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‎src/data-structures/tree/binary-search-tree/README.md‎

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_Read this in other languages:_
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[_Português_](README.pt-BR.md)
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In computer science, **binary search trees** (BST), sometimes called
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ordered or sorted binary trees, are a particular type of container:
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data structures that store "items" (such as numbers, names etc.)
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in memory. They allow fast lookup, addition and removal of
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items, and can be used to implement either dynamic sets of
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items, or lookup tables that allow finding an item by its key
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In computer science, **binary search trees** (BST), sometimes called
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ordered or sorted binary trees, are a particular type of container:
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data structures that store "items" (such as numbers, names etc.)
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in memory. They allow fast lookup, addition and removal of
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items, and can be used to implement either dynamic sets of
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items, or lookup tables that allow finding an item by its key
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(e.g., finding the phone number of a person by name).
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Binary search trees keep their keys in sorted order, so that lookup
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and other operations can use the principle of binary search:
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when looking for a key in a tree (or a place to insert a new key),
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they traverse the tree from root to leaf, making comparisons to
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keys stored in the nodes of the tree and deciding, on the basis
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of the comparison, to continue searching in the left or right
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subtrees. On average, this means that each comparison allows
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the operations to skip about half of the tree, so that each
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lookup, insertion or deletion takes time proportional to the
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logarithm of the number of items stored in the tree. This is
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much better than the linear time required to find items by key
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in an (unsorted) array, but slower than the corresponding
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Binary search trees keep their keys in sorted order, so that lookup
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and other operations can use the principle of binary search:
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when looking for a key in a tree (or a place to insert a new key),
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they traverse the tree from root to leaf, making comparisons to
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keys stored in the nodes of the tree and deciding, on the basis
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of the comparison, to continue searching in the left or right
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subtrees. On average, this means that each comparison allows
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the operations to skip about half of the tree, so that each
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lookup, insertion or deletion takes time proportional to the
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logarithm of the number of items stored in the tree. This is
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much better than the linear time required to find items by key
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in an (unsorted) array, but slower than the corresponding
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operations on hash tables.
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A binary search tree of size 9 and depth 3, with 8 at the root.
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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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![Trie](./images/binary-search-tree.jpg)
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*Made with [okso.app](https://okso.app)*
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## Pseudocode for Basic Operations
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end if
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end insert
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```
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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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end if
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end contains
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```
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### Deletion
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```text
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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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```text
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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.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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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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end if
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end postorder
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```
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## Complexities
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### Time Complexity

‎src/data-structures/tree/binary-search-tree/README.pt-BR.md‎

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na raíz.
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As folhas não foram desenhadas.
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![Trie](./images/binary-search-tree.jpg)
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![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg)
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*Made with [okso.app](https://okso.app)*
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## Pseudocódigo para Operações Básicas
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end if
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end insert
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```
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```text
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insertNode(current, value)
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end if
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end contains
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```
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### Remoção
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```text
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end if
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end findNode
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```
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### Encontrar Mínimo
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```text
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findMin(root.left)
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end findMin
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```
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### Encontrar Máximo
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```text
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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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#### Na Ordem Traversal (InOrder Traversal)
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end if
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end preorder
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```
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#### Pós Ordem Traversal (PostOrder Traversal)
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```text
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end if
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end postorder
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```
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## Complexidades
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### Complexidade de Tempo
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