Tree

class TreeNode {
  int val;
  TreeNode left;
  TreeNode right;
  TreeNode(int x) {
    val = x;
  }
}

DFS
Preorder:
Iterative using stack:

public class Solution {
    public List<Integer> preorderTraversal(TreeNode root) {
        Stack<TreeNode> stack = new Stack<TreeNode>();
        List<Integer> preorder = new ArrayList<Integer>();
        
        if (root == null) {
            return preorder;
        }
        
        stack.push(root);
        while (!stack.empty()) {
            TreeNode node = stack.pop();
            preorder.add(node.val);
            if (node.right != null) {
                stack.push(node.right);
            }
            if (node.left != null) {
                stack.push(node.left);
            }
        }
        
        return preorder;
    }
}

Recursive:

public class Solution {
    public ArrayList<Integer> preorderTraversal(TreeNode root) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        traverse(root, result);
        return result;
    }
    // 把root为跟的preorder加入result里面
    private void traverse(TreeNode root, ArrayList<Integer> result) {
        if (root == null) {
            return;
        }

        result.add(root.val);
        traverse(root.left, result);
        traverse(root.right, result);
    }
}

Inorder:
Recursive:

class Solution {
    public List < Integer > inorderTraversal(TreeNode root) {
        List < Integer > res = new ArrayList < > ();
        helper(root, res);
        return res;
    }

    public void helper(TreeNode root, List < Integer > res) {
        if (root != null) {
            if (root.left != null) {
                helper(root.left, res);
            }
            res.add(root.val);
            if (root.right != null) {
                helper(root.right, res);
            }
        }
    }
}

Iterative:

public class Solution {
    public ArrayList<Integer> inorderTraversal(TreeNode root) {
        Stack<TreeNode> stack = new Stack<TreeNode>();
        ArrayList<Integer> result = new ArrayList<Integer>();
        TreeNode curt = root;
        while (curt != null || !stack.empty()) {
            while (curt != null) {
                stack.add(curt);
                curt = curt.left;
            }
            curt = stack.pop();
            result.add(curt.val);
            curt = curt.right;
        }
        return result;
    }
}

Postorder:
Recursive:

public ArrayList<Integer> postorderTraversal(TreeNode root) {
    ArrayList<Integer> result = new ArrayList<Integer>();

    if (root == null) {
        return result;
    }

    result.addAll(postorderTraversal(root.left));
    result.addAll(postorderTraversal(root.right));
    result.add(root.val);

    return result;   
}

Iterative:

public ArrayList<Integer> postorderTraversal(TreeNode root) {
    ArrayList<Integer> result = new ArrayList<Integer>();
    Stack<TreeNode> stack = new Stack<TreeNode>();
    TreeNode prev = null; // previously traversed node
    TreeNode curr = root;

    if (root == null) {
        return result;
    }

    stack.push(root);
    while (!stack.empty()) {
        curr = stack.peek();
        if (prev == null || prev.left == curr || prev.right == curr) { // traverse down the tree
            if (curr.left != null) {
                stack.push(curr.left);
            } else if (curr.right != null) {
                stack.push(curr.right);
            }
        } else if (curr.left == prev) { // traverse up the tree from the left
            if (curr.right != null) {
                stack.push(curr.right);
            }
        } else { // traverse up the tree from the right
            result.add(curr.val);
            stack.pop();
        }
        prev = curr;
    }

    return result;
}

Recursive: Validate binary search tree

public class Solution {

    public boolean isValidBST(TreeNode root) {
        return divConq(root, Long.MIN_VALUE, Long.MAX_VALUE);
    }
    
    private boolean divConq(TreeNode root, long min, long max){
        if (root == null){
            return true;
        }
        if (root.val <= min || root.val >= max){
            return false;
        }
        return divConq(root.left, min, Math.min(max, root.val)) && 
                divConq(root.right, Math.max(min, root.val), max);
    }
}

Level Order BFS

class Solution {
    public List<List<Integer>> levelOrder(TreeNode root) {
        Queue<TreeNode> queue = new LinkedList<TreeNode>();
        List<List<Integer>> wrapList = new LinkedList<List<Integer>>();
        
        if(root == null) return wrapList;
        
        queue.offer(root);
        
        while(!queue.isEmpty()) {
            int levelNum = queue.size();
            List<Integer> sublist = new LinkedList<Integer>();
            for(int i=0; i<levelNum; i++) {
                if(queue.peek().left != null) queue.offer(queue.peek().left);
                if(queue.peek().right != null) queue.offer(queue.peek().right);
                sublist.add(queue.poll().val);
            }
            wrapList.add(sublist);
        }
        return wrapList;
    }
}