Closest Binary Search Tree Value II

Given a non-empty binary search tree and a target value, findkvalues 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.

Example

Input:
 root = [4,2,5,1,3], target = 3.714286, and 
k = 2

    4
   / \
  2   5
 / \
1   3

Output:
 [4,3]

Note

直接做法是转化成有序数组，然后用双指针

高级做法是直接在树上双指针：

最优算法，时间复杂度O(k + logn)O(k+logn)，空间复杂度O(logn)O(logn)

实现如下的子函数：

1. getStack() => 在假装插入 target 的时候，看看一路走过的节点都是哪些，放到 stack 里，用于 iterate

2. moveUpper(stack) => 根据 stack，挪动到 next node

3. moveLower(stack) => 根据 stack, 挪动到 prev node

有了这些函数之后，就可以把整个树当作一个数组一样来处理，只不过每次 i++ 的时候要用 moveUpper，i--的时候要用 moveLower

Code

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        List<Integer> res = new ArrayList<>();
        List<Integer> list = new ArrayList<>();

        traverse(root, list);

        int start = 0, end = list.size();
        while (start < end) {
            if (list.get(start) >= target) {
                break;
            }
            start++;
        }

        int low = start - 1, high = start;
        for (int i = 0; i < k; i++) {
            if (isLeftClose(list, target, low, high)) {
                res.add(list.get(low--));
            } else {
                res.add(list.get(high++));
            }
        }

        return res;
    }

    private boolean isLeftClose(List<Integer> list, double target,
                                int low, int high) {
        if (low < 0) {
            return false;
        }
        if (high > list.size() - 1) {
            return true;
        }

        if (target - list.get(low) != list.get(high) - target) {
            return (target - list.get(low) < list.get(high) - target);
        }
        return true;
    }

    private void traverse(TreeNode root, List<Integer> list) {
        if (root == null) {
            return;
        }
        traverse(root.left, list);
        list.add(root.val);
        traverse(root.right, list);
    }
}

class Solution {
    public List<Integer> closestKValues(TreeNode root, double target, int k) {
        List<Integer> values = new ArrayList<>();

        if (k == 0 || root == null) {
            return values;
        }

        Stack<TreeNode> lowerStack = getStack(root, target);
        Stack<TreeNode> upperStack = new Stack<>();
        upperStack.addAll(lowerStack);
        if (target < lowerStack.peek().val) {
            moveLower(lowerStack);
        } else {
            moveUpper(upperStack);
        }

        for (int i = 0; i < k; i++) {
            if (lowerStack.isEmpty() ||
                   !upperStack.isEmpty() && target - lowerStack.peek().val > upperStack.peek().val - target) {
                values.add(upperStack.peek().val);
                moveUpper(upperStack);
            } else {
                values.add(lowerStack.peek().val);
                moveLower(lowerStack);
            }
        }

        return values;
    }

    private Stack<TreeNode> getStack(TreeNode root, double target) {
        Stack<TreeNode> stack = new Stack<>();

        while (root != null) {
            stack.push(root);

            if (target < root.val) {
                root = root.left;
            } else {
                root = root.right;
            }
        }

        return stack;
    }

    public void moveUpper(Stack<TreeNode> stack) {
        TreeNode node = stack.peek();
        if (node.right == null) {
            node = stack.pop();
            while (!stack.isEmpty() && stack.peek().right == node) {
                node = stack.pop();
            }
            return;
        }

        node = node.right;
        while (node != null) {
            stack.push(node);
            node = node.left;
        }
    }

    public void moveLower(Stack<TreeNode> stack) {
        TreeNode node = stack.peek();
        if (node.left == null) {
            node = stack.pop();
            while (!stack.isEmpty() && stack.peek().left == node) {
                node = stack.pop();
            }
            return;
        }

        node = node.left;
        while (node != null) {
            stack.push(node);
            node = node.right;
        }
    }
}