本文主要是介绍数据结构与算法（JAVA篇）之树（一），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
/*** 概念介绍：** 树：树由边连接的节点构成。* 多路树：节点可以多于两个。* 路径：顺着连接点的边从一个节点到另一个节点，所以过的节点顺序排列就称做路径。* 根：树的顶端节点称为根。* 父节点：每个节点都有一条边向上连接到另一个节点，这个节点就称为父节点。* 子节点：每个节点都可能有一条或多条边向下连接其它节点，下面这些节点就称为子节点。* 叶节点：没有子节点的节点为叶子节点或叶节点。* 子树：每个节点都可以作为子树的根，它和它所有的子节点都包含在子树中。* 访问：当程序控制流程到达某个节点时，就称为“访问”这个节点。* 遍历：遍历树意味着要遵循某种特定的顺序访问树中所有的节点。* 层：一个节点的层数是指从根开始到这个节点有多少“代”。一般根为第0层。* 关键字：对象中通常会有一个数据域被指定为关键字，通常使用这个关键字进行查询等操作。* 二叉树：如果树中每个节点最多只能有两个子节点，这样的特殊的树就是二叉树。* 二叉搜索树：二叉树的一个节点的左子节点的关键字值小于这个节点，右子节点的关键字值大* 于或等于这个父节点。* 平衡树与非平衡树：左子节点与左子节点对称的树为平衡树，否则就是非平衡树。* 完全二叉树：二叉树的最后一层都是叶子结点，其它各层都有左右子树，也叫满二叉树。** 为什么用二叉树：1.二叉树结合了另外两种数据结构的优点：一种是有序数组，另一种是链表。* 在树中查找数据的速度和在有序数组中查找的速度一样快，同时插入的速度* 和删除的速度和链表的速度一样。* 2.在有序数组中插入数据项太慢：用二分查找法可以在有序数据中快速的查找* 特定的值，查找所需时间复杂度为O(logN)。然而插入和删除是非常低效的。* 3.在链表中查找太慢：链表的插入和删除操作都很快，时间复杂度是O(1)。* 然而查找数据项是非常低效的。* 二叉树的效率：时间复杂度为O(logN)。树对所有的数据存储操作都很高效。** 程序介绍：对树的一些常用操作进行了封装，包括查询，插入，删除，遍历二叉树（中序，后序，前序）* 以及以树的方式显示二对树的各个结点。**/
/**** @author SunnyMoon*/import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;/*** 定义树的结点类*/
class Node {public int iData;//关键字public double dData;//数据项public Node leftChild;//左子树public Node rightChild;//右子树public void displayNode() {//输出结点内容System.out.print("【");System.out.print("关键字: "+iData);System.out.print(",");System.out.print("值："+dData);System.out.print("】");}
}/*** 定义二叉树类*/
class Tree {private Node root;public Tree() {root = null;}/*** 查找* @param key* @return*/public Node find(int key) {Node current = root;while (current.iData != key) {if (key < current.iData) {current = current.leftChild;} else {current = current.rightChild;}if (current == null) {return null;}}return current;}
/*** 插入* @param id* @param dd*/public void insert(int id, double dd) {Node newNode = new Node();newNode.iData = id;newNode.dData = dd;if (root == null) {root = newNode;} else {Node current = root;Node parent;while (true) {parent = current;if (id < current.iData) {current = current.leftChild;if (current == null) {parent.leftChild = newNode;return;}} else {current = current.rightChild;if (current == null) {parent.rightChild = newNode;return;}}}}}/*** 删除* @param key* @return*/public boolean delete(int key) {Node current = root;Node parent = root;boolean isLeftChild = true;while (current.iData != key) {parent = current;if (key < current.iData) {isLeftChild = true;current = current.leftChild;} else {isLeftChild = false;current = current.rightChild;}if (current == null) {return false;}}if (current.leftChild == null && current.rightChild == null) {if (current == root) {root = null;} else if (isLeftChild) {parent.leftChild = null;} else {parent.rightChild = null;}} else if (current.rightChild == null) {if (current == root) {root = current.leftChild;} else if (isLeftChild) {parent.leftChild = current.leftChild;} else {parent.rightChild = current.leftChild;}} else if (current.leftChild == null) {if (current == root) {root = current.rightChild;} else if (isLeftChild) {parent.leftChild = current.rightChild;} else {parent.rightChild = current.rightChild;}} else {Node successor = getSuccessor(current);if (current == root) {root = successor;} else if (isLeftChild) {parent.leftChild = successor;} else {parent.rightChild = successor;}successor.leftChild = current.leftChild;}return true;}
/*** 遍历二叉树* @param traverseType*/public void traverse(int traverseType) {switch (traverseType) {case 1:System.out.print("\n" + "前序遍历（Preorder traversal）: ");preOrder(root);break;case 2:System.out.print("\n" + "中序遍历（Inorder traversal）: ");inOrder(root);break;case 3:System.out.print("\n" + "后序遍历（Postorder traversal）: ");postOrder(root);break;}System.out.println();}
/*** 定义定位到后序结点方法* @param delNode* @return*/private Node getSuccessor(Node delNode) {Node successorParent = delNode;Node successor = delNode;Node current = delNode.rightChild;while (current != null) {successorParent = successor;successor = current;current = current.leftChild;}if (successor != delNode.rightChild) {successorParent.leftChild = successor.rightChild;successor.rightChild = delNode.rightChild;}return successor;}
/*** 前序遍历* @param localRoot*/private void preOrder(Node localRoot) {if (localRoot != null) {System.out.print(localRoot.iData + " ");preOrder(localRoot.leftChild);preOrder(localRoot.rightChild);}}
/*** 中序遍历* @param localRoot*/private void inOrder(Node localRoot) {if (localRoot != null) {inOrder(localRoot.leftChild);System.out.print(localRoot.iData + " ");inOrder(localRoot.rightChild);}}
/*** 后序遍历* @param localRoot*/private void postOrder(Node localRoot) {if (localRoot != null) {postOrder(localRoot.leftChild);postOrder(localRoot.rightChild);System.out.print(localRoot.iData + " ");}}
/*** 把关键字按树型输出* ‘--’表示树中这个位置的结点不存在。*/public void displayTree() {Stack globalStack = new Stack(1000);globalStack.push(root);int nBlanks = 32;boolean isRowEmpty = false;System.out.println("-----------------------------------------------------------------------");while (isRowEmpty == false) {Stack localStack = new Stack(1000);isRowEmpty = true;for (int j = 0; j < nBlanks; j++) {System.out.print(" ");}while (globalStack.isEmpty() == false) {Node temp = (Node) globalStack.pop();if (temp != null) {System.out.print(temp.iData);localStack.push(temp.leftChild);localStack.push(temp.rightChild);if (temp.leftChild != null || temp.rightChild != null) {isRowEmpty = false;}} else {System.out.print("..");localStack.push(null);localStack.push(null);}for (int j = 0; j < nBlanks * 2 - 2; j++) {System.out.print(" ");}}System.out.println();nBlanks /= 2;while (localStack.isEmpty() == false) {globalStack.push(localStack.pop());}}System.out.println("-----------------------------------------------------------------------");}
}/*** 使用的栈* @author Administrator*/
class Stack {private int maxSize;private Object[] stackArray;private int top;public Stack(int s) {maxSize = s;stackArray = new Object[maxSize];top = -1;}public void push(Object p) {stackArray[++top] = p;}public Object pop() {return stackArray[top--];}public Object peek() {return stackArray[top];}boolean isEmpty() {if (top == -1) {return true;} else {return false;}}
}
/*** 主方法* @author Administrator*/
class TreeAaa {public static void main(String[] args) throws IOException {int value;Tree theTree = new Tree();theTree.insert(12, 1.5);theTree.insert(15, 2.4);theTree.insert(22, 5.6);theTree.insert(33, 7.1);theTree.insert(55, 3.3);theTree.insert(26, 8.7);theTree.insert(17, 2.3);theTree.insert(8, 6.9);theTree.insert(6, 8.4);theTree.insert(14, 7.0);theTree.insert(23, 1.8);theTree.insert(38, 2.9);while (true) {System.out.print("输入想执行的操作的英文首字母：");System.out.print("插入（Insert）, 查找（Find）, 删除（Delete）, 遍历（Traverse）: ");int choice = getChar();switch (choice) {case 's':theTree.displayTree();break;case 'i':System.out.print("输入想要插入的值: ");value = getInt();theTree.insert(value, value + 0.9);break;case 'f':System.out.print(("输入想要查找的关键字: "));value = getInt();Node found = theTree.find(value);if (found != null) {System.out.print("成功查找: ");found.displayNode();System.out.print("\n");} else {System.out.print("不存在所查询关键字");}System.out.print("输入的关键字：" + value + "\n");break;case 'd':System.out.print("输入想要删除的关键字: ");value = getInt();boolean didDelete = theTree.delete(value);if (didDelete) {System.out.print("删除的值：" + value + "\n");} else {System.out.print("不能执行删除操作");}System.out.println(value);//System.out.print(value + "\n");break;case 't':System.out.print("输入遍历类型 1, 2 或 3:");value = getInt();theTree.traverse(value);break;default:System.out.println("非法输入");}}}public static String getString() throws IOException {InputStreamReader isr = new InputStreamReader(System.in);BufferedReader br = new BufferedReader(isr);String s = br.readLine();return s;}public static char getChar() throws IOException {String s = getString();return s.charAt(0);}public static int getInt() throws IOException {String s = getString();return Integer.parseInt(s);}/*** 运行结果：* 输入想执行的操作的英文首字母：插入（Insert）, 查找（Find）, 删除（Delete）, 遍历（Traverse）: s*-----------------------------------------------------------------------* 12* 8 15* 6 .. 14 22* .. .. .. .. .. .. 17 33* .. .. .. .. .. .. .. .. .. .. .. .. .. .. 26 55* ........................................................23..38..*-----------------------------------------------------------------------*输入想执行的操作的英文首字母：插入（Insert）, 查找（Find）, 删除（Delete）, 遍历（Traverse）: i*输入想要插入的值: 3*输入想执行的操作的英文首字母：插入（Insert）, 查找（Find）, 删除（Delete）, 遍历（Traverse）: f*输入想要查找的关键字: 14*成功查找: {14,7.0}*输入的关键字：14*输入想执行的操作的英文首字母：插入（Insert）, 查找（Find）, 删除（Delete）, 遍历（Traverse）:*//*** 总结：* 树结合了数组和链表的优点，是一种非常高效的数据结构。*/这篇关于数据结构与算法（JAVA篇）之树（一）的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！
