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Aya Bouchiha

Posted on • Updated on

# deletion in binary search tree

hi, this is part 5 of tree data structure, and the #day_17 of algorithms and data structure, In the last posts, we talked about the binary search tree, its advantages, disadvantages, time and space complexity of its basic operations such as searching, insertion, and also their implementation using python
In this post, we'll discuss deletion :)

## Deletion in the binary search tree

there are 3 cases in deletion in binary search tree (reference):

1. if the node to be deleted is the leaf, this is the easiest case, we will only remove it without moving anything :)
2. if the node to be deleted has one child, in this case, we will replace the child with the node and delete the child
3. if the node to be deleted has two children, in this case, we need to find a successor (the min of right sub-tree) or a predecessor (the max of left sub-tree), and copy it to the node to be deleted, then delete the successor (or the predecessor)

### Deletion implementation

before the implementation of deletion, we need to create a function that returns to us a successor.

#### getSuccessor function

``````def getSuccessor(currentNode):
while currentNode.left:
currentNode = currentNode.left
return currentNode
``````

#### Delete function

``````def delete(value: int, root):
"""
[code is from] => https://www.geeksforgeeks.org/binary-search-tree-set-2-delete/
"""
# if the tree is empty
if root is None:
return root
# if value is smaller than the root's value
if value < root.value:
root.left = delete(value , root.left)
# if value is greater than the root's value
elif(value > root.value):
root.right = delete(value, root.right)
else:
#! case1 or case2 (node has not children or has only one)
if root.left is None:
temp = root.right
root = None
return temp

elif root.right is None:
temp = root.left
root = None
return temp
#! case: node has 2 children
# getting  successor
temp = getSuccessor(root.right)
# Copy the  successor's value to the node's value
root.value = temp.value
# Delete the successor
root.right = delete(temp.value, root.right)
return root
``````