Difference between binary tree and binary search tree

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Can anyone please explain the difference between binary tree and binary search tree with an example

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A binary tree is a tree whose children are never more than two  A binary search tree follows the invariant that the left child should have a smaller value than the root node s key  while the right child should have a greater value than the root node s key

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In a Binary search tree  all the nodes are arranged in a specific order - nodes to the left of a root node have a smaller value than its root  and all the nodes to the right of a node have values greater than the value of the root

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Binary tree  Tree where each node has up to two leaves    1      2   3     Binary search tree  Used for searching  A binary tree where the left child contains only nodes with values less than the parent node  and where the right child only contains nodes with values greater than or equal to the parent     2      1   3

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A binary tree is made of nodes  where each node contains a  left  pointer  a  right  pointer  and a data element  The  root  pointer points to the topmost node in the tree  The left and right pointers recursively point to smaller  subtrees  on either side  A null pointer represents a binary tree with no elements -- the empty tree  The formal recursive definition is  a binary tree is either empty  represented by a null pointer   or is made of a single node  where the left and right pointers  recursive definition ahead  each point to a binary tree   A binary search tree  BST  or  ordered binary tree  is a type of binary tree where the nodes are arranged in order  for each node  all elements in its left subtree are less to the node   lt    and all the elements in its right subtree are greater than the node               5          3   6           1   4   9       The tree shown above is a binary search tree -- the  root  node is a 5  and its left subtree nodes  1  3  4  are  lt  5  and its right subtree nodes  6  9  are   5  Recursively  each of the subtrees must also obey the binary search tree constraint  in the  1  3  4  subtree  the 3 is the root  the 1  lt  3 and 4   3    Watch out for the exact wording in the problems -- a  binary search tree  is different from a  binary tree

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Binary tree   Binary tree can be anything which has 2 child and 1 parent  It can be implemented as linked list or array  or with your custom API  Once you start to add more specific rules into it  it becomes more specialized tree  Most common known implementation is that  add smaller nodes on left and larger ones on right   For example  a labeled binary tree of size 9 and height 3  with a root node whose value is 2  Tree is unbalanced and not sorted  https   en wikipedia org wiki Binary tree    For example  in the tree on the left  A has the 6 children  B C D E F G   It can be converted into the binary tree on the right     Binary Search   Binary Search is technique algorithm which is used to find specific item on node chain  Binary search works on sorted arrays   Binary search compares the target value to the middle element of the array  if they are unequal  the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful or the remaining half is empty  https   en wikipedia org wiki Binary search algorithm    A tree representing binary search  The array being searched here is  20  30  40  50  90  100   and the target value is 40     Binary search tree   This is one of the implementations of binary tree  This is specialized for searching   Binary search tree and B-tree data structures are based on binary search   Binary search trees  BST   sometimes called ordered or sorted binary trees  are a particular type of container  data structures that store  items   such as numbers  names etc   in memory  https   en wikipedia org wiki Binary search tree  A binary search tree of size 9 and depth 3  with 8 at the root  The leaves are not drawn     And finally great schema for performance comparison of well-known data-structures and algorithms applied     Image taken from Algorithms  4th Edition

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A tree can be called as a binary tree if and only if the maximum number of children of any of the nodes is two   A tree can be called as a binary search tree if and only if the maximum number of children of any of the nodes is two and the left child is always smaller than the right child

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Binary Tree stands for a data structure which is made up of nodes that can only have two children references   Binary Search Tree  BST  on the other hand  is a special form of Binary Tree data structure where each node has a comparable value  and smaller valued children attached to left and larger valued children attached to the right   Thus  all BST s are Binary Tree however only some Binary Tree s may be also BST  Notify that BST is a subset of Binary Tree   So  Binary Tree is more of a general data-structure than Binary Search Tree  And also you have to notify that Binary Search Tree is a sorted tree whereas there is no such set of rules for generic Binary Tree   Binary Tree  A Binary Tree which is not a BST            5                                 9       2                   15   17  19  21   Binary Search Tree  sorted Tree   A Binary Search Tree which is also a Binary Tree            50                                   25      75                    20    30 70   80   Binary Search Tree Node property  Also notify that for any parent node in the BST    All the left nodes have smaller value than the value of the parent node  In the upper example  the nodes with values   20  25  30   which are all located on the left  left descendants  of 50  are smaller than 50  All the right nodes have greater value than the value of the parent node   In the upper example  the nodes with values   70  75  80   which are all located on the right  right descendants  of 50  are greater than 50    There is no such a rule for Binary Tree Node  The only rule for Binary Tree Node is having two childrens so it self-explains itself that why called binary

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To check wheather or not a given Binary Tree is Binary Search Tree here s is an Alternative Approach    Traverse Tree In Inorder Fashion  i e  Left Child --  Parent --  Right Child     Store Traversed Node Data in a temporary Variable lets say temp   just before storing into temp   Check wheather current Node s data is higher then previous one or not   Then just break it out   Tree is not Binary Search Tree else traverse untill end   Below is an example with Java   public static boolean isBinarySearchTree Tree root        if root  null          return false       isBinarySearchTree root left       if tree data lt temp          return false      else         temp tree data      isBinarySearchTree root right       return true      Maintain temp variable outside

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Binary search tree  when inorder traversal is made on binary tree  you get sorted values of inserted items Binary tree  no sorted order is found in any kind of traversal

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Binary Tree is a specialized form of tree with two child  left child and right Child   It is simply representation of data in Tree structure  Binary Search Tree  BST  is a special type of Binary Tree that follows following condition    left child node is smaller than its parent Node right child node is greater than its parent Node

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A binary search tree is a special kind of binary tree which exhibits the following property  for any node n  every descendant node s value in the left subtree of n is less than the value of n  and every descendant node s value in the right subtree is greater than the value of n

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As everybody above has explained about the difference between binary tree and binary search tree  i am just adding how to test whether the given binary tree is binary search tree   boolean b   new Sample   isBinarySearchTree n1  Integer MIN VALUE  Integer MAX VALUE                           public boolean isBinarySearchTree TreeNode node  int min  int max         if node    null                return true             boolean left   isBinarySearchTree node getLeft    min  node getValue         boolean right   isBinarySearchTree node getRight    node getValue    max        return left  amp  amp  right  amp  amp   node getValue   lt max   amp  amp   node getValue   gt  min        Hope it will help you  Sorry if i am diverting from the topic as i felt it s worth mentioning this here

[data-structures] Difference between binary tree and binary search tree

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