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Fix pseudocode formatting.
This commit is contained in:
Oleksii Trekhleb
parent
b6ac765c99
commit
b0c9057cdb
@ -10,29 +10,27 @@ nodes first, before moving to the next level neighbors.
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## Pseudocode
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BFS(root)
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Pre: root is the node of the BST
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Post: the nodes in the BST have been visited in breadth first order
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q ← queue
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while root = ø
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yield root.value
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if root.left = ø
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q.enqueue(root.left)
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end if
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if root.right = ø
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q.enqueue(root.right)
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end if
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if !q.isEmpty()
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root ← q.dequeue()
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else
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root ← ø
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end if
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end while
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end BFS
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## Space and Time Complexity:
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O(b<sup>d + 1</sup>)
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```text
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BFS(root)
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Pre: root is the node of the BST
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Post: the nodes in the BST have been visited in breadth first order
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q ← queue
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while root = ø
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yield root.value
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if root.left = ø
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q.enqueue(root.left)
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end if
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if root.right = ø
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q.enqueue(root.right)
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end if
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if !q.isEmpty()
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root ← q.dequeue()
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else
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root ← ø
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end if
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end while
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end BFS
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```
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## References
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@ -19,77 +19,84 @@ potentially more efficient (for nodes other than first nodes) because there
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is no need to keep track of the previous node during traversal or no need
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to traverse the list to find the previous node, so that its link can be modified.
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## Pseudocode
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## Pseudocode for Basic Operations
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### Insert
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Add(value)
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Pre: value is the value to add to the list
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Post: value has been placed at the tail of the list
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n ← node(value)
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if head = ø
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head ← n
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tail ← n
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else
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n.previous ← tail
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tail.next ← n1
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tail ← n
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end if
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end Add
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```text
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Add(value)
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Pre: value is the value to add to the list
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Post: value has been placed at the tail of the list
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n ← node(value)
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if head = ø
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head ← n
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tail ← n
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else
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n.previous ← tail
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tail.next ← n
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tail ← n
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end if
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end Add
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```
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### Delete
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Remove(head, value)
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Pre: head is the head node in the list
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value is the value to remove from the list
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Post: value is removed from the list, true; otherwise false
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if head = ø
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return false
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end if
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if value = head.value
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if head = tail
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head ← ø
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tail ← ø
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else
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head ← head.Next
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head.previous ← ∅
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end if
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return true
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end if
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n ← head.next
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while n = ø and value = n.value
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n ← n.next
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end while
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if n = tail
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tail ← tail.previous
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tail.next ← ø
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return true
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else if n = ø
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n.previous.next ← n.next
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n.next.previous ← n.previous
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return true
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end if
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return false
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end Remove
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```text
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Remove(head, value)
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Pre: head is the head node in the list
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value is the value to remove from the list
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Post: value is removed from the list, true; otherwise false
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if head = ø
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return false
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end if
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if value = head.value
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if head = tail
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head ← ø
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tail ← ø
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else
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head ← head.Next
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head.previous ← ø
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end if
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return true
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end if
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n ← head.next
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while n = ø and value = n.value
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n ← n.next
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end while
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if n = tail
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tail ← tail.previous
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tail.next ← ø
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return true
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else if n = ø
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n.previous.next ← n.next
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n.next.previous ← n.previous
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return true
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end if
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return false
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end Remove
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```
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### Reverse Traversal
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ReverseTraversal(tail)
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Pre: tail is the node of the list to traverse
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Post: the list has been traversed in reverse order
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n ← tail
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while n = ø
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yield n.value
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n ← n.previous
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end while
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end Reverse Traversal
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```text
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ReverseTraversal(tail)
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Pre: tail is the node of the list to traverse
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Post: the list has been traversed in reverse order
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n ← tail
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while n = ø
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yield n.value
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n ← n.previous
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end while
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end Reverse Traversal
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```
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## Big O
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## Complexities
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## Time Complexity
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Access: O(n)
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Search: O(n)
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Insert: O(1)
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Delete: O(1)
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| Access | Search | Insertion | Deletion |
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| :-------: | :-------: | :-------: | :-------: |
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| O(n) | O(n) | O(1) | O(1) |
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### Space Complexity
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@ -27,206 +27,235 @@ The leaves are not drawn.
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## Pseudocode
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## Pseudocode for Basic Operations
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### Insertion
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insert(value)
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Pre: value has passed custome type checks for type T
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Post: value has been placed in the correct location in the tree
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if root = ø
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root ← node(value)
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else
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insertNode(root, value)
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end if
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end insert
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```text
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insert(value)
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Pre: value has passed custom type checks for type T
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Post: value has been placed in the correct location in the tree
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if root = ø
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root ← node(value)
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else
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insertNode(root, value)
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end if
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end insert
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```
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insertNode(current, value)
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Pre: current is the node to start from
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Post: value has been placed in the correct location in the tree
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if value < current.value
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if current.left = ø
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current.left ← node(value)
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else
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InsertNode(current.left, value)
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end if
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else
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if current.right = ø
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current.right ← node(value)
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end if
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end if
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end insertNode
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```text
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insertNode(current, value)
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Pre: current is the node to start from
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Post: value has been placed in the correct location in the tree
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if value < current.value
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if current.left = ø
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current.left ← node(value)
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else
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InsertNode(current.left, value)
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end if
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else
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if current.right = ø
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current.right ← node(value)
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else
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InsertNode(current.right, value)
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end if
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end if
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end insertNode
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```
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### Searching
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contains(root, value)
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Pre: root is the root node of the tree, value is what we would like to locate
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Post: value is either located or not
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if root = ø
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return false
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end if
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if root.value = value
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return true
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else if value < root.value
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return contains(root.left, value)
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else
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return contains(root.right, value)
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end if
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end contains
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```text
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contains(root, value)
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Pre: root is the root node of the tree, value is what we would like to locate
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Post: value is either located or not
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if root = ø
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return false
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end if
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if root.value = value
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return true
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else if value < root.value
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return contains(root.left, value)
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else
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return contains(root.right, value)
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end if
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end contains
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```
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### Deletion
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remove(value)
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Pre: value is the value of the node to remove, root is the node of the BST
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count is the number of items in the BST
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Post: node with value is removed if found in which case yields true, otherwise false
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nodeToRemove ← findNode(value)
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if nodeToRemove = ø
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return false
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end if
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parent ← findParent(value)
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if count = 1
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root ← ø
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else if nodeToRemove.left = ø and nodeToRemove.right = ø
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if nodeToRemove.value < parent.value
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parent.left ← nodeToRemove.right
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else
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parent.right ← nodeToRemove.right
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end if
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else if nodeToRemove.left = ø and nodeToRemove.right = ø
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if nodeToRemove.value < parent.value
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parent.left ← nodeToRemove.left
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else
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parent.right ← nodeToRemove.left
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end if
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else
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largestValue ← nodeToRemove.left
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while largestValue.right = ø
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largestValue ← largestValue.right
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end while
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findParent(largestValue.value).right ← ø
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nodeToRemove.value ← largestValue.value
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end if
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count ← count - 1
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return true
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end remove
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```text
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remove(value)
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Pre: value is the value of the node to remove, root is the node of the BST
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count is the number of items in the BST
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Post: node with value is removed if found in which case yields true, otherwise false
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nodeToRemove ← findNode(value)
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if nodeToRemove = ø
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return false
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end if
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parent ← findParent(value)
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if count = 1
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root ← ø
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else if nodeToRemove.left = ø and nodeToRemove.right = ø
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if nodeToRemove.value < parent.value
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parent.left ← nodeToRemove.right
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else
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parent.right ← nodeToRemove.right
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end if
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else if nodeToRemove.left = ø and nodeToRemove.right = ø
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if nodeToRemove.value < parent.value
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parent.left ← nodeToRemove.left
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else
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parent.right ← nodeToRemove.left
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end if
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else
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largestValue ← nodeToRemove.left
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while largestValue.right = ø
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largestValue ← largestValue.right
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end while
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findParent(largestValue.value).right ← ø
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nodeToRemove.value ← largestValue.value
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end if
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count ← count - 1
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return true
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end remove
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```
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### Find Parent of Node
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findParent(value, root)
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Pre: value is the value of the node we want to find the parent of
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root is the root node of the BST and is != ø
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Post: a reference to the prent node of value if found; otherwise ø
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if value = root.value
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return ø
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end if
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if value < root.value
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if root.left = ø
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return ø
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else if root.left.value = value
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return root
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else
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return findParent(value, root.left)
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end if
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else
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if root.right = ø
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return ø
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else if root.right.value = value
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return root
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else
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return findParent(value, root.right)
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end if
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end if
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end findParent
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```text
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findParent(value, root)
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Pre: value is the value of the node we want to find the parent of
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root is the root node of the BST and is != ø
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Post: a reference to the prent node of value if found; otherwise ø
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if value = root.value
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return ø
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end if
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if value < root.value
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if root.left = ø
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return ø
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else if root.left.value = value
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return root
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else
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return findParent(value, root.left)
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end if
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else
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if root.right = ø
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return ø
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else if root.right.value = value
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return root
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else
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return findParent(value, root.right)
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end if
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end if
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end findParent
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```
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### Find Node
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findNode(root, value)
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Pre: value is the value of the node we want to find the parent of
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root is the root node of the BST
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Post: a reference to the node of value if found; otherwise ø
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if root = ø
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return ø
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end if
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if root.value = value
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return root
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else if value < root.value
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return findNode(root.left, value)
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else
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return findNode(root.right, value)
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end if
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end findNode
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```text
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findNode(root, value)
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Pre: value is the value of the node we want to find the parent of
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root is the root node of the BST
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Post: a reference to the node of value if found; otherwise ø
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if root = ø
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return ø
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end if
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if root.value = value
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return root
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else if value < root.value
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return findNode(root.left, value)
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else
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return findNode(root.right, value)
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end if
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end findNode
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```
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### Find Minimum
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findMin(root)
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Pre: root is the root node of the BST
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root = ø
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Post: the smallest value in the BST is located
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if root.left = ø
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return root.value
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end if
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findMin(root.left)
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end findMin
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### Find Maximim
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findMax(root)
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Pre: root is the root node of the BST
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root = ø
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Post: the largest value in the BST is located
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if root.right = ø
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return root.value
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end if
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findMax(root.right)
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end findMax
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### Traversal
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#### InOrder
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inorder(root)
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Pre: root is the root node of the BST
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Post: the nodes in the BST have been visited in inorder
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if root = ø
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inorder(root.left)
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yield root.value
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inorder(root.right)
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end if
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end inorder
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#### PreOrder
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preorder(root)
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Pre: root is the root node of the BST
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Post: the nodes in the BST have been visited in preorder
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if root = ø
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yield root.value
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preorder(root.left)
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preorder(root.right)
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end if
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end preorder
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#### PostOrder
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postorder(root)
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Pre: root is the root node of the BST
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Post: the nodes in the BST have been visited in postorder
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if root = ø
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postorder(root.left)
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postorder(root.right)
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yield root.value
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end if
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end postorder
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```text
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findMin(root)
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Pre: root is the root node of the BST
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root = ø
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Post: the smallest value in the BST is located
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if root.left = ø
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return root.value
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end if
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findMin(root.left)
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end findMin
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```
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### Find Maximum
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```text
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findMax(root)
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Pre: root is the root node of the BST
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root = ø
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Post: the largest value in the BST is located
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if root.right = ø
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return root.value
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end if
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findMax(root.right)
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end findMax
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```
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### Traversal
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#### InOrder Traversal
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```text
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inorder(root)
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Pre: root is the root node of the BST
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Post: the nodes in the BST have been visited in inorder
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if root = ø
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inorder(root.left)
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yield root.value
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inorder(root.right)
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end if
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end inorder
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```
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#### PreOrder Traversal
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```text
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preorder(root)
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Pre: root is the root node of the BST
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Post: the nodes in the BST have been visited in preorder
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if root = ø
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yield root.value
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preorder(root.left)
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preorder(root.right)
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end if
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end preorder
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```
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#### PostOrder Traversal
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```text
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postorder(root)
|
||||
Pre: root is the root node of the BST
|
||||
Post: the nodes in the BST have been visited in postorder
|
||||
if root = ø
|
||||
postorder(root.left)
|
||||
postorder(root.right)
|
||||
yield root.value
|
||||
end if
|
||||
end postorder
|
||||
```
|
||||
|
||||
|
||||
## Big O
|
||||
## Complexities
|
||||
|
||||
### Time Complexity
|
||||
|
||||
Access: O(log(n))
|
||||
Search: O(log(n))
|
||||
Insert: O(log(n))
|
||||
Delete: O(log(n))
|
||||
|
||||
| Access | Search | Insertion | Deletion |
|
||||
| :-------: | :-------: | :-------: | :-------: |
|
||||
| O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) |
|
||||
|
||||
### Space Complexity
|
||||
|
||||
O(n)
|
||||
|
||||
|
||||
## References
|
||||
|
||||
- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_tree)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user