[LeetCode] 272. Closest Binary Search Tree Value II 最近的二叉搜索树的值 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:

1. Consider implement these two helper functions:
　　i. getPredecessor(N), which returns the next smaller node to N.
　　ii. getSuccessor(N), which returns the next larger node to N.
2. Try to assume that each node has a parent pointer, it makes the problem much easier.
3. Without parent pointer we just need to keep track of the path from the root to the current node using a stack.
4. You would need two stacks to track the path in finding predecessor and successor node separately.

270. Closest Binary Search Tree Value 的拓展，270题只要找出离目标值最近的一个节点值，而这道题要找出离目标值最近的k个节点值。

解法1：Brute Force, 中序遍历或者其它遍历，同时维护一个大小为k的max heap。

Java:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        LinkedList<Integer> res = new LinkedList<>();
        inOrderTraversal(root, target, k, res);
        return res;
    }
 
    private void inOrderTraversal(TreeNode root, double target, int k, LinkedList<Integer> res) {
        if (root == null) {
            return;
        }
        inOrderTraversal(root.left, target, k, res);
        if (res.size() < k) {
            res.add(root.val);
        } else if(res.size() == k) {
            if (Math.abs(res.getFirst() - target) > (Math.abs(root.val - target))) {
                res.removeFirst();
                res.addLast(root.val);
            } else {
                return;
            }
        }
        inOrderTraversal(root.right, target, k, res);
    }
}

Java:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    private PriorityQueue<Integer> minPQ;
    private int count = 0;
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        minPQ = new PriorityQueue<Integer>(k);
        List<Integer> result = new ArrayList<Integer>();
 
        inorderTraverse(root, target, k);
 
        // Dump the pq into result list
        for (Integer elem : minPQ) {
            result.add(elem);
        }
 
        return result;
    }
 
    private void inorderTraverse(TreeNode root, double target, int k) {
        if (root == null) {
            return;
        }
 
        inorderTraverse(root.left, target, k);
 
        if (count < k) {
            minPQ.offer(root.val);
        } else {
            if (Math.abs((double) root.val - target) < Math.abs((double) minPQ.peek() - target)) {
                minPQ.poll();
                minPQ.offer(root.val);
            }
        }
        count++;
 
        inorderTraverse(root.right, target, k);
    }
}　

Java:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {  
 
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        PriorityQueue<Double> maxHeap = new PriorityQueue<Double>(k, new Comparator<Double>() {
            @Override
            public int compare(Double x, Double y) {
                return (int)(y-x);
            }
        });
        Set<Integer> set = new HashSet<Integer>();  
 
        rec(root, target, k, maxHeap, set);  
 
        return new ArrayList<Integer>(set);
    }  
 
    private void rec(TreeNode root, double target, int k, PriorityQueue<Double> maxHeap, Set<Integer> set) {
        if(root==null) return;
        double diff = Math.abs(root.val-target);
        if(maxHeap.size()<k) {
            maxHeap.offer(diff);
            set.add(root.val);
        } else if( diff < maxHeap.peek() ) {
            double x = maxHeap.poll();
            if(! set.remove((int)(target+x))) set.remove((int)(target-x));
            maxHeap.offer(diff);
            set.add(root.val);
        } else {
            if(root.val > target) rec(root.left, target, k, maxHeap,set);
            else rec(root.right, target, k, maxHeap, set);
            return;
        }
        rec(root.left, target, k, maxHeap, set);
        rec(root.right, target, k, maxHeap, set);
    }
}

Java: A time linear solution, The time complexity would be O(k + (n - k) logk). Space complexity is O(k).

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

C++:

class Solution {
public:
    vector<int> closestKValues(TreeNode* root, double target, int k) {
        vector<int> res;
        priority_queue<pair<double, int>> q;
        inorder(root, target, k, q);
        while (!q.empty()) {
            res.push_back(q.top().second);
            q.pop();
        }
        return res;
    }
    void inorder(TreeNode *root, double target, int k, priority_queue<pair<double, int>> &q) {
        if (!root) return;
        inorder(root->left, target, k, q);
        q.push({abs(root->val - target), root->val});
        if (q.size() > k) q.pop();
        inorder(root->right, target, k, q);
    }
};　　

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