tree data structure - OpenGenus IQ: Learn Computer Science

Interval Trees: One step beyond BST

Interval tree is a variant of BST and is able to handle intervals in logarithmic time for search, insert and delete operations and is used in geometry.

data structure

Persistent Segment Tree

Our aim is to introduce persistency in segment trees but also ensure that the space and time complexity is not affected.

data structure

Rope: the Data Structure used by text editors to handle large strings

Rope data structure is widely used by software such as text editors like Sublime, email systems like Gmail and text buffers to handle large strings efficiently.

data structure

Count inversions in an array using Fenwick Tree

Fenwick tree is usually used for range query problems but it can be used to solve the problem of finding the number of inversions in an array efficiently.

data structure

Understanding Fenwick tree (Binary Indexed Tree) with Range product

Fenwick tree is a tree based data structure that is widely used to solve range query problems in logarithmic time O(log N) which would otherwise have taken linear time O(N). In this article, we have explained it in depth using the range product query problem.

algorithm

Learn how to traverse a Binary Tree (Inorder , Preorder , Postorder)

In this article we will learn three Depth first traversals namely inorder, preorder and postorder and their use. These three types of traversals generally used in different types of binary tree. In summary, Inorder: left, root, right; Preorder: root, left, right and Postorder: left, right, root

data structure

Understand everything about Binary Search Tree

Binary search tree is a data structure that quickly allows us to maintain a sorted list of numbers in a tree data structure. It can be used to search for the presence of a number in O(log(n)) time and a simple traversal gives the numbers in sorted order.

data structure

Fibonacci Heap

A Fibonacci heap is a heap data structure similar to the binomial heap. It uses Fibonacci numbers and also used to implement the priority queue element in Dijkstra’s shortest path algorithm which reduces the time complexity from O(m log n) to O(m + n log n)

data structure

Binary Tree

A binary tree is a tree data structure in which each node has upto two children (that is a maximum of two children nodes), which are referred to as the left child and the right child. Implementation and applications of binary tree

data structure

Max Heap and Min Heap

A min heap is a heap where every single parent node, including the root, is less than or equal to the value of its children nodes. The most important property of a min heap is that the node with the smallest, or minimum value, will always be the root node. Max heap is similar

data structure

K Dimensional Tree / (K D Tree)

K Dimensional tree (or k-d tree) is a tree data structure that is used to represent points in a k-dimensional space. It is used for various applications like nearest point (in k-dimensional space), efficient storage of spatial data, range search. We implemented it in C++ and explained the operations

data structure

Octree data structure

Octree is a tree data structure where each internal node has 8 children. An octree is generally used to represent relation between objects in a 3-dimensional space. It is used in 3D computer graphics. Octrees are also used for nearest neighbor search which can be done easily in logarithmic time.

data structure

Palindromic Tree (Eertree)

Palindromic tree (Eertree) is a tree based data structure that is specifically used to tackle problems involving palindromes of a string like 'longest palindrome in a string', 'count of plaindromic substrings'. It keeps track of all palindromic substrings of a string in linear time and space

data structure

Fusion Tree

Fusion tree is a tree data structure that implements associative array in a known universe size. Fusion trees are used to solve predecessor and successor problem. We have covered sketch, parallel comparison, predecessor and successor and insert operations in O(log N) time and O(N) space complexity

data structure

Quadtree

Quadtree is a tree data structure which is used to represent 2-dimensional space. It finds major applications in computer graphics where it is used to represent relations between objects in a 2D space and for image compression. We discussed point region (PR) quadtree which store points in a 2D space

data structure

Y fast trie

Y-fast trie is a data structure used to store integers from a bounded domain. It has two data structures X fast trie and balanced binary search tree with the change being we operate on representative values r in X-fast tries, and the leaf nodes point to balanced binary search trees instead of values

data structure

X-fast trie

X-fast trie is a data structure used to store integers from a bounded domain. It is a bitwise trie, i.e. a binary tree where each subtree stores values having binary representations with common prefix. It is a trie of hash tables and supports successor and predecessor operations in log log U time

data structure

Treap / Randomized cartesian tree

A treap is a height balanced binary tree with heap properties. It is used to store a sequence in a tree, which allows for various applications like searching. It takes O(log N) time complexity for search, insert and delete operations and takes O(N) space complexity

data structure

Cartesian Tree

A Cartesian tree is a binary rooted tree data structure that can answer range queries can be answered by finding least common ancestors in the tree. An inorder traversal of the tree would give the original sequence used to form the tree. It is used as binary search tree for an ordered sequence

data structure

2D Fenwick Tree / 2D Binary Indexed Tree

Fenwick Tree is used to answer range or interval queries in an array in logarithmic time. Fenwick tree can be generalized to multiple dimensions. 2D Fenwick tree is one such implementation used to answer sub-matrix queries, i.e. queries in 2 dimensions. It requires the operation to be invertible.

data structure

2D Segment Tree

Segment Tree is used to answer range queries in an array. The data structure can be extended to 2 dimensions to answer sub-matrix queries in logarithmic time. Some examples of these queries are Maximum element in sub-matrix It can be seen as a segment tree of segment trees. We give an example for it

data structure

Fenwick Tree (Binary Indexed Tree)

Fenwick Tree / Binary indexed tree (BIT) is a data structure used to process interval/range based queries. Compared to segment tree data structure, Fenwick tree uses less space and is simpler to implement. One disadvantage is that it can be only used with an operation that is invertible.

data structure

Segment Tree

A segment tree is a divide and conquer based data structure used to store information about intervals of some linear data structure. It is a height-balanced binary tree where every node corresponds to an interval of the array. It allows processing interval or range queries in logarithmic time

data structure

Trie data structure

A trie (digital tree, radix tree, prefix tree) is a kind of an ordered search tree data structure that is used to store a dynamic set or associative array where the keys are usually strings. Worst case search time complexity is Θ(key_length) and trie is widely used in real life applications

data structure

B-Tree Deletion

A B-tree is a tree data structure that keeps data sorted and allows searches, insertions, and deletions in logarithmic amortized time. Deletion in a B Tree is similar to insertion. At first the node from which a value is to be deleted is searched. If found out, then the value is deleted.