270: Closest Binary Search Tree Value II

Given a non-empty binary search tree and a target value, find k values in the BST that are closest to the target.

Note:

Given target value is a floating point.

You may assume k is always valid, that is: k ≤ total nodes.

You are guaranteed to have only one unique set of k values in the BST that are closest to the target.

Follow up:

Assume that the BST is balanced, could you solve it in less than O(n) runtime (where n = total nodes)?

Hint:

Consider implement these two helper functions:

getPredecessor(N), which returns the next smaller node to N.

getSuccessor(N), which returns the next larger node to N.

Try to assume that each node has a parent pointer, it makes the problem much easier.

Without parent pointer we just need to keep track of the path from the root to the current node using a stack.

You would need two stacks to track the path in finding predecessor and successor node separately.

https://leetcode.com/discuss/69220/2-ms-o-n-and-6-ms-o-logn-java-solution

O(lgN):

public class Solution {
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        LinkedList<Integer> list = new LinkedList<Integer>();
        closestKValuesHelper(list, root, target, k);
        return list;
    }

    /**
     * @return <code>true</code> if result is already found.
     */
    private boolean closestKValuesHelper(LinkedList<Integer> list, TreeNode root, double target, int k) {
        if (root == null) {
            return false;
        }

        if (closestKValuesHelper(list, root.left, target, k)) {
            return true;
        }

        if (list.size() == k) {
            if (Math.abs(list.getFirst() - target) < Math.abs(root.val - target)) {
                return true;
            } else {
                list.removeFirst();
            }
        }

        list.addLast(root.val);
        return closestKValuesHelper(list, root.right, target, k);
    }
}

O(lgN):

public List<Integer> closestKValues(TreeNode root, double target, int k) {
    List<Integer> list = new ArrayList<>();
    Stack<TreeNode> pred = new Stack<>(), succ = new Stack<>();
    initStack(pred, succ, root, target);
    while(k-- > 0){
        if(succ.isEmpty() || !pred.isEmpty() && target - pred.peek().val < succ.peek().val - target){
            list.add(pred.peek().val);
            getPredecessor(pred);
        }
        else{//Since N > k, always have something to add
            list.add(succ.peek().val);
            getSuccessor(succ);
        }
    }
    return list;
}

private void initStack(Stack<TreeNode> pred, Stack<TreeNode> succ, TreeNode root, double target){
    while(root != null){
        if(root.val <= target){
            pred.push(root);
            root = root.right;
        }
        else{
            succ.push(root);
            root = root.left;
        }
    }
}
private void getPredecessor(Stack<TreeNode> st){
    TreeNode node = st.pop();
    if(node.left != null){
        st.push(node.left);
        while(st.peek().right != null)  st.push(st.peek().right);
    }
}
private void getSuccessor(Stack<TreeNode> st){
    TreeNode node = st.pop();
    if(node.right != null){
        st.push(node.right);
        while(st.peek().left != null)   st.push(st.peek().left);
    }
}

public class Solution {
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        List<Integer> result = new ArrayList<>();
        if (root == null) {
            return result;
        }

        Stack<Integer> precedessor = new Stack<>();
        Stack<Integer> successor = new Stack<>();

        getPredecessor(root, target, precedessor);
        getSuccessor(root, target, successor);

        for (int i = 0; i < k; i++) {
            if (precedessor.isEmpty()) {
                result.add(successor.pop());
            } else if (successor.isEmpty()) {
                result.add(precedessor.pop());
            } else if (Math.abs((double) precedessor.peek() - target) < Math.abs((double) successor.peek() - target)) {
                result.add(precedessor.pop());
            } else {
                result.add(successor.pop());
            }
        }

        return result;
    }

    private void getPredecessor(TreeNode root, double target, Stack<Integer> precedessor) {
        if (root == null) {
            return;
        }

        getPredecessor(root.left, target, precedessor);

        if (root.val > target) {
            return;
        }

        precedessor.push(root.val);

        getPredecessor(root.right, target, precedessor);
    }

    private void getSuccessor(TreeNode root, double target, Stack<Integer> successor) {
        if (root == null) {
            return;
        }

        getSuccessor(root.right, target, successor);

        if (root.val <= target) {
            return;
        }

        successor.push(root.val);

        getSuccessor(root.left, target, successor);
    }
}