A segment tree is a data structure used to effectively query and update ranges of array members. It’s typically implemented as a binary tree, with each node representing a segment or range of array elements.
Segment tree
Characteristics of Segment Tree:
- A segment tree is a binary tree with a leaf node for each element in the array.
- Each internal node represents a segment or a range of elements in the array.
- The root node represents the entire array.
- Each node stores information about the segment it represents, such as the sum or minimum of the elements in the segment.
Types of Segment tree:
Based on the type of information stored in the nodes, the tree can be divided into the following few types:
- Sum segment tree: It stores the sum of elements in each segment of the array and is used in a problem where efficient answer queries are needed about the sum of elements.
- Min/Max segment tree: It basically stores the minimum or maximum element in each segment of the array.
- Range update segment tree / Lazy Tree: It allows you to update a range of array elements with a given value. It is used to efficiently update a range of array elements.
Applications of Segment Tree:
- In finding the sum or minimum or maximum of a range of elements in an array.
- In finding the number of elements in a range that satisfy a certain condition, such as being greater than a certain value.
- It can be used in several problems of computational geometry.
To learn more about applications of segment tree, refer to this article.
Advantages of Segment Tree:
- It allows efficient querying and updating of ranges of elements in an array.
- It can help in solving a wide range of problems that involve a range of queries or updates.
- It has a time complexity of O(logN) for both query and update operations where N is the number of nodes in the tree.
To learn more about advantages of segment tree, refer to this article.
Disadvantages of Segment Tree:
- It requires additional memory to store the tree structure and information about the segments
- It may not be the most optimal solution for certain problems.
To learn more about the disadvantages of segment tree, refer to this article.