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Posts published in “Binary Search Tree”

LeetCode 108. Convert Sorted Array to Binary Search Tree (javascript)

By stone on April 17, 2021

Given an integer array nums where the elements are sorted in ascending order, convert it to a height-balanced binary search tree.

A height-balanced binary tree is a binary tree in which the depth of the two subtrees of every node never differs by more than one.

Example 1:

Input: nums = [-10,-3,0,5,9]
Output: [0,-3,9,-10,null,5]
Explanation: [0,-10,5,null,-3,null,9] is also accepted:

Example 2:

Input: nums = [1,3]
Output: [3,1]
Explanation: [1,3] and [3,1] are both a height-balanced BSTs.

Constraints:

  • 1 <= nums.length <= 104
  • -104 <= nums[i] <= 104
  • nums is sorted in a strictly increasing order.

Idea:

Recursion + Divide and Conquer

Time complexity: O(n)
Space complexity: O(logn)

Solution:

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {number[]} nums
 * @return {TreeNode}
 */
var sortedArrayToBST = function(nums) {
    return createBST(nums, 0, nums.length - 1);
};

function createBST(nums, l, r) {
    // exit recursion condition
    if (l > r) return null;
    
    let mid = l + Math.floor((r - l) / 2);
    let root = new TreeNode(nums[mid]);
    root.left = createBST(nums, l, mid - 1);
    root.right = createBST(nums, mid + 1, r);
    return root;
}

LeetCode 99. Recover Binary Search Tree (javascript)

By stone on April 16, 2021

You are given the root of a binary search tree (BST), where exactly two nodes of the tree were swapped by mistake. Recover the tree without changing its structure.

Follow up: A solution using O(n) space is pretty straight forward. Could you devise a constant space solution?

Example 1:

Input: root = [1,3,null,null,2]
Output: [3,1,null,null,2]
Explanation: 3 cannot be a left child of 1 because 3 > 1. Swapping 1 and 3 makes the BST valid.

Example 2:

Input: root = [3,1,4,null,null,2]
Output: [2,1,4,null,null,3]
Explanation: 2 cannot be in the right subtree of 3 because 2 < 3. Swapping 2 and 3 makes the BST valid.

Constraints:

  • The number of nodes in the tree is in the range [2, 1000].
  • -231 <= Node.val <= 231 - 1

Idea:

Because inorder traverse BST, all values are sorted. We can use inorder traversal to find two nodes that have prev.val > root. val and swap them

Time complexity: O(n)
Space complexity: O(height)

Solution:

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {void} Do not return anything, modify root in-place instead.
 */
var recoverTree = function(root) {
    // javascript can't pass value by reference 
    // so pass array object by reference
    let first = [null];
    let second = [null];
    let prev = [null];
    inorder(root, first, second, prev);
    [first[0].val, second[0].val] = [second[0].val, first[0].val];
};

function inorder(root, first, second, prev) {
    // Because inorder traverse BST, all values are sorted.
    // Using inorder traversal to find two nodes that have prev.val > root.val
    if (root === null) return;
    inorder(root.left, first, second, prev);
    if (prev[0] && prev[0].val > root.val) {
        if (first[0] === null) first[0] = prev[0];
        second[0] = root;
    }
    prev[0] = root;
    inorder(root.right, first, second, prev);
}

LeetCode 230. Kth Smallest Element in a BST (javascript)

By stone on April 11, 2021

Given the root of a binary search tree, and an integer k, return the kth (1-indexed) smallest element in the tree.

Example 1:

Input: root = [3,1,4,null,2], k = 1
Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3
Output: 3

Constraints:

  • The number of nodes in the tree is n.
  • 1 <= k <= n <= 104
  • 0 <= Node.val <= 104

Idea:

 Recursive Inorder Traversal

Solution:

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} k
 * @return {number}
 */
var kthSmallest = function(root, k) {
    const nums = [];
    inorder(root, nums);
    return nums[k - 1];
};

function inorder(root, nums) {
    if (root === null) return;
    inorder(root.left, nums);
    nums.push(root.val);
    inorder(root.right, nums);
}

LeetCode 701. Insert into a Binary Search Tree (javascript)

By stone on April 5, 2021

You are given the root node of a binary search tree (BST) and a value to insert into the tree. Return the root node of the BST after the insertion. It is guaranteed that the new value does not exist in the original BST.

Notice that there may exist multiple valid ways for the insertion, as long as the tree remains a BST after insertion. You can return any of them.

Example 1:

Input: root = [4,2,7,1,3], val = 5
Output: [4,2,7,1,3,5]
Explanation: Another accepted tree is:

Example 2:

Input: root = [40,20,60,10,30,50,70], val = 25
Output: [40,20,60,10,30,50,70,null,null,25]

Example 3:

Input: root = [4,2,7,1,3,null,null,null,null,null,null], val = 5
Output: [4,2,7,1,3,5]

Constraints:

  • The number of nodes in the tree will be in the range [0, 104].
  • -108 <= Node.val <= 108
  • All the values Node.val are unique.
  • -108 <= val <= 108
  • It’s guaranteed that val does not exist in the original BST.

Solution: (Recursion)

  • Time complexity: O(logn ~ n)
  • Space complexity: O(logn ~ n)
/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} val
 * @return {TreeNode}
 */
var insertIntoBST = function(root, val) {
    // empty tree case:
    if (root === null) return new TreeNode(val);
    if (val > root.val) {
        root.right = insertIntoBST(root.right, val);
    } else {
        root.left = insertIntoBST(root.left, val);
    }
    return root;
};

LeetCode 450. Delete Node in a BST (javascript)

By stone on April 5, 2021

Given a root node reference of a BST and a key, delete the node with the given key in the BST. Return the root node reference (possibly updated) of the BST.

Basically, the deletion can be divided into two stages:

  1. Search for a node to remove.
  2. If the node is found, delete the node.

Follow up: Can you solve it with time complexity O(height of tree)?

Example 1:

Input: root = [5,3,6,2,4,null,7], key = 3
Output: [5,4,6,2,null,null,7]
Explanation: Given key to delete is 3. So we find the node with value 3 and delete it.
One valid answer is [5,4,6,2,null,null,7], shown in the above BST.
Please notice that another valid answer is [5,2,6,null,4,null,7] and it's also accepted.

Example 2:

Input: root = [5,3,6,2,4,null,7], key = 0
Output: [5,3,6,2,4,null,7]
Explanation: The tree does not contain a node with value = 0.

Example 3:

Input: root = [], key = 0
Output: []

Constraints:

  • The number of nodes in the tree is in the range [0, 104].
  • -105 <= Node.val <= 105
  • Each node has a unique value.
  • root is a valid binary search tree.
  • -105 <= key <= 105

Solution: (Recursion)

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} key
 * @return {TreeNode}
 */
var deleteNode = function(root, key) {
    if (root === null) return root;
    if (key > root.val) {
        root.right = deleteNode(root.right, key);
    } else if (key < root.val) {
        root.left = deleteNode(root.left, key);
    } else { // found the key
        // has children
        if (root.left !== null && root.right !== null) {
            let min = new TreeNode();
            min = root.right;
            while (min.left !== null) min = min.left;
            root.val = min.val;
            root.right = deleteNode(root.right, min.val);
        } else { // no children
            let newRoot = new TreeNode();
            newRoot = root.left === null ? root.right : root.left;
            root.left = root.right = null;
            return newRoot;
        }
    }
    return root;
};

LeetCode 98. Validate Binary Search Tree (javascript)

By stone on April 5, 2021

Given the root of a binary tree, determine if it is a valid binary search tree (BST).

A valid 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.

Example 1:

Input: root = [2,1,3]
Output: true

Example 2:

Input: root = [5,1,4,null,null,3,6]
Output: false
Explanation: The root node's value is 5 but its right child's value is 4.

Constraints:

  • The number of nodes in the tree is in the range [1, 104].
  • -231 <= Node.val <= 231 - 1

Idea:

Use Binary Tree Inorder Traveral Template

Solution 1:

/**
 * Definition for a binary tree node.
 * function TreeNode(val, left, right) {
 *     this.val = (val===undefined ? 0 : val)
 *     this.left = (left===undefined ? null : left)
 *     this.right = (right===undefined ? null : right)
 * }
 */
/**
 * @param {TreeNode} root
 * @return {boolean}
 */
var isValidBST = function(root) {
    // use inorder traversal template (2 whiles, 里左外右)
    let preVal = -Infinity;
    let stack = [];
    
    while (root !== null || stack.length !== 0) {
        while (root !== null) {
            stack.push(root);
            root = root.left;
        }
        root = stack.pop();
        if (root.val <= preVal) return false;
        preVal = root.val;
        root = root.right;
    }
    return true;
};

Solution 2: (Recursion)

var isValidBST = function(root) {
    return helper(root, null, null);
}

function helper(node, low, high) {
    if (node === null) return true;
    const val = node.val;
    if ((low !== null && val <= low) || (high !== null && val >= high)) 
        return false;
    return helper(node.right, val, high) && helper(node.left, low, val);
}