What is heavy light decomposition?

In combinatorial mathematics and theoretical computer science, heavy path decomposition (also called heavy-light decomposition) is a technique for decomposing a rooted tree into a set of paths. The selected edges form the paths of the decomposition.

How does heavy light decomposition work?

The main idea of Heavy Light Decomposition of a unbalanced tree is to club vertices of long (or heavy) paths together in chains so that these linear chains can be queried in O(Log n) time using a data structure like Segment Tree.

What is hld in cp?

Sum of the numbers on the path between two vertices. Repainting the edges of the path between two vertices. Implementation. Practice problems. Heavy-light decomposition is a fairly general technique that allows us to effectively solve many problems that come down to queries on a tree .

What is Mo’s algorithm?

Mo’s algorithm is a generic idea. It applies to the following class of problems: You are given array Arr of length N and Q queries. Each query is represented by two numbers L and R, and it asks you to compute some function Func with subarray Arr[L..

What is sqrt Decomposition?

Sqrt Decomposition is a method (or a data structure) that allows you to perform some common operations (finding sum of the elements of the sub-array, finding the minimal/maximal element, etc.) in O(√n) operations, which is much faster than O(n) for the trivial algorithm.

Why does sqrt decomposition?

Sqrt (or Square Root) Decomposition Technique is one of the most common query optimization technique used by competitive programmers. This technique helps us to reduce Time Complexity by a factor of sqrt(n). The key concept of this technique is to decompose given array into small chunks specifically of size sqrt(n).

Who invented Mo’s algorithm?

It was first used to tackle a problem from 2009 China IOI Camp: 小Z的袜子(hose) — authored by 莫涛 himself. The problem was: given a sequence of integers, for any given interval, calculate the probability of choosing any 2 numbers and the 2 numbers are equal. Now let’s start.

Is this square root decomposition?

What is Mo algorithm?

What is sqrt decomposition?

What is the purpose of using square root decomposition?

Where does the term heavy light decomposition come from?

HLD can also be seen as ‘coloring ’ of the tree’s edges. The ‘Heavy-Light’ comes from the way we segregate edges. We use size of the subtrees rooted at the nodes as our criteria.

How to do heavy light decomposition in Python?

If edge number e with weight w exists between nodes u and v, we shall store e at tree [u] [v] and tree [v] [u], and the weight w in a separate linear array of edge weights (n-1 edges). 2. Setting up the subtree size, depth and parent for each node: Next we do a DFS on the tree to set up arrays that store parent, subtree size and depth of each node.

How is heavy path decomposition used in Combinatorial Science?

In combinatorial mathematics and theoretical computer science, heavy path decomposition (also called heavy-light decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition, each non-leaf node selects one “heavy edge”, the edge to the child…

How does the heavy light decomposition work in Haskell?

Essentially the decomposition tells you which, if any, subtrees at a node N take up more than half the weight of the tree rooted at N. Such a subtree gets an edge coloured with the word “Heavy” the rest get coloured “Light”. Note that there can be at most one heavy subtree at any given node. Here is an implementation in Haskell.