[LeetCode] Binary Tree Inorder Traversal

题目：

Given a binary tree, return the inorder traversal of its nodes' values.

For example:
Given binary tree {1,#,2,3},

   1
    \
     2
    /
   3

return [1,3,2].

思路：

借这个题来复习下树的先序、中序、后序遍历，递归以及非递归的实现。具体思路以及方法都在代码注释中写明。

Binary_Tree_Inorder_Traversal.java 主要的算法类

import java.util.ArrayList;
import java.util.List;
import java.util.Stack;

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */

public class Binary_Tree_Inorder_Traversal {
	public class TreeNode {
		int val;
		TreeNode left;
		TreeNode right;
		boolean isFirst;//whether is the secondly visiting
		TreeNode(int x) { val = x; }
	}
	
	//build tree
	public TreeNode buildTree(int[] numbers) {
		TreeNode[] nodes = new TreeNode[numbers.length];
		for(int i = 0;i<nodes.length;i++) {
			nodes[i] = new TreeNode(numbers[i]);
		}
		for(int i = 0;i<numbers.length;i++) {
			if(2*i+1 < numbers.length) {
				nodes[i].left = nodes[2*i+1];
			}
			if(2*i+2 < numbers.length) {
				nodes[i].right = nodes[2*i+2];
			}
		}
		return nodes[0];
	}
	
	/* * * * * * * * * * * * * * * * * * *
	 * 递归实现先序，中序，后序遍历
	 * *  * * * * * * * * * * * * * * * * */
	//preorder
	public void preorderRecursiveSub(List<Integer> result, TreeNode node) {
		result.add(node.val);
		if(node.left != null) preorderRecursiveSub(result, node.left);
		if(node.right != null) preorderRecursiveSub(result, node.right);
	}

	public List<Integer> preorderRecursive(TreeNode root) {
		List<Integer> result = new ArrayList<Integer>();
		preorderRecursiveSub(result, root);
		return result;
	}
	
	//inorder
	public void inorderRecursiveSub(List<Integer> result, TreeNode node) {
			if(node.left != null) inorderRecursiveSub(result, node.left);
			result.add(node.val);
			if(node.right != null) inorderRecursiveSub(result, node.right);
	}
	
	public List<Integer> inorderRecursive(TreeNode root) {
		List<Integer> result = new ArrayList<Integer>();
		inorderRecursiveSub(result, root);
		return result;
	}
	
	//postorder
	public void postorderRecursiveSub(List<Integer> result, TreeNode node) {
		if(node.left != null) postorderRecursiveSub(result, node.left);
		if(node.right != null) postorderRecursiveSub(result, node.right);
		result.add(node.val);
	}
	
	public List<Integer> postorderRecursive(TreeNode root) {
		List<Integer> result = new ArrayList<Integer>();
		postorderRecursiveSub(result, root);
		return result;
	}
	
	/* * * * * * * * * * * * * * * * * * * *
	 * 非递归实现先序，中序，后序遍历
	 * *  * * * * * * * * * * * * * * * * */
	
	/* * * * * * * * * * * * * * * * * * * *
	 * 先序遍历思路：先让根进栈，只要栈不为空，就可以做弹出操作， 
	 * 每次弹出一个结点，记得把它的左右结点都进栈，记得右子树先进栈，
	 * 这样可以保证右子树在栈中总处于左子树的下面。  (preorderTraversal1)
	 * 	或者
	 * 按照根节点->左孩子->右孩子的顺序深度遍历树，在这个过程中，
	 * 输出根节点的顺序就决定了是否是先序或者中序遍历。
	 * 当在深度搜索左孩子的时候，同时输出该节点，则为先序遍历；(preorderTraversal2)
	 * 当完成深度搜索左孩子之后，再输出该节点，则为中序遍历；(inorderTraversal)
	 * 
	 * *  * * * * * * * * * * * * * * * * */
    public List<Integer> preorderTraversal1(TreeNode root) {
    	List<Integer> result = new ArrayList<Integer>();
    	Stack<TreeNode> stack = new Stack<TreeNode>();
    	TreeNode current = root;
    	
    	if(root == null) {
    		return result;
    	}
    	
    	stack.push(root);
    	while(!stack.empty()) {
    		current = stack.pop();
    		result.add(current.val);
    		if(current.right != null) {
    			stack.push(current.right);
    		}
    		if(current.left != null) {
    			stack.push(current.left);
    		}
    	}
    	return result;
    }
	
    public List<Integer> preorderTraversal2(TreeNode root) {
    	List<Integer> result = new ArrayList<Integer>();
    	Stack<TreeNode> stack = new Stack<TreeNode>();
    	TreeNode current = root;
    	
    	if(root == null) {
    		return result;
    	}
    	
    	while(current != null || !stack.empty()) {
    		while(current != null) {
    			result.add(current.val);//add
    			stack.push(current);
    			current = current.left;
    		}
    		if(!stack.empty()) {
    			current = stack.pop();
    			current = current.right;
    		}
    	}
    	return result;
    }
    
	public List<Integer> inorderTraversal(TreeNode root) {
    	List<Integer> result = new ArrayList<Integer>();
    	Stack<TreeNode> stack = new Stack<TreeNode>();
    	TreeNode current = root;
    	
    	if(root == null) {
    		return result;
    	}
    	
    	while(!stack.empty() || current != null) {
    		while(current != null) {
    			stack.push(current);
    			current = current.left;
    		}
    		
    		if(!stack.empty()) {
    			current = stack.pop();
    			result.add(current.val);//add
    			current = current.right;
    		}
    	}
    	return result;
    }
	
	/* * * * * * * * * * * * * * * * * * * *
	 * 后序遍历思路：因为后序遍历需要先将左右孩子都遍历，才能将自己输出，
	 * 所以实际access根节点为两次，所以设置一个标志位来判断是否是第二次访问。(postorderTraversal1)
	 * 	或者
	 * 要保证根结点在左孩子和右孩子访问之后才能访问，因此对于任一结点P，先将其入栈。
	 * 如果P不存在左孩子和右孩子，则可以直接访问它；
	 * 或者P存在左孩子或者右孩子，但是其左孩子和右孩子都已被访问过了，则同样可以直接访问该结点。
	 * 若非上述两种情况，则将P的右孩子和左孩子依次入栈，这样就保证了每次取栈顶元素的时候，
	 * 左孩子在右孩子前面被访问，左孩子和右孩子都在根结点前面被访问。(postorderTraversal2)
	 * 
	 * *  * * * * * * * * * * * * * * * * */
	public List<Integer> postorderTraversal1(TreeNode root) {
    	List<Integer> result = new ArrayList<Integer>();
    	Stack<TreeNode> stack = new Stack<TreeNode>();
    	TreeNode current = root;
    	
    	if(root == null) {
    		return result;
    	}
    	
    	while(!stack.empty() || current != null) {
    		while(current != null) {
    			stack.push(current);
    			current.isFirst = true;
    			current = current.left;
    		}
    		
    		if(!stack.empty()) {
    			current = stack.pop();
    			if(current.isFirst) {
    				current.isFirst = false;
    				stack.push(current);
    				current = current.right;
    			}else{
    				result.add(current.val);//add
    				current = null;
    			}
    		}
    	}
    	return result;
    }
	
	public List<Integer> postorderTraversal2(TreeNode root) {
    	List<Integer> result = new ArrayList<Integer>();
    	Stack<TreeNode> stack = new Stack<TreeNode>();
    	TreeNode current = root;
    	TreeNode pre = root;
    	
    	if(root == null) {
    		return result;
    	}
    	
    	stack.push(root);
    	while(!stack.empty()) {
    		current = stack.peek();
    		if((current.left == null && current.right == null) ||
    		   (pre != null && (pre == current.left || pre == current.right))) {
    			result.add(current.val);//add
    			stack.pop();
    			pre = current;
    		}else{
    			//ensure the sequence
    			if(current.right != null) {
    				stack.push(current.right);
    			}
    			if(current.left != null) {
    				stack.push(current.left);
    			}
    		}
    	}
    	return result;
    }
}

MainClass.java主要的测试类。

import java.util.ArrayList;
import java.util.List;


public class MainClass {
	public static void main(String[] args) {
		Binary_Tree_Inorder_Traversal bt = new Binary_Tree_Inorder_Traversal();
		int[] numbers = {1,2,3,4,5,6,7};
		
		/******************************************/
		System.out.println("preorder testing:");
		System.out.println("	Recursive:");
		System.out.print("	");
		List<Integer> result = bt.preorderRecursive(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		System.out.println("	Non-Recursive:");
		System.out.print("	");
		result = bt.preorderTraversal1(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		System.out.print("	");
		result = bt.preorderTraversal1(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		/******************************************/
		System.out.println("inorder testing:");
		System.out.println("	Recursive:");
		System.out.print("	");
		result = bt.inorderRecursive(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		System.out.println("	Non-Recursive:");
		System.out.print("	");
		result = bt.inorderTraversal(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		/******************************************/
		System.out.println("postorder testing:");
		System.out.println("	Recursive:");
		System.out.print("	");
		result = bt.postorderRecursive(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		System.out.println("	Non-Recursive:");
		System.out.print("	");
		result = bt.postorderTraversal1(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
		
		System.out.print("	");
		result = bt.postorderTraversal2(bt.buildTree(numbers));
		for(int i = 0;i<result.size();i++) {
			System.out.print(result.get(i)+" ");
		}
		System.out.println();
	}
}

主要参考：

[1] http://blog.youkuaiyun.com/hackbuteer1/article/details/6583988

[2] http://www.cnblogs.com/dolphin0520/archive/2011/08/25/2153720.html