A binary search tree is defined by the following properties: each node has a maximum of two children, the left child is always smaller than the parent node, and the right child is always larger than the parent node.

In a balanced binary search tree, the time complexity of searching for a specific element is O(log n), where n is the number of elements in the tree.

Depth-first search (DFS) is a recursive algorithm that traverses a binary tree by exploring each branch to its deepest node before backtracking.

A Huffman tree is used in data compression to represent characters with variable-length codes, reducing the size of the compressed data and improving the speed of data transmission.

A heap is a tree data structure that allows for efficient retrieval of the maximum or minimum element in O(1) time.

In a balanced binary search tree, the time complexity of inserting an element is O(log n), where n is the number of elements in the tree.

Dijkstra's algorithm is used to find the shortest path between two nodes in a weighted graph.

A spanning tree is a subset of a graph that connects all nodes with the minimum number of edges.

Prim's algorithm is used to find a minimum spanning tree in a weighted graph.

The time complexity of finding the minimum spanning tree using Prim's algorithm is O(E log V), where V is the number of vertices and E is the number of edges in the graph.

A directory tree is a tree data structure that is commonly used to represent a hierarchical structure, such as a file system.

A trie data structure is used to store strings in a way that allows for efficient retrieval, find the longest common substring among a set of strings, and perform spell checking.

Huffman's algorithm is used to construct a Huffman tree.

The time complexity of constructing a Huffman tree is O(n log n), where n is the number of elements in the tree.

A binary search tree (BST) is a type of tree data structure that allows for efficient searching and retrieval of data based on a key.