二叉树删除

二叉树的删除操作

伪代码：

1.若节点p是叶子，则直接删除节点p；
2.若节点p只有左子树，则只需重接p的左子树；
  若节点p只有右子树，则只需重接p的右子树；
3.若p的左右子树均不空，则
  3.1 查找节点p的右子树上最左下节点s以及s的父节点par；
  3.2 将节点s的数据域替换到被删节点p的数据域；
  3.3 若p的右孩子无左子树，则将s的右子树接到par的右子树上；
      否则，将s的右子树接到节点par的左子树上；
  3.4 删除节点s；

package graphic;public class BinarySearchTree {  private TreeNode root = null;/** * 中序遍历 * @param root */public void inOrder_tree_walk(){inOrder(root);}private void inOrder(TreeNode root){if(root==null){return;}inOrder(root.left);System.out.print(root+" ");inOrder(root.right);}/** * 返回指向key的节点指针 * @param root * @param key * @return */public TreeNode treeSearch(int key){if(root==null)return null;TreeNode cur = root;while(cur!=null && cur.value!=key){if(cur.value >key){cur = cur.left;}else{cur = cur.right;}}return cur;}/** * 返回包含最小key的节点指针 */public TreeNode treeMinimum(TreeNode root){if(root==null)return null;TreeNode cur = root;while(cur.left!=null){cur = cur.left;}return cur;}/** * 返回包含最大key的节点指针 * @param root * @return */public TreeNode treeMaximum(TreeNode root){if(root==null)return null;TreeNode cur = root;while(cur.right!=null){cur = cur.right;}return cur;}/** * 返回node 节点的后继节点 * @param root * @param node * @return */public TreeNode treeSuccessor(TreeNode node){//rigth branch is not nullif(node.right!=null)return treeMinimum(node.right);//if the right branch is nullTreeNode cur = node.parent;while(cur!=null && node == cur.right){node = cur;cur = cur.parent;}return cur;}/** * 返回node 节点的前继节点 * @param root * @param node * @return */public TreeNode treePredecessor(TreeNode node){if(root.left!=null) return treeMaximum(root.left);//the left branch is nullTreeNode cur = node.parent;while(cur!=null && node==cur.left){node = cur;cur = cur.parent;}return cur;}/** * 插入新节点 * @param root * @param insert */public void treeInsert(TreeNode insert){if(root==null){root = insert;return ;}TreeNode cur = root;TreeNode parent =null;while(cur!=null){parent = cur;if(insert.value >=cur.value){cur = cur.right;}else{cur = cur.left;}}if(insert.value >=parent.value){parent.right = insert;insert.parent = parent;}else{parent.left = insert;insert.parent = parent;}}/** * 删除目标节点 * @param root * @param target */public void delete(TreeNode target){//find the node need to be deletedTreeNode delNode;       //只有一个孩子或者是叶子节点</span>if(target.left==null || target.right==null){delNode = target;       }else{                //如果有两个孩子就找到后继节点作为删除的节点delNode = treeSuccessor(target);}//对于所有情况，要删除的节点最多只有一个孩子        //这个时候需要找到删除节点的孩子节点和父亲节点，并把父亲节点指向孩子节点，        //孩子节点的指针也指回新的父亲节点TreeNode child;if(delNode.left ==null){child = delNode.right;}else{child = delNode.left;}TreeNode parent = delNode.parent;if(parent.left == delNode){parent.left = child;}else{parent.right = child;}if(child!=null){child.parent = parent;}//delete the successorif(delNode!=target){target.value = delNode.value;}freeNode(delNode);}/** * 删除包含key的第一个节点 * @param root * @param key */public void treeDelete(int key){TreeNode searched = treeSearch(key);delete(searched);}private void freeNode(TreeNode node){node.parent =null;node.left = null;node.right = null;}private void addNode(TreeNode node){treeInsert(node);}private class TreeNode{TreeNode parent = null;TreeNode left = null;TreeNode right = null;int value = 0;@Overridepublic String toString() {return value+"";}public TreeNode(int value) {this.value = value;}}public static void main(String[] args) {BinarySearchTree tree = new BinarySearchTree();TreeNode node =  tree.new TreeNode(15);tree.addNode(node);node =  tree.new TreeNode(6);tree.addNode(node);node =  tree.new TreeNode(18);tree.addNode(node);node =  tree.new TreeNode(3);tree.addNode(node);node =  tree.new TreeNode(7);tree.addNode(node);node =  tree.new TreeNode(17);tree.addNode(node);node =  tree.new TreeNode(20);tree.addNode(node);node =  tree.new TreeNode(2);tree.addNode(node);node =  tree.new TreeNode(4);tree.addNode(node);node =  tree.new TreeNode(13);TreeNode node13= node;tree.addNode(node);node =  tree.new TreeNode(9);tree.addNode(node);tree.inOrder_tree_walk();System.out.println();System.out.println(tree.treeSearch(15).parent);System.out.println(tree.treeSuccessor(node13));tree.treeDelete(6); tree.inOrder_tree_walk();}}