From b55e79aed2fa35fc0c6b47cc24f4747bb712c95e Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Fri, 19 Aug 2022 19:20:48 +0200 Subject: [PATCH] Update BST image. --- .../tree/binary-search-tree/README.md | 56 +++++++++--------- .../tree/binary-search-tree/README.pt-BR.md | 19 +++--- .../images/binary-search-tree.jpg | Bin 0 -> 149145 bytes 3 files changed, 39 insertions(+), 36 deletions(-) create mode 100644 src/data-structures/tree/binary-search-tree/images/binary-search-tree.jpg diff --git a/src/data-structures/tree/binary-search-tree/README.md b/src/data-structures/tree/binary-search-tree/README.md index f3e448a9..d05a8915 100644 --- a/src/data-structures/tree/binary-search-tree/README.md +++ b/src/data-structures/tree/binary-search-tree/README.md @@ -3,32 +3,34 @@ _Read this in other languages:_ [_Português_](README.pt-BR.md) -In computer science, **binary search trees** (BST), sometimes called -ordered or sorted binary trees, are a particular type of container: -data structures that store "items" (such as numbers, names etc.) -in memory. They allow fast lookup, addition and removal of -items, and can be used to implement either dynamic sets of -items, or lookup tables that allow finding an item by its key +In computer science, **binary search trees** (BST), sometimes called +ordered or sorted binary trees, are a particular type of container: +data structures that store "items" (such as numbers, names etc.) +in memory. They allow fast lookup, addition and removal of +items, and can be used to implement either dynamic sets of +items, or lookup tables that allow finding an item by its key (e.g., finding the phone number of a person by name). -Binary search trees keep their keys in sorted order, so that lookup -and other operations can use the principle of binary search: -when looking for a key in a tree (or a place to insert a new key), -they traverse the tree from root to leaf, making comparisons to -keys stored in the nodes of the tree and deciding, on the basis -of the comparison, to continue searching in the left or right -subtrees. On average, this means that each comparison allows -the operations to skip about half of the tree, so that each -lookup, insertion or deletion takes time proportional to the -logarithm of the number of items stored in the tree. This is -much better than the linear time required to find items by key -in an (unsorted) array, but slower than the corresponding +Binary search trees keep their keys in sorted order, so that lookup +and other operations can use the principle of binary search: +when looking for a key in a tree (or a place to insert a new key), +they traverse the tree from root to leaf, making comparisons to +keys stored in the nodes of the tree and deciding, on the basis +of the comparison, to continue searching in the left or right +subtrees. On average, this means that each comparison allows +the operations to skip about half of the tree, so that each +lookup, insertion or deletion takes time proportional to the +logarithm of the number of items stored in the tree. This is +much better than the linear time required to find items by key +in an (unsorted) array, but slower than the corresponding operations on hash tables. A binary search tree of size 9 and depth 3, with 8 at the root. The leaves are not drawn. -![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg) +![Trie](./images/binary-search-tree.jpg) + +*Made with [okso.app](https://okso.app)* ## Pseudocode for Basic Operations @@ -45,7 +47,7 @@ insert(value) end if end insert ``` - + ```text insertNode(current, value) Pre: current is the node to start from @@ -84,8 +86,8 @@ contains(root, value) end if end contains ``` - - + + ### Deletion ```text @@ -186,7 +188,7 @@ findNode(root, value) end if end findNode ``` - + ### Find Minimum ```text @@ -200,7 +202,7 @@ findMin(root) findMin(root.left) end findMin ``` - + ### Find Maximum ```text @@ -214,7 +216,7 @@ findMax(root) findMax(root.right) end findMax ``` - + ### Traversal #### InOrder Traversal @@ -244,7 +246,7 @@ preorder(root) end if end preorder ``` - + #### PostOrder Traversal ```text @@ -258,7 +260,7 @@ postorder(root) end if end postorder ``` - + ## Complexities ### Time Complexity diff --git a/src/data-structures/tree/binary-search-tree/README.pt-BR.md b/src/data-structures/tree/binary-search-tree/README.pt-BR.md index 4565538a..1e717141 100644 --- a/src/data-structures/tree/binary-search-tree/README.pt-BR.md +++ b/src/data-structures/tree/binary-search-tree/README.pt-BR.md @@ -26,8 +26,9 @@ Uma pesquisa de árvore binária de tamanho 9 e profundidade 3, com valor 8 na raíz. As folhas não foram desenhadas. +![Trie](./images/binary-search-tree.jpg) -![Binary Search Tree](https://upload.wikimedia.org/wikipedia/commons/d/da/Binary_search_tree.svg) +*Made with [okso.app](https://okso.app)* ## Pseudocódigo para Operações Básicas @@ -44,7 +45,7 @@ insert(value) end if end insert ``` - + ```text insertNode(current, value) Pre: current is the node to start from @@ -83,8 +84,8 @@ contains(root, value) end if end contains ``` - - + + ### Remoção ```text @@ -185,7 +186,7 @@ findNode(root, value) end if end findNode ``` - + ### Encontrar Mínimo ```text @@ -199,7 +200,7 @@ findMin(root) findMin(root.left) end findMin ``` - + ### Encontrar Máximo ```text @@ -213,7 +214,7 @@ findMax(root) findMax(root.right) end findMax ``` - + ### Traversal #### Na Ordem Traversal (InOrder Traversal) @@ -243,7 +244,7 @@ preorder(root) end if end preorder ``` - + #### Pós Ordem Traversal (PostOrder Traversal) ```text @@ -257,7 +258,7 @@ postorder(root) end if end postorder ``` - + ## 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