二叉树的几种遍历

二叉树遍历

二叉树结构

public class TreeNode {
    int val;
    TreeNode left;
    TreeNode right;

    public TreeNode() {}

    public TreeNode(int val){
        this(val, null, null);
    }

    public TreeNode(int val, TreeNode left, TreeNode right){
        this.val = val;
        this.left = left;
        this.right = right;
    }
}

---

前序遍历

递归

List<Integer> list = new ArrayList<>();
public List<Integer> preOrder(TreeNode root){
    if(root == null) return list;
    list.add(root.val);
    preOrder(root.left);
    preOrder(root.right);
    return list;
}

非递归

public List<Integer> preOrder(TreeNode root) {
	List<Integer> list = new ArrayList<>();
    if(root == null) return list;
    Stack<TreeNode> stack = new Stack<>();
    while(!stack.isEmpty()) {
    	TreeNode e = stack.pop();
        if(e != null) {
        	if(e.right != null) stack.push(e.right);
            if(e.left != null) stack.push(e.left);
            stack.push(e);
            stack.push(null);
        } else {
        	list.add(stack.pop().val);
        }
    }
    return list;
}

Morris前序遍历（非递归，空间 O(1) ，时间 O(n) ）

public List<Integer> preOrder(TreeNode root) {
	List<Integer> list = new ArrayList<>();
    TreeNode curr = root, prev = null;
    while(curr != null) {
    	if(curr.left == null){
        	list.add(curr.val);
            curr = curr.right;
        } else {
        	prev = curr.left;
            while(prev.right != null && prev.right != curr)
                prev = prev.right;
            if(prev.right == null) {
            	list.add(curr.val);
                prev.right = curr;
                curr = curr.left;
            } else {
            	prev.right = null;
                curr = curr.right;
            }
        }
    }
    return list;
}

---

中序遍历

递归

List<Integer> list = new ArrayList<>();
public List<Integer> inOrder(TreeNode root){
    if (root == null) return list;
    inOrder(root.left);
    list.add(root.val);
    inOrder(root.right);
    return list;
}

非递归

public List<Integer> inOrder(TreeNode root) {
	List<Integer> list = new ArrayList<>();
    if(root == null) return list;
    Stack<TreeNode> stack = new Stack<>();
    stack.push(root);
    while(!stack.isEmpty()) {
    	TreeNode e = stack.pop();
        if(e != null) {
        	if(e.right != null) stack.push(e.right);
            stack.push(e);
            stack.push(null);
            if(e.left != null) stack.push(e.left);
        } else {
        	list.add(stack.pop().val);
        }
    }
    return list;
}

Morris中序遍历（非递归，空间 O(1) ，时间 O(n) ）：

public List<Integer> inOrder(TreeNode root){
	List<Integer> list = new ArrayList<>();
    TreeNode curr = root, prev = null;
    while(curr != null){
    	if(curr.left == null){
        	list.add(curr.val);
            curr = curr.right;
        }
        else {
        	prev = curr.left;
            while(prev.right != null && prev.right != curr)
                prev = prev.right;
            if(prev.right == null) {
            	prev.right = curr;
                curr = curr.left;
            } else {
            	prev.right = null;
                list.add(curr.val);
                curr = curr.right;
            }
        }
        return list;
    }
}

---

后序遍历

递归

List<Integer> list = new ArrayList<>();
public List<Integer> postOrder(TreeNode root){
    if(root == null)
        return list;
    postOrder(root.left);
    postOrder(root.right);
    list.add(root.val);
    return list;
}

非递归

public List<Integer> postOrder(TreeNode root) {
	List<Integer> list = new ArrayList<>();
    if(root == null) return list;
    Stack<TreeNode> stack = new Stack<>();
    stack.push(root);
    while(!stack.isEmpty()) {
    	TreeNode e = stack.pop();
        if(e != null) {
        	stack.push(e);
            stack.push(null);
            if(e.right != null) stack.push(e.right);
            if(e.left != null) stack.push(e.left);
        } else {
        	list.add(stack.pop().val);
        }
    }
    return list;
}

Moirrs后序遍历（非递归，空间 O(1) ，时间 O(n) ）

List<Integer> list = new ArrayList<>();
public List<Integer> postOrder(TreeNode root){
	TreeNode dump = new TreeNode(0);
    dump.left = root;
    TreeNode curr = dump, prev = null;
    while (curr != null) {
    	if(curr.left == null)
            curr = curr.right;
        else {
        	prev = curr.left;
            while(prev.right != null && prev.right != curr)
                prev = prev.right;
            if(prev.right == null) {
            	prev.right = curr;
                curr = curr.left;
            } else {
            	visit(curr.left, prev);
                prev.right = null;
                curr = curr.right;
            }
        }
    }
    return list;
}

private void visit(TreeNode from, TreeNode to) {
	reverse(from, to);
    TreeNode p = to;
    while(true) {
    	list.add(p.val);
        if(p == from) break;
        p = p.right;
    }
    reverse(to, from);
}

private void reverse(TreeNode from, TreeNode to) {
	if(from == to) return;
    TreeNode prev = from, curr = from.right, next = null;
    while(true) {
    	next = curr.right;
        curr.right = prev;
        prev = curr;
        curr = next;
        if(prev == to) break;
    }
}

---

层序遍历

非递归

public static List<List<Integer>> levelOrder(TreeNode root) {
	List<List<Integer>> res = new LinkedList<>();
    if(root == null) return res;
    
    Deque<TreeNode> queue = new LinkedList<>();
    queue.addLast(root);
    while(!queue.isEmpty()) {
    	int size = queue.size();
        List<Integer> row = new LinkedList<>();
        for(int i = 0; i < size; i++) {
        	TreeNode remove = queue.removeFirst();
            row.add(remove.val);
            if(remove.left != null) queue.add(remove.left);
            if(remove.right != null) queue.add(remove.right);
        }
        res.add(row);
    }
    return res;
}