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Update README.md (trekhleb#165)
Add Pseudocode and Big O
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‎src/data-structures/tree/binary-search-tree/README.md‎

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@@ -27,6 +27,206 @@ The leaves are not drawn.
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![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg)
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## Pseudocode
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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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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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### 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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### 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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### 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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### 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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### 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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## Big O
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### Time Complexity
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Access: O(log(n))
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Search: O(log(n))
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Insert: O(log(n))
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Delete: O(log(n))
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### Space Complexity
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O(n)
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## References
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- [Wikipedia](https://en.wikipedia.org/wiki/Binary_search_tree)

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