java语言实现的二叉树的各种操作(包括递归与非递归遍历二叉树,求二叉树的高度，节点总数，叶子节点等)

 

/*java语言实现的二叉树的各种操作(包括递归与非递归遍历二叉树,求二叉树的高度，节点总数，叶子节点等)*/

BiTree.java

import java.util.Stack; public class BiTree { private BiTree leftTree;// 左子树 private BiTree rightTree;// 右子树 private Object data;// 节点数据 public final static int MAX = 40; BiTree[] elements = new BiTree[MAX];// 层次遍历时保存各个节点 int front;// 层次遍历时队首 int rear;// 层次遍历时队尾 // 构造函数 public BiTree() { // TODO Auto-generated constructor stub } public BiTree(Object data) { this.data = data; } public BiTree(Object data, BiTree lefTree, BiTree righTree) { this.data = data; this.leftTree = lefTree; this.rightTree = righTree; } // 递归前序遍历二叉树 public void preOrder(BiTree tree) { if (tree != null) { visit(tree.data); preOrder(tree.leftTree); preOrder(tree.rightTree); } } // 非递归实现前序遍历 public void iterativePreOrder(BiTree tree) { Stack<BiTree> stack = new Stack<BiTree>(); if (tree != null) { stack.push(tree); while (!stack.isEmpty()) { tree = stack.pop(); visit(tree.data); if (tree.rightTree != null) stack.push(tree.rightTree); if (tree.leftTree != null) stack.push(tree.leftTree); } } } // 递归中序遍历二叉树 public void inOrder(BiTree tree) { if (tree != null) { inOrder(tree.leftTree); visit(tree.data); inOrder(tree.rightTree); } } // 非递归实现中序遍历 public void iterativeInOrder(BiTree tree) { Stack<BiTree> stack = new Stack<BiTree>(); while (tree != null) { while (tree != null) { if (tree.rightTree != null) stack.push(tree.rightTree);// 当前节点右子入栈 stack.push(tree);// 当前节点入栈 tree = tree.leftTree; } tree = stack.pop(); while (!stack.empty() && tree.rightTree == null) { visit(tree.data); tree = stack.pop(); } visit(tree.data); if (!stack.empty()) tree = stack.pop(); else tree = null; } } // 递归后序遍历二叉树 public void postOrder(BiTree tree) { if (tree != null) { postOrder(tree.leftTree); postOrder(tree.rightTree); visit(tree.data); } } // 非递归实现后序遍历 public void iterativePostOrder(BiTree tree) { BiTree tempTree = tree; Stack<BiTree> stack = new Stack<BiTree>(); while (tree != null) { // 左子树入栈 for (; tree.leftTree != null; tree = tree.leftTree) stack.push(tree); // 当前节点无右子或右子已经输出 while (tree != null && (tree.rightTree == null || tree.rightTree == tempTree)) { visit(tree.data); tempTree = tree;// 记录上一个已输出节点 if (stack.empty()) return; tree = stack.pop(); } // 处理右子 stack.push(tree); tree = tree.rightTree; } } // 层次遍历二叉树 public void LayerOrder(BiTree tree) { elements[0] = tree; front = 0; rear = 1; while (front < rear) { try { if (elements[front].data != null) { System.out.print(elements[front].data + " "); if (elements[front].leftTree != null) elements[rear++] = elements[front].leftTree; if (elements[front].rightTree != null) elements[rear++] = elements[front].rightTree; front++; } } catch (Exception e) { break; } } } // 求二叉树的高度 public static int height(BiTree tree) { if (tree == null) return 0; else { int leftTreeHeight = height(tree.leftTree); int rightTreeHeight = height(tree.rightTree); return leftTreeHeight > rightTreeHeight ? leftTreeHeight + 1 : rightTreeHeight + 1; } } // 求data所对应结点的层数，如果对象不在树中,结果返回-1;否则结果返回该对象在树中所处的层次,规定根节点为第一层 public int level(Object data) { int leftLevel, rightLevel; if (this == null) return -1; if (data == this.data) return 1; leftLevel = leftTree == null ? -1 : leftTree.level(data); rightLevel = rightTree == null ? -1 : rightTree.level(data); if (leftLevel < 0 && rightLevel < 0) return -1; return leftLevel > rightLevel ? leftLevel + 1 : rightLevel + 1; } // 求二叉树的结点总数 public static int nodes(BiTree tree) { if (tree == null) return 0; else { int left = nodes(tree.leftTree); int right = nodes(tree.rightTree); return left + right + 1; } } // 求二叉树叶子节点的总数 public static int leaf(BiTree tree) { if (tree == null) return 0; else { int left = leaf(tree.leftTree); int right = leaf(tree.rightTree); if (tree.leftTree == null && tree.rightTree == null) return left + right + 1; else return left + right; } } // 求二叉树父节点个数 public static int fatherNodes(BiTree tree) { if (tree == null || (tree.leftTree == null && tree.rightTree == null)) return 0; else { int left = fatherNodes(tree.leftTree); int right = fatherNodes(tree.rightTree); return left + right + 1; } } // 求只有一个孩子结点的父节点个数 public static int oneChildFather(BiTree tree) { int left, right; if (tree == null || (tree.rightTree == null && tree.leftTree == null)) return 0; else { left = oneChildFather(tree.leftTree); right = oneChildFather(tree.rightTree); if ((tree.leftTree != null && tree.rightTree == null) || (tree.leftTree == null && tree.rightTree != null)) return left + right + 1; else return left + right;/* 加1是因为要算上根节点 */ } } // 求二叉树只拥有左孩子的父节点总数 public static int leftChildFather(BiTree tree) { if (tree == null) return 0; else { int left = leftChildFather(tree.leftTree); int right = leftChildFather(tree.rightTree); if ((tree.leftTree != null && tree.rightTree == null)) return left + right + 1; else return left + right; } } // 求二叉树只拥有右孩子的结点总数 public static int rightChildFather(BiTree tree) { if (tree == null || tree.rightTree == null) return 0; else { int left = rightChildFather(tree.leftTree); int right = rightChildFather(tree.rightTree); if (tree.leftTree == null && tree.rightTree != null) return left + right + 1; else return left + right; } } // 计算有两个节点的父节点的个数 public static int doubleChildFather(BiTree tree) { int left, right; if (tree == null) return 0; else { left = doubleChildFather(tree.leftTree); right = doubleChildFather(tree.rightTree); if (tree.leftTree != null && tree.rightTree != null) return (left + right + 1);/* 加1是因为要算上根节点 */ else return (left + right); } } // 访问根节点 public void visit(Object data) { System.out.print(data + " "); } // 将树中的每个节点的孩子对换位置 public void exChange() { if (this == null) return; if (leftTree != null) leftTree.exChange(); if (rightTree != null) rightTree.exChange(); BiTree temp = leftTree; leftTree = rightTree; rightTree = temp; } //递归求所有结点的和 public static int getSumByRecursion(BiTree tree){ if(tree==null){ return 0; } else{ int left=getSumByRecursion(tree.leftTree); int right=getSumByRecursion(tree.rightTree); return Integer.parseInt(tree.data.toString())+left+right; } } //非递归求二叉树中所有结点的和 public static int getSumByNoRecursion(BiTree tree){ Stack<BiTree> stack = new Stack<BiTree>(); int sum=0; if(tree!=null){ stack.push(tree); while(!stack.isEmpty()){ tree=stack.pop(); sum+=Integer.parseInt(tree.data.toString()); if(tree.leftTree!=null) stack.push(tree.leftTree); if(tree.rightTree!=null) stack.push(tree.rightTree); } } return sum; } /** * @param args */ public static void main(String[] args) { // TODO Auto-generated method stub BiTree e = new BiTree(5); BiTree g = new BiTree(7); BiTree h = new BiTree(8); BiTree l = new BiTree(12); BiTree m = new BiTree(13); BiTree n = new BiTree(14); BiTree k = new BiTree(11, n, null); BiTree j = new BiTree(10, l, m); BiTree i = new BiTree(9, j, k); BiTree d = new BiTree(4, null, g); BiTree f = new BiTree(6, h, i); BiTree b = new BiTree(2, d, e); BiTree c = new BiTree(3, f, null); BiTree tree = new BiTree(1, b, c); System.out.println("递归前序遍历二叉树结果: "); tree.preOrder(tree); System.out.println(); System.out.println("非递归前序遍历二叉树结果: "); tree.iterativePreOrder(tree); System.out.println(); System.out.println("递归中序遍历二叉树的结果为:"); tree.inOrder(tree); System.out.println(); System.out.println("非递归中序遍历二叉树的结果为:"); tree.iterativeInOrder(tree); System.out.println(); System.out.println("递归后序遍历二叉树的结果为:"); tree.postOrder(tree); System.out.println(); System.out.println("非递归后序遍历二叉树的结果为:"); tree.iterativePostOrder(tree); System.out.println(); System.out.println("层次遍历二叉树结果: "); tree.LayerOrder(tree); System.out.println(); System.out.println("递归求二叉树中所有结点的和为:"+getSumByRecursion(tree)); System.out.println("非递归求二叉树中所有结点的和为:"+getSumByNoRecursion(tree)); System.out.println("二叉树中,每个节点所在的层数为:"); for (int p = 1; p <= 14; p++) System.out.println(p + "所在的层为:" + tree.level(p)); System.out.println("二叉树的高度为:" + height(tree)); System.out.println("二叉树中节点总数为:" + nodes(tree)); System.out.println("二叉树中叶子节点总数为:" + leaf(tree)); System.out.println("二叉树中父节点总数为:" + fatherNodes(tree)); System.out.println("二叉树中只拥有一个孩子的父节点数:" + oneChildFather(tree)); System.out.println("二叉树中只拥有左孩子的父节点总数:" + leftChildFather(tree)); System.out.println("二叉树中只拥有右孩子的父节点总数:" + rightChildFather(tree)); System.out.println("二叉树中同时拥有两个孩子的父节点个数为:" + doubleChildFather(tree)); System.out.println("--------------------------------------"); tree.exChange(); System.out.println("交换每个节点的左右孩子节点后......"); System.out.println("递归前序遍历二叉树结果: "); tree.preOrder(tree); System.out.println(); System.out.println("非递归前序遍历二叉树结果: "); tree.iterativePreOrder(tree); System.out.println(); System.out.println("递归中序遍历二叉树的结果为:"); tree.inOrder(tree); System.out.println(); System.out.println("非递归中序遍历二叉树的结果为:"); tree.iterativeInOrder(tree); System.out.println(); System.out.println("递归后序遍历二叉树的结果为:"); tree.postOrder(tree); System.out.println(); System.out.println("非递归后序遍历二叉树的结果为:"); tree.iterativePostOrder(tree); System.out.println(); System.out.println("层次遍历二叉树结果: "); tree.LayerOrder(tree); System.out.println(); System.out.println("递归求二叉树中所有结点的和为:"+getSumByRecursion(tree)); System.out.println("非递归求二叉树中所有结点的和为:"+getSumByNoRecursion(tree)); System.out.println("二叉树中,每个节点所在的层数为:"); for (int p = 1; p <= 14; p++) System.out.println(p + "所在的层为:" + tree.level(p)); System.out.println("二叉树的高度为:" + height(tree)); System.out.println("二叉树中节点总数为:" + nodes(tree)); System.out.println("二叉树中叶子节点总数为:" + leaf(tree)); System.out.println("二叉树中父节点总数为:" + fatherNodes(tree)); System.out.println("二叉树中只拥有一个孩子的父节点数:" + oneChildFather(tree)); System.out.println("二叉树中只拥有左孩子的父节点总数:" + leftChildFather(tree)); System.out.println("二叉树中只拥有右孩子的父节点总数:" + rightChildFather(tree)); System.out.println("二叉树中同时拥有两个孩子的父节点个数为:" + doubleChildFather(tree)); } }