Given a binary tree, determine if it is a valid binary search tree (BST).
Assume a BST is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
confused what "{1,#,2,3}"
means? > read more on how binary tree is serialized on OJ.
Solution_1: In_Order Approach
Idea: simply do In_Order traversal, then check
If In_Order traversal of a binary tree is sorted,
then the binary tree is BST. else not
public static boolean isValidBSTInOrder(TreeNode root) {
if(root==null) return true;
ArrayList<Integer> res=new ArrayList<Integer>();
Stack<TreeNode> stack=new Stack<TreeNode>();
while(!stack.empty() || root!=null){
if(root!=null){
stack.add(root);
root=root.left;
}else {
root=stack.pop();
res.add(root.val);
root=root.right;
}
}
//System.out.println(res);
int num=res.get(0);
for(int i=1;i<res.size();i++){
if(res.get(i)<=num){
return false;
}
num=res.get(i);
}
return true;
}
Solution_2:
Key to solve: DFS Traversal with ceiling && flooring cases
return false, if there is invalid case was found
public static boolean isValidBST(TreeNode root) {
return helper(root,Integer.MIN_VALUE,Integer.MAX_VALUE);
}
private static boolean helper(TreeNode root,int flooring, int ceiling){
if(root==null) return true;
//check for invalid case
if(root.val>=ceiling || root.val<=flooring) return false;
//check both flooring && ceiling case
//case1: Left subtree nodes=> flooring: min, ceiling: root.val
//case2: Right subtree nodes => flooring:root.val, ceiling: max
return helper(root.left,flooring,root.val)
&& helper(root.right,root.val,ceiling);
}