二叉树的遍历 递归非递归 思路和 java实现

package com.mzsx.binarytree;

import java.util.Stack;
public class BinaryTree {
protected Node root;

public BinaryTree(Node root) {
this.root = root;
}

public Node getRoot() {
return root;
}
/*
H
/     \
D       G
/   \       \
B     C       F
\          /
A        E

*/
/** 构造树 */
public static Node init() {
Node a = new Node('A');
Node b = new Node('B', null, a);
Node c = new Node('C');
Node d = new Node('D', b, c);
Node e = new Node('E');
Node f = new Node('F', e, null);
Node g = new Node('G', null, f);
Node h = new Node('H', d, g);
return h;// root
}

/** 访问节点 */
public static void visit(Node p) {
System.out.print(p.getKey() + " ");
}

/** 递归实现前序遍历 */
protected static void preorder(Node p) {
if (p != null) {
visit(p);
preorder(p.getLeft());
preorder(p.getRight());
}
}

/** 递归实现中序遍历 */
protected static void inorder(Node p) {
if (p != null) {
inorder(p.getLeft());
visit(p);
inorder(p.getRight());
}
}

/** 递归实现后序遍历 */
protected static void postorder(Node p) {
if (p != null) {
postorder(p.getLeft());
postorder(p.getRight());
visit(p);
}
}
/**********************************************************************************************/
/** 非递归实现前序遍历 */
protected static void iterativePreorder(Node p) {
Stack<Node> stack = new Stack<Node>();
if (p != null) {
stack.push(p);
while (!stack.empty()) {
p = stack.pop();
visit(p);
if (p.getRight() != null)
stack.push(p.getRight());
if (p.getLeft() != null)  //为什么p.getLeft() 在后，getRight()在前应为while 循环第一句就是pop visit所以要把left放上，先访问。之中方法是即压即访问法。
stack.push(p.getLeft());
}
}
}

/** 非递归实现中序遍历 */  //思路与上面iterativePreorder 一致。
protected static void iterativeInorder(Node p) {
Stack<Node> stack = new Stack<Node>();
while (p != null) {
while (p != null) {
if (p.getRight() != null)
stack.push(p.getRight());// 当前节点右子入栈
stack.push(p);// 当前节点入栈
p = p.getLeft();
}
p = stack.pop();
while (!stack.empty() && p.getRight() == null) {
visit(p);
p = stack.pop();
}
visit(p);
if (!stack.empty())
p = stack.pop();
else
p = null;
}
}

/*******************************************************************************/

/*******************************************************************************/
/** 非递归实现前序遍历2 */
protected static void iterativePreorder2(Node p) {
Stack<Node> stack = new Stack<Node>();
Node node = p;
while (node != null || stack.size() > 0) {
while (node != null) {//压入所有的左节点，压入前访问它。左节点压入完后pop访问右节点。像这样算法时思考规律性的东西在哪。不管哪个节点都要压所节点判断右节点。
visit(node);
stack.push(node);
node = node.getLeft();
}
if (stack.size() > 0) {//
node = stack.pop();
node = node.getRight();
}
}
}

/** 非递归实现中序遍历2 */
protected static void iterativeInorder2(Node p) {
Stack<Node> stack = new Stack<Node>();
Node node = p;
while (node != null || stack.size() > 0) {
while (node != null) {
stack.push(node);
node = node.getLeft();
}
if (stack.size() > 0) {
node = stack.pop();
visit(node);   //与iterativePreorder2比较只有这句话的位置不一样，弹出时再访问。
node = node.getRight();
}
}
}

/*******************************************************************************/

/** 非递归实现后序遍历 */
protected static void iterativePostorder(Node p) {
Node q = p;
Stack<Node> stack = new Stack<Node>();
while (p != null) {
// 左子树入栈
for (; p.getLeft() != null; p = p.getLeft())
stack.push(p);
// 当前节点无右子或右子已经输出
while (p != null && (p.getRight() == null || p.getRight() == q)) {
visit(p);
q = p;// 记录上一个已输出节点
if (stack.empty())
return;
p = stack.pop();
}
// 处理右子
stack.push(p);
p = p.getRight();
}
}

/** 非递归实现后序遍历 双栈法 */
protected static void iterativePostorder2(Node p) {//理解左子树   右子树 根递归性质，把它运用到循环当中去。
Stack<Node> lstack = new Stack<Node>();//左子树栈
Stack<Node> rstack = new Stack<Node>();//右子树栈
Node node = p, right;
do {
while (node != null) {
right = node.getRight();
lstack.push(node);
rstack.push(right);
node = node.getLeft();
}
node = lstack.pop();
right = rstack.pop();
if (right == null) {
visit(node);
} else {
lstack.push(node);
rstack.push(null);
}
node = right;
} while (lstack.size() > 0 || rstack.size() > 0);
}

/** 非递归实现后序遍历 单栈法*/
protected static void iterativePostorder3(Node p) {
Stack<Node> stack = new Stack<Node>();
Node node = p, prev = p;
while (node != null || stack.size() > 0) {
while (node != null) {
stack.push(node);
node = node.getLeft();
}
if (stack.size() > 0) {
Node temp = stack.peek().getRight();
if (temp == null || temp == prev) {
node = stack.pop();
visit(node);
prev = node;
node = null;
} else {
node = temp;
}
}

}
}

/** 非递归实现后序遍历4 双栈法*/
protected static void iterativePostorder4(Node p) {
Stack<Node> stack = new Stack<Node>();
Stack<Node> temp = new Stack<Node>();
Node node = p;
while (node != null || stack.size() > 0) {
while (node != null) {
temp.push(node);
stack.push(node);
node = node.getRight();
}
if (stack.size() > 0) {
node = stack.pop();
node = node.getLeft();
}
}
while (temp.size() > 0) {//把插入序列都插入到了temp。
node = temp.pop();
visit(node);
}
}

/**
* @param args
*/
public static void main(String[] args) {
BinaryTree tree = new BinaryTree(init());
System.out.print(" 递归遍历 \n");
System.out.print(" Pre-Order:");
preorder(tree.getRoot());

System.out.print(" \n In-Order:");
inorder(tree.getRoot());

System.out.print("\n Post-Order:");
postorder(tree.getRoot());

System.out.print(" \n非递归遍历");
System.out.print(" \n Pre-Order:");
iterativePreorder(tree.getRoot());

System.out.print("\n Pre-Order2:");
iterativePreorder2(tree.getRoot());

System.out.print(" \n In-Order:");
iterativeInorder(tree.getRoot());

System.out.print("\n In-Order2:");
iterativeInorder2(tree.getRoot());

System.out.print("\n Post-Order:");
iterativePostorder(tree.getRoot());

System.out.print("\n Post-Order2:");
iterativePostorder2(tree.getRoot());

System.out.print("\n Post-Order3:");
iterativePostorder3(tree.getRoot());

System.out.print("\n Post-Order4:");
iterativePostorder4(tree.getRoot());

}

}

class Node {
private char key;
private Node left, right;

public Node(char key) {
this(key, null, null);
}

public Node(char key, Node left, Node right) {
this.key = key;
this.left = left;
this.right = right;
}

public char getKey() {
return key;
}

public void setKey(char key) {
this.key = key;
}

public Node getLeft() {
return left;
}

public void setLeft(Node left) {
this.left = left;
}

public Node getRight() {
return right;
}

public void setRight(Node right) {
this.right = right;
}
}