Lazy Propagation

What is Segment Tree?

Segment Tree is a data structure that stores data about range of elements in nodes as a tree. It is mostly used to handle range queries with updates in an efficient manner. For example, we can perform a range summation of an array between the range L to R while also modifying the array from range L to R all in log(N) time complexity....

Types of Operations:

The operations that the segment tree can perform must be binary and associative. Some of the examples of operations are:...

Applications of Segment Tree:

Interval scheduling: Segment trees can be used to efficiently schedule non-overlapping intervals, such as scheduling appointments or allocating resources. Range-based statistics: Segment trees can be used to compute range-based statistics such as variance, standard deviation, and percentiles. Image processing: Segment trees are used in image processing algorithms to divide an image into segments based on color, texture, or other attributes....

Basics of Segment Tree:

Segment Tree meaning in DSA Introduction to Segment Trees – Data Structure and Algorithm Tutorials Persistent Segment Tree Segment tree | Efficient implementation Iterative Segment Tree Range Sum and Update in Array : Segment Tree using Stack Dynamic Segment Trees Applications, Advantages and Disadvantages of Segment Tree...

Lazy Propagation:

Lazy Propagation in Segment Tree Lazy Propagation in Segment Tree | Set 2 Flipping Sign Problem...

Range Queries:

Queries to check if any non-repeating element exists within range [L, R] of an Array Range Minimum Query Querying maximum number of divisors that a number in a given range has Min-Max Range Queries in Array Range LCM Queries Number of primes in a subarray (with updates) Range query for Largest Sum Contiguous Subarray Range Queries for Longest Correct Bracket Subsequence Maximum Occurrence in a Given Range Queries to find maximum product pair in range with updates Range and Update Query for Chessboard Pieces String Range Queries to find the number of subsets equal to a given String Binary Array Range Queries to find the minimum distance between two Zeros Queries to evaluate the given equation in a range [L, R] Find element with maximum weight in given price range for Q queries...

Some interesting problem on Segment Tree:

Length of Longest Increasing Subsequences (LIS) using Segment Tree Maximize length of longest subarray consisting of same elements by at most K decrements Generate original permutation from given array of inversions Maximum of all subarrays of size K using Segment Tree Build a segment tree for N-ary rooted tree Length of Longest Subarray with same elements in atmost K increments Count number of increasing sub-sequences : O(NlogN) Calculate the Sum of GCD over all subarrays Cartesian tree from inorder traversal LIS using Segment Tree Reconstructing Segment Tree...