结点 |
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* @throws Exception |
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* 若树为空,则抛出异常 |
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*/ |
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public TreeNode minElemNode(TreeNode node) throws Exception { |
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if (node == null) { |
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throw new Exception("树为空!"); |
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} |
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TreeNode pNode = node; |
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while (pNode.leftChild != null) { |
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pNode = pNode.leftChild; |
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} |
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return pNode; |
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} |
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/** |
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* maxElemNode: 获取二叉查找树中的最大关键字结点 |
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* |
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* @return 二叉查找树的最大关键字结点 |
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* @throws Exception |
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* 若树为空,则抛出异常 |
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*/ |
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public TreeNode maxElemNode(TreeNode node) throws Exception { |
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if (node == null) { |
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throw new Exception("树为空!"); |
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} |
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TreeNode pNode = node; |
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while (pNode.rightChild != null) { |
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pNode = pNode.rightChild; |
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} |
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return pNode; |
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} |
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/** |
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* successor: 获取给定结点在中序遍历顺序下的后继结点 |
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* |
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* @param node |
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* 给定树中的结点 |
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* @return 若该结点存在中序遍历顺序下的后继结点,则返回其后继结点;否则返回 null |
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* @throws Exception |
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*/ |
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public TreeNode successor(TreeNode node) throws Exception { |
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if (node == null) { |
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return null; |
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} |
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// 若该结点的右子树不为空,则其后继结点就是右子树中的最小关键字结点 |
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if (node.rightChild != null) { |
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return minElemNode(node.rightChild); |
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} |
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// 若该结点右子树为空 |
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TreeNode parentNode = node.parent; |
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while (parentNode != null && node == parentNode.rightChild) { |
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node = parentNode; |
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parentNode = parentNode.parent; |
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} |
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return parentNode; |
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} |
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/** |
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* precessor: 获取给定结点在中序遍历顺序下的前趋结点 |
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* |
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* @param node |
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* 给定树中的结点 |
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* @return 若该结点存在中序遍历顺序下的前趋结点,则返回其前趋结点;否则返回 null |
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* @throws Exception |
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*/ |
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public TreeNode precessor(TreeNode node) throws Exception { |
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if (node == null) { |
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return null; |
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} |
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// 若该结点的左子树不为空,则其前趋结点就是左子树中的最大关键字结点 |
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if (node.leftChild != null) { |
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return maxElemNode(node.leftChild); |
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} |
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// 若该结点左子树为空 |
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TreeNode parentNode = node.parent; |
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while (parentNode != null && node == parentNode.leftChild) { |
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node = parentNode; |
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parentNode = parentNode.parent; |
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} |
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return parentNode; |
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} |
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/** |
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* insert: 将给定关键字插入到二叉查找树中 |
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* |
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* @param key |
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* 给定关键字 |
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*/ |
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public void insert(int key) { |
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TreeNode parentNode = null; |
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TreeNode newNode = new TreeNode(key, null, null, null); |
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TreeNode pNode = root; |
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if (root == null) { |
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root = newNode; |
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return; |
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} |
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while (pNode != null) { |
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parentNode = pNode; |
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if (key < pNode.key) { |
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pNode = pNode.leftChild; |
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} else if (key > pNode.key) { |
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pNode = pNode.rightChild; |
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} else { |
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// 树中已存在匹配给定关键字的结点,则什么都不做直接返回 |
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return; |
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} |
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} |
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if (key < parentNode.key) { |
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parentNode.leftChild = newNode; |
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newNode.parent = parentNode; |
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} else { |
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parentNode.rightChild = newNode; |
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newNode.parent = parentNode; |
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} |
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} |
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/** |
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* insert: 从二叉查找树中删除匹配给定关键字相应的树结点 |
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* |
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* @param key |
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* 给定关键字 |
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*/ |
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public void delete(int key) throws Exception { |
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TreeNode pNode = search(key); |
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if (pNode == null) { |
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throw new Exception("树中不存在要删除的关键字!"); |
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} |
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delete(pNode); |
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} |
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/** |
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* delete: 从二叉查找树中删除给定的结点. |
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* |
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* @param pNode |
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* 要删除的结点 |
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* |
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* 前置条件: 给定结点在二叉查找树中已经存在 |
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* @throws Exception |
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*/ |
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private void delete(TreeNode pNode) throws Exception { |
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if (pNode == null) { |
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return; |
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} |
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if (pNode.leftChild == null && pNode.rightChild == null) { // 该结点既无左孩子结点,也无右孩子结点 |
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TreeNode parentNode = pNode.parent; |
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if (pNode == parentNode.leftChild) { |
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parentNode.leftChild = null; |
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} else { |
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parentNode.rightChild = null; |
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} |
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return; |
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} |
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if (pNode.leftChild == null && pNode.rightChild != null) { // 该结点左孩子结点为空,右孩子结点非空 |
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TreeNode parentNode = pNode.parent; |
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if (pNode == parentNode.leftChild) { |
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parentNode.leftChild = pNode.rightChild; |
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pNode.rightChild.parent = parentNode; |
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} else { |
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parentNode.rightChild = pNode.rightChild; |
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pNode.rightChild.parent = parentNode; |
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} |
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return; |
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} |
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if (pNode.leftChild != null && pNode.rightChild == null) { // 该结点左孩子结点非空,右孩子结点为空 |
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TreeNode parentNode = pNode.parent; |
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if (pNode == parentNode.leftChild) { |
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parentNode.leftChild = pNode.leftChild; |
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pNode.rightChild.parent = parentNode; |
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} else { |
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parentNode.rightChild = pNode.leftChild; |
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pNode.rightChild.parent = parentNode; |
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} |
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return; |
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} |
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// 该结点左右孩子结点均非空,则删除该结点的后继结点,并用该后继结点取代该结点 |
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TreeNode successorNode = successor(pNode); |
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delete(successorNode); |
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pNode.key = successorNode.key; |
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} |
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/** |
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* inOrderTraverseList: 获得二叉查找树的中序遍历结点列表 |
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* |
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* @return 二叉查找树的中序遍历结点列表 |
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*/ |
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public List<TreeNode> inOrderTraverseList() { |
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if (nodelist != null) { |
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nodelist.clear(); |
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} |
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inOrderTraverse(root); |
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return nodelist; |
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} |
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/** |
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* inOrderTraverse: 对给定二叉查找树进行中序遍历 |
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* |
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* @param root |
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* 给定二叉查找树的根结点 |
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*/ |
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private void inOrderTraverse(TreeNode root) { |
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if (root != null) { |
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inOrderTraverse(root.leftChild); |
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nodelist.add(root); |
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inOrderTraverse(root.rightChild); |
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} |
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} |
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/** |
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* toStringOfOrderList: 获取二叉查找树中关键字的有序列表 |
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* |
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* @return 二叉查找树中关键字的有序列表 |
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*/ |
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public String toStringOfOrderList() { |
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StringBuilder sbBuilder = new StringBuilder(" [ "); |
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for (TreeNode p : inOrderTraverseList()) { |
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sbBuilder.append(p.key); |
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sbBuilder.append(" "); |
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} |
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sbBuilder.append("]"); |
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return sbBuilder.toString(); |
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} |
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/** |
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* 获取该二叉查找树的字符串表示 |
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*/ |
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public String toString() { |
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StringBuilder sbBuilder = new StringBuilder(" [ "); |
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for (TreeNode p : inOrderTraverseList()) { |
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sbBuilder.append(p); |
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sbBuilder.append(" "); |
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} |
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sbBuilder.append("]"); |
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return sbBuilder.toString(); |
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} |
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public TreeNode getRoot() { |
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return root; |
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} |
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public static void testNode(BinarySearchTree bst, TreeNode pNode) |
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throws Exception { |
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System.out.println("本结点: " + pNode); |
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System.out.println("前趋结点: " + bst.precessor(pNode)); |
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System.out.println("后继结点: " + bst.successor(pNode)); |
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} |
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public static void testTraverse(BinarySearchTree bst) { |
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System.out.println("二叉树遍历:" + bst); |
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System.out.println("二叉查找树转换为有序列表: " + bst.toStringOfOrderList()); |
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} |
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public static void main(String[] args) { |
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try { |
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BinarySearchTree bst = new BinarySearchTree(); |
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System.out.println("查找树是否为空? " + (bst.isEmpty() ? "是" : "否")); |
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int[] keys = new int[] { 15, 6, 18, 3, 7, 13, 20, 2, 9, 4 }; |
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for (int key : keys) { |
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bst.insert(key); |
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} |
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System.out.println("查找树是否为空? " + (bst.isEmpty() ? "是" : "否")); |
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TreeNode minkeyNode = bst.minElemNode(bst.getRoot()); |
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System.out.println("最小关键字: " + minkeyNode.getKey()); |
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testNode(bst, minkeyNode); |
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TreeNode maxKeyNode = bst.maxElemNode(bst.getRoot()); |
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System.out.println("最大关键字: " + maxKeyNode.getKey()); |
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testNode(bst, maxKeyNode); |
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System.out.println("根结点关键字: " + bst.getRoot().getKey()); |
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testNode(bst, bst.getRoot()); |
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testTraverse(bst); |
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System.out.println("****************************** "); |
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testTraverse(bst); |
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} catch (Exception e) { |
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System.out.println(e.getMessage()); |
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e.printStackTrace(); |
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} |
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} |
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} |