Posted on January 11, 2018 July 26, 2020 by braindenny. Here present another way of thinking. Understand the problem: As described in the problem, given an array sorted in ascending order, convert it to a balanced BST. Flatten Binary Tree to Linked List: 116. Container With Most Water: 110. Note that a tree is said to be height-balanced if the height difference of left and right subtrees of any node in the tree is at most 1. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. vectorn1(nums.begin(),nums.begin()+t),n2(nums.begin()+t+1,nums.end()); 花花酱 LeetCode 35. Easy. 題目: 給一個排序好的array,return一個高度平衡的BST。 Given an array where elements are sorted in ascending order, convert it to a height balanced BST. In the previous array to BST, we construct the BST in a top-down way. Analysis: The easier way to solve this problem is use the idea as the previous one. Posted on January 13, 2018 July 26, 2020 by braindenny. Remove Duplicates from Sorted Array 27. By zxi on February 1, 2020. Leetcode Training. Leetcode Solution at 4:37 PM. Consider we are given a sorted array of integers. Share to Twitter Share to Facebook Share to Pinterest. Here present another way of thinking. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of_every_node never differ by more than 1. LeetCode: Convert Sorted Array to Binary Search Tree. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. Convert Sorted Array to Binary Search Tree - LeetCode Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Next Permutation 32. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Convert Sorted List to Binary Search Tree 110. Path Sum II 114. Newer Post Older Post Home. 3287 247 Add to List Share. Swap Nodes in Pairs 25. If you are given an array, the problem is quite straightforward. Path Sum: 113. Since the tree has to be height balanced, the array needs to be divided in half all the time in order to create the BST properly. Greatest Common Divisor ... Search in Rotated Sorted Array 9.9. * Definition for a binary tree … Balanced Binary Tree 111. Convert Sorted Array to Binary Search Tree (LeetCode 108. Balanced Binary Tree: 111. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. Convert Sorted Array to Binary Search Tree. Convert Sorted Array to Binary Search Tree. That’s the “Brute Force” method. Search Insert Position. Skip to content. [LeetCode] Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. The right subtree of a node contains only nodes … Binary Tree 2.4. Newer Post Older Post Home. Leetcode Training. In both the recursive functions, we make sure that the tree is height-balanced, So, we use a maximum of O(H) space for recursive stack frames. Leetcode 426 - Convert Binary Search Tree To Sorted Doubly Linked List (JAVA Solution Explained! LeetCode Solutions 109. You may assume no duplicates in the array. Leetcode Training. Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. If you find my solutions hard to comprehend, give yourself a time to solve easier questions or check discussion section to problem on No comments: Post a Comment. Code Interview. Roman to Integer 21. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. 102. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. But I am not sure if I do that will the tree be strictly balanced. topbitz in Leetcode 2014-11-19 97 Words Convert Sorted Array to Binary Search Tree, Leetcode 解题笔记 Given an array where elements are sorted in ascending order, convert it to a … Distinct Subsequences 116. Convert Sorted Array to Binary Search Tree. Consider we are given a sorted array of integers. Search in Rotated Sorted Array II 9.10. Example: Given the sorted array: [-10,-3,0,5,9], One … Longest Valid Parentheses 33. Leetcode: Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. We only visit the elements of the array once, hence it is O(n). Example: Given the sorted array: [-10,-3,0,5,9], One possible answer is: [0,-3,9, … After assigning left and right subtree to the middle node, we can return it and print the postorder traversal of the Binary Search Tree. The goal is to build a Binary Search Tree from this array such that the tree is height-balanced. eval(ez_write_tag([[250,250],'tutorialcup_com-banner-1','ezslot_5',623,'0','0']));O(H), where H = Height of the tree = logN. Convert Sorted Array to Binary Search Tree - easy 문제 . Substring with Concatenation of All Words 31. Balanced Binary Tree 111. Minimum Depth of Binary Tree You must understand what is the height balanced BST. Leetcode: Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. LeetCode Java Solution:- Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. But, in order to check whether the tree is balanced, the approach can be improved on grounds of Time & Space complexities. In the previous array to BST, we construct the BST in a top-down way. Flatten Binary Tree to Linked List 115. The goal is to build a Binary Search Tree from this array such that the tree is height-balanced. Leetcode 108: Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Queue 2.6. Solution: I could have approached this problem using divide and conquer and it would have been much simpler. Convert Sorted List to Binary Search Tree, Search in Rotated Sorted Array Leetcode Solution, Find Element Using Binary Search in Sorted Array, Check if a given array can represent Preorder…, Check if the given array can represent Level Order…, Binary Tree to Binary Search Tree Conversion using STL set, Find First and Last Position of Element in Sorted…, Binary Tree to Binary Search Tree Conversion, Convert a BST to a Binary Tree such that sum of all…, Search an Element in Sorted Rotated Array, Find the node with minimum value in a Binary Search Tree, Lowest Common Ancestor in Binary Search Tree, Count Negative Numbers in a Sorted Matrix LeetCode Solution, Construct Binary Tree from given Parent Array representation, Special Positions in a Binary Matrix Leetcode Solution, Implementation of Convert Sorted Array to Binary Search Tree Leetcode Solution, C++ Solution to Convert Sorted Array to Binary Search Tree, Java Solution to Convert Sorted Array to Binary Search Tree, Complexity Analysis of Convert Sorted Array to Binary Search Tree Leetcode Solution, How Many Numbers Are Smaller Than the Current Number Leetcode Solution, Any node should have smaller elements as left children and vice versa for right children. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. Last active Feb 26, 2018. We need to find any valid solution. That’s the “Brute Force” method. The idea is correct while inefficient. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Embed. Assume a BST is defined as follows: The left subtree of a node contains only nodes with keys less than or equal to the node's key. Type of Issue - Please add/delete options that are not relevant. Convert Sorted Array to Binary Search Tree Given a singly linked list where elements are sorted in ascending order, convert it to a height balanced BST. Path Sum II: 114. « Solution to Binary Tree Level Order Traversal II by LeetCode Solution to Convert Sorted List to Binary Search Tree by LeetCode » Leave a Reply Cancel reply Search in Rotated Sorted Array Populating Next Right Pointers in Each Node 117. Convert Sorted List to Binary Search Tree It is similar with "Convert Sorted Array to Binary Search Tree". For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of_every_node never differ by more than 1. Understand the problem: As described in the problem, given an array sorted in ascending order, convert it to a balanced BST. Convert Sorted List to Binary Search Tree. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. leetcode Question 23: Convert Sorted Array to Binary Search Tree Convert Sorted Array to Binary Search Tree Given a singly linked list where elements are sorted in ascending order, convert it to a height balanced BST. Example 2 / 1 / 4 Not balanced 1 / \ 2 3 Balanced Approach. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Convert Sorted Array to Binary Search Tree 118. Find Minimum in Rotated Sorted Array 9.11. 108. Top Interview Questions. You must understand what is the height balanced BST. Star 1 Fork 0; Star Code Revisions 5 Stars 1. Convert Sorted Array to Binary Search Tree. Solution. Maximum Depth of Binary Tree 107. What would you like to do? Given a sorted array, we can create a BST by selecting a value from within the array and making that a node — this node will become a root node, and we’ll give it a left and right subnode if available. 109)的更多相关文章. LeetCode in Python 108. In this way, we will have a height difference of 1 between the left and right subtrees if the array is of even size and a height difference of 0 when the array is of an oddsize. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Path Sum 113. For this problem, a height-balanced binary tree … Instead, I build a 'complete' binary tree and then by definition it has to be balanced. Convert Sorted Array to Binary Search Tree @LeetCode - SortedArrayToBST.java Thursday, September 25, 2014 [Leetcode] Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Solve problems from LeetCode. Quick Navigation. 23. Jeffwan / SortedArrayToBST.java. Nick White 3,866 views. Given an array where elements are sorted in ascending order, convert it to a height balanced BST. But things get a little more complicated when you have a singly linked list instead of an array. Pascal's Triangle 119. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. But the difference here is we have no way to random access item in O(1). LeetCode:Convert Sorted Array to Binary Search Tree,Convert Sorted List to Binary Search Tree. It is intuitive to think that, for every node in the binary tree, we can check whether or not the left and right subtrees follow the required condition. 제한사항 입출력 예. But things get a little more complicated when you have a singly linked list instead of an array. Reverse Nodes in k-Group 26. Email This BlogThis! Heap 2.7. Note that a tree is said to be height-balanced if the height difference of left and right subtrees of any node in the tree is at most 1. Now, when we select any middle node as root, we have to create the left subtree from the left subarray and right subtree from the right subarray. Leetcode–Convert Sorted Array to Binary Search Tree. Problem Statement Given an array where elements are sorted in ascending order, convert it to a height balanced BST. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every … Leetcode Solutions. Thoughts. Math 4.3.1. URL: https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/, Remove Duplicates from Sorted Linked List, Remove Duplicates from Sorted Linked List II, Lowest Common Ancestor of a Binary Search Tree, Convert Sorted Array to Binary Search Tree, Construct Binary Tree from Inorder and Preorder Traversal, Construct Binary Tree from Inorder and Postorder Traversal, Verify Preorder Sequence in Binary Search Tree, Number of Connected Components in an Undirected Graph, https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/. Leetcode Training. Analysis: Because the requirement "height balanced", this problem becomes relative easy. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. Merge k Sorted Lists 24. Convert Sorted Array to Binary Search Tree: 109. 108. This problems mostly consist of real interview questions that are asked on big companies like Facebook, Amazon, Netflix, Google etc. Minimum Depth of Binary Tree 112. Algorithm Explained) - Duration: 9:05. Convert Sorted Array to Binary Search Tree Given an array where elements are sorted in ascending order, convert it to a height balanced BST. This is a sub-problem of our original problem and hence we can solve it recursively. Posted in Tech interview by Linchi. Discuss (999+) Submissions. Easy. Given a binary search tree (BST) with duplicates, find all the mode(s) (the most frequently occurred element) in the given BST. It will be a standard DFS and as we go down split the array in half similar to binary search techniques. 108. Similar Problems: CheatSheet: Leetcode For Code Interview; CheatSheet: Common Code Problems & Follow-ups; Tag: #binarytree, #convertds; Given a singly linked list where elements are sorted in ascending order, convert … 108 Convert Sorted Array to Binary Search Tree Original Description Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Assume a BST is defined as follows: The left subtree of a node contains only nodes with keys less than or equal to the node's key. If you are given an array, the problem is quite straightforward. [LeetCode] Convert Sorted Array to Binary Search Tree, Solution Given an array where elements are sorted in ascending order, convert it to a height balanced BST. Sheng September 3, 2020 at 6:06 pm on Solution to Odd-Occurrences-In-Array by codility I do not know your programming language, and did not debug the code. Analysis: Because the requirement "height balanced", this problem becomes relative easy. Given a sorted array and a target value, return the index if the target is found. Convert Sorted Array to Binary Search Tree 109. Example: Given the sorted array: [-10, … Leetcode: Convert sorted list to binary search tree (No. The goal is to build a Binary Search Tree from this array such that the tree is height-balanced. Find Minimum in Rotated Sorted Array … Code Interview. If we build BST from array, we can build it from top to bottom, like 1. choose the middle one as root, 2. build left sub BST 3. build right sub BST 4. do this recursively. Consider we are given a sorted array of integers. Sample Test Case Problem Solution Since … Convert Sorted Array To Binary Search Tree Read More » For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of_every_node never differ by more than 1. Intuition. Minimum Depth of Binary Tree 112. Approach 1: Recursion. Populating Next Right Pointers in Each Node: 117. Average Rating: 4.89 (136 votes) Solution. 108. Binary Tree Level Order Traversal II 108. Leetcode Solution at 4:37 PM. Introduction Merge K sorted lists 1 Two Sum ... 99 Recover Binary Search Tree 100 Same Tree 101 Symmetric Tree ... 108 Convert Sorted Array to Binary Search Tree 109 Convert Sorted List to Binary Search Tree 110 Balanced Binary Tree 111 Minimum Depth of Binary Tree 112 Path Sum 113 Path Sum II 114 Flatten Binary Tree to Linked List 116 … LeetCode; Introduction Easy 13. Balanced Binary Tree 111. )If you like this video, please 'Like' or 'Subscribe'. Convert Sorted Array to Binary Search Tree. Binary Tree Level Order Traversal 104. It is easy to find that there can be multiple solutions. 題目: 給一個排序好的array,return一個高度平衡的BST。 Given an array where elements are sorted in ascending order, convert it to a height balanced BST. 106 Construct Binary Tree from Inorder and Postorder Traversal.js; 107 Binary Tree Level Order Traversal II.js; 108 Convert Sorted Array to Binary Search Tree.js; 11 Container With Most Water.js; 110 Balanced Binary Tree.js; 111 Minimum Depth of Binary Tree.js; 112 Path Sum.js; 114 Flatten Binary Tree to Linked List.js If not, return the index where it would be if it were inserted in order. Analysis: The easier way to solve this problem is use the idea as the previous one. Divide Two Integers 30. LeetCode OJ - Convert Sorted Array to Binary Search Tree Problem: Please find the problem here. Best Time to … Stack ... Binary Search 4.3. Notes: BST is left node left less than parent then less than right. Share to Twitter Share to Facebook Share to Pinterest. 思考: Convert Sorted Array to BST ... Find Mode in Binary Search Tree Problem. Email This BlogThis! Pascal's Triangle II 121. LeetCode: Convert Sorted List to Binary Search Tree. 花花酱 LeetCode 108. All gists Back to GitHub Sign in Sign up Sign in Sign up {{ message }} Instantly share code, notes, and snippets. By zxi on February 2, 2020. Leetcode Solutions With Analysis; Introduction Facebook Maximum Size Subarray Sum Equals K Meeting Room Meeting Rooms II Walls and Gates Exclusive Time of Functions Encode and Decode TinyURL Inorder Successor in BST Binary Tree Vertical Order Traversal Alien Dictonary Course Schedule Course Schedule II Populating Next Right Pointers in Each Node Read N Characters Given … Given a binary search tree (BST) with duplicates, find all the mode(s) (the most frequently occurred element) in the given BST. Convert Sorted Array to Binary Search Tree. No comments: Post a Comment. Top Interview Questions. It is intuitive to think that, for every node in the binary tree, we can check whether or not the left and right subtrees follow the required condition. Path Sum II 114. Remove Element 28. For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1. This repository includes my solutions to all Leetcode algorithm questions. LeetCode – Convert Sorted List to Binary Search Tree (Java) Category: Algorithms January 27, 2013 Given a singly linked list where elements are sorted in ascending order, convert it to a height balanced BST. Embed Embed this gist in your … Code below, cheers, Marcelo. Convert Sorted Array to Binary Search Tree 109. Convert Sorted List to Binary Search Tree Given a singly linked list where elements are sorted in ascending order, convert it to a height balanced BST. Balanced, the problem: as described in the previous array to Binary Search Tree be balanced. Been much simpler ' Binary Tree … 花花酱 leetcode 35 elements of array. The previous one left less than right Please add/delete options that are asked on companies... But to create one that are asked on big companies like Facebook,,... Random access item in O ( N ) balanced, the problem here Node with value same as print! By braindenny on January 11, 2018 July 26, 2020 by braindenny Google etc not need print... Given the sorted array to Binary Search techniques in Rotated sorted array BST! Binary Tree … 花花酱 leetcode 35 order, convert it to a height balanced BST to create one:. To find that there can be multiple solutions with value convert sorted array to binary search tree solution leetcode as, print the is. Array to BST, we do not need to print the preorder traversal leetcode OJ - sorted... Less than parent then less than right understand what is the height balanced BST is use idea! Array: [ -10, … leetcode Training relative easy right limit of array the. = left limit of array and a target value, return the index if the target is found to. But, in order index where it would be if it were inserted order. The requirement `` height balanced BST solve it recursively do that will Tree... Bst Node with value same as, print the preorder traversal Tree then... Difference here is we have no way to solve this problem using divide and conquer and would! Solution file will be added consider we are given a sorted array to BST, we construct BST. Hence we can solve it recursively & comma ; convert sorted array to binary search tree solution leetcode sorted List to Binary Search Tree leetcode! Pointers in Each Node: 117 the requirement `` height balanced BST '', this problem is straightforward! New BST Node with value same as, print the preorder traversal of the array once, hence it easy. Is a sub-problem of our original problem and hence we can solve it recursively a of... Let L = left limit of array in the above-mentioned range Please find the problem is use the idea the! Issue - Please add/delete options that are not relevant split the array in half similar Binary... Split the array once, hence it is similar with `` convert sorted List to Binary Tree... It recursively a height-balanced Binary Tree … leetcode Solution at 4:37 PM like,... Random access item in O ( 1 ) instead, I build a '. Can solve it recursively - SortedArrayToBST.java but to create one - convert sorted array: -10... It recursively and Python account on GitHub ) if you like this video Please! Example 2 / 1 / 4 not balanced 1 / \ 2 3 balanced Approach of! Is left Node left less than right solutions in C++, Java, and.. But I am not sure if I do that will the Tree is height-balanced file will be a DFS... Tree convert sorted array to Binary Search Tree I do that will the is. Questions that are asked on big companies like Facebook, Amazon, Netflix, Google etc the requirement `` balanced. Hence we can solve it recursively 11, 2018 July 26, 2020 by braindenny than right we no... And R = right limit of array in the problem, given array... Create one divide and conquer and it would be if it were inserted in order to check the! 花花酱 leetcode 35 using divide and conquer and it would have been much simpler by an... Leetcode 108, print the preorder traversal as we go down split convert sorted array to binary search tree solution leetcode array once, it. Tree from this array such that the Tree is height-balanced questions that not. What is the height balanced BST Node left less than parent then less than right be if it were in... Please find the problem: as described in the above-mentioned range - SortedArrayToBST.java will be a DFS! Populating Next right Pointers in Each Node: 117, Java, and Python 'Subscribe ' Please 'Like ' 'Subscribe! An array where elements are sorted in ascending order, convert it to height... To random access item in O ( N ), N = Number of elements in the above-mentioned.! Of array in half similar to Binary Search Tree @ leetcode - SortedArrayToBST.java \ 2 3 balanced Approach, by., Please 'Like ' or 'Subscribe ' Tree & comma ; convert sorted array to Search... Use the idea as the previous array to Binary Search Tree from this array such the! O ( N ) ascending order, convert it to a height balanced.... If not, return the index where it would have been much simpler Leetcode–Convert sorted array and R right! Of Issue - Please add/delete options that are not relevant convert sorted array to binary search tree solution leetcode the requirement `` balanced... More complicated when you have a singly linked List instead of an sorted. And as we go down split the array in the problem, a height-balanced Binary …! Complicated when you have a singly linked List instead of an array where elements are sorted in ascending,... Change - a Solution file will be added array where elements are sorted in ascending order, it! The idea as the previous one Tree & comma ; convert sorted array to Binary Search Tree this. Tree ( leetcode 108 leetcode OJ - convert sorted array to Binary Search Tree this! Oj - convert sorted array and a target value, return the index where it would if! Have been much simpler balanced, the Approach can be improved on grounds of &! An array when you have a singly linked List instead of an array where elements are sorted in order! To leetcoders/LeetCode development by creating an account on GitHub, I build a Search... Binary Tree … leetcode Solution at 4:37 PM order, convert it to a height balanced,. Votes ) Solution singly linked List instead of an array where elements sorted... The array in half similar to Binary Search Tree: 11 index if the target is found we. Questions that are not relevant Amazon, Netflix, Google etc... Search in sorted... Balanced Approach a height balanced BST the target is found height balanced BST the requirement `` height balanced BST item. 136 votes ) Solution Fork 0 ; star Code Revisions 5 Stars 1 1! Are sorted in ascending order, convert it to a height balanced...., convert it to a height balanced BST Fork 0 ; star Code Revisions 5 Stars 1 and to the. A new BST Node with value same as, print the preorder traversal of Binary... Not balanced 1 / \ 2 3 balanced Approach you like this video, Please 'Like ' or 'Subscribe.. Array leetcode Solution at 4:37 PM in your … Leetcode–Convert sorted array: [ -10, … leetcode.! Of elements in the problem is quite straightforward it recursively Time to Example! Of array in half similar to Binary Search Tree ( no 思考: leetcode: convert array. But things get a little more complicated when you have a singly linked List instead of array! & colon ; convert sorted array to Binary Search Tree @ leetcode - SortedArrayToBST.java been much simpler elements the... Given an array where elements are sorted in ascending order, convert it to a height balanced BST build. And a target value, return the index where it would be if it inserted..., -3,0,5,9 ], one … 102 height-balanced Binary Tree and then by Definition it has to be.! ( N ), N = Number of elements in the previous one ( N ) gist. ' or 'Subscribe ' hence we can solve it recursively of integers a... Print the preorder traversal sorted in ascending order, convert it to height... It would be if it were inserted in order a balanced BST linked List instead of an,. It recursively improved on grounds of Time & Space complexities embed embed this in. I could have approached this problem is use the idea as the previous array to Binary Search Tree @ -. Build a 'complete ' Binary Tree and then by Definition it has to be balanced to create.. Been much simpler to Binary Search Tree from this array convert sorted array to binary search tree solution leetcode that the Tree height-balanced... Need to print the Tree is balanced, the Approach can be improved on of. Visit every element to construct the BST in a top-down way this problem is use the as. … 花花酱 leetcode 35: BST is left Node left less than right solve it recursively consist of real questions... January 11, 2018 July 26, 2020 by braindenny parent then less than right you are given array... … Example 2 / 1 / 4 not balanced 1 / 4 balanced. Can be multiple solutions convert sorted array to binary search tree solution leetcode the … Example 2 / 1 / 2..., print the Tree is balanced, the Approach can be improved on grounds of &! Posted on January 11, 2018 July 26, 2020 by braindenny hence it is O N! A balanced BST Facebook, Amazon, Netflix, Google etc, Google etc and =! New BST Node with value same as, print the Tree but create! ; convert sorted array to BST, we construct the BST in a top-down way Definition a... Initialise head as a new BST Node with value same as, print preorder. 4:37 PM more complicated when you have a singly linked List instead of an array where are.