Binary Search Tree

Binary Search treeInsertion, Search and Deletion operation and BST sort

Team Members
Israt Jahan Fateha (151-15-5036)
Md. Eyakub Sorkar (151-15-4674)
Mehedi Imam Shafi (151-15-5248)
Sajiya (151-15-5256)
Sanjida Tasnim (143-15-4397)

Condition for a binary tree to be a BST
Left child is smaller than parent
Right child is greater than parent

55
45 65
58 675335
Example of binary search tree

Basic Operations
• Insertion
• Search
• Deletion
• Traversal
• Sort

 There are three rules before we go to the binary insertion search. The first rule is , A parent node
should not have more than two children. If it does, it is not binary search tree. The second rule is,
the value of parent is always greater than the right child. And the third rule is, the value of parent
is always smaller than the left child.
40
8010

Binary search tree insertion
Key is 6
inserted
10
-5 16
-8 7 18
6

Key is 17
inserted
10
-5 16
-8 7 18
6 17

Key is 19
inserted
10
15
16
18
19

Time complexity
How much time doe it take to insertion into binary search tree. The worst case, the time it takes
to insert into binary search tree is O(n). Its possible all the nodes have just one child and they are
linear like this one and the worst case here will be O(n).
10
15
16
18
19

Time complexity
If the tree is a balanced tree, the worst case to insert into such kind of tree is O(log(n)).
10
-5 16
-8 7 18
6 17

65
9
-4 5
4
5 is less than 6
go to the left child
5 is more than 4
go to the right child
Searched value has
been found

Algorithm:
Here k is the key that is searched for and x is the start
node.
BST-Search(x, k)
1. y ← x
2. while y ≠ nil do
3. if key[y] = k then return y
4. else if key[y] < k then y ← right[y]
5. else y ← left[y]
6. return (“NOT FOUND”)

CODE in C++:
bool BinarySearchTree::search( int value) {
if (root == NULL)
return false;
else
return root->search(value);
}
bool BSTNode::search( int value) {
if (value == this->value)
return true;
else if (value < this->value) {
if (left == NULL)
return false;
else
return left->search(value);
} else if (value > this->value) {
if (right == NULL)
return false;
else
return right->search(value);
}
return false;
}

Time Complexity of Searching in
Binary Search Tree
O( log(n) )O(n)

Deleting a node has no child:
5
182
-4 3
5
18
2
3

Deleting a node with one child:
5
-4
2
25
18
21
19
3
5
-4
2
19
21
253

Deleting a node with two children:
5
9
12
19
213-4
2
21
5
9
19
213-4
2
2519

Already sorted during the step of insertion

TraversalPre-order In-order Post-order

55
45 65
58 675335
In-order traversal: 35 45 53 55 58 65 67

55
45 65
58 675335
Pre-order traversal: 55 45 35 53 65 58 67

55
45 65
58 675335
Post-order: 35 53 45 58 67 65 55

Real Life Use of Binary Search Tree

References:
1. http://en.wikipedia.org/binary=search-tree/
2. http://geeksourceforge.com/bst-basic
3. http://github.com/cpp@master/binary-tree/bst.cpp
4. https://www.quora.com/What-are-the-real-world-examples-of-binary-trees-not-search-tree
5. http://www.geeksforgeeks.org/618/

Thank You all
For being with us.

Binary Search Tree

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