One Pager Cheat Sheet

• A Segment Tree is a special binary tree data structure used for storing information about segments or intervals, facilitating faster querying like finding the sum, minimum, or maximum of these intervals.
• A Segment Tree is a binary tree that provides summarized information about various segments of an array, allowing efficient responses to range queries; each node represents an array interval, storing aggregate information about that interval, and the tree is structured such that any sub-interval can be accessed in logarithmic time. The Segment Tree is built recursively, splitting intervals into halves represented by child nodes, and allows for quick queries and updates by traversing from the root node and updating from the leaf up. The Segment Tree stands out for its power and efficiency in complex data structures, offering logarithmic time complexities for both updates and queries, and flexibility for a variety of range-query problems.
• The SegmentTree class in Python includes an initialization function that prepares a tree of four times the size of the original array, and a build function that recursively constructs the segment tree; if at a leaf node, the function stores the array element, otherwise, it constructs left and right subtrees and stores their sum. This allows efficient querying of a range of values and updating of individual values in the segment tree.
• The query and update functions in the Segment Tree allow you to respectively retrieve the sum of the tree node values between two indices and adjust a tree node value, exemplified here with a bread rating system where bread slice ratings can be adjusted and their sum queried for.
• Segment Trees are an invaluable coding tool that simplify tasks involving array intervals, blending theory and practicality for more efficient coding.