Skip to main content

Graph

Graph is a very useful data structure which has versatile applications in many fields. It is impossible to cover all the aspects of graph-related algorithm, (the same as all the other topics in the posts), we will focus on some basics, especially that may be useful in code interview.

The two basic components of a graph is vertex (or node) and edge. Vertices are connected by edges. Graph can be directed graph or un-directed graph. The directed graph has directed edges; the undirected has undirected edges.

The common representation of a graph can be adjacent matrix or list. If use adjacent matrix, the element is usually set as 0 or 1. 0 means there is no edge, and 1 mean connected. If use adjacent list, usually the index of the list is the source node, and the elements in the list is the connected nodes from the source.

Other important concepts are the indegrees and outdegrees.  The indegree of a node means the number of edges pointing to it; the outdegree of a node means the number of edges originating from it. These two concepts are very useful in topologic sort: when the nodes has dependencies.

Besides to the common breadth-first-search (bfs), depth-first-searh (dfs), union-find (uf), there are many graph algorithm named after someone's name, such as Dijkstra algorithm. In general, the algorithm named after someone's name are designed only for some specific questions (Dijkstra however is an outlier), the chance to see them in tech interview is not very high.

To sum up,

1. graph is a useful data structure having many applications;

2. the edge could have directions;

3. the nodes could have dependencies;

4. the common basic algorithms about graph are dfs, bfs, and uf;

5. there are many algorithms about graph named after someone's' name(s), which is good to know.



Question List


Upper Layer

Comments

Post a Comment

Popular posts from this blog

Brute Force - Question 2

2105. Watering Plants II Alice and Bob want to water n plants in their garden. The plants are arranged in a row and are labeled from 0 to n - 1 from left to right where the ith plant is located at x = i. Each plant needs a specific amount of water. Alice and Bob have a watering can each, initially full. They water the plants in the following way: Alice waters the plants in order from left to right, starting from the 0th plant. Bob waters the plants in order from right to left, starting from the (n - 1)th plant. They begin watering the plants simultaneously. It takes the same amount of time to water each plant regardless of how much water it needs. Alice/Bob must water the plant if they have enough in their can to fully water it. Otherwise, they first refill their can (instantaneously) then water the plant. In case both Alice and Bob reach the same plant, the one with more water currently in his/her watering can should water this plant. If they have the same amount of water, then Alice ...
Post a Comment
Read more

Graph Question - Hard Level - Question 1

2246. Longest Path With Different Adjacent Characters You are given a tree (i.e. a connected, undirected graph that has no cycles) rooted at node 0 consisting of n nodes numbered from 0 to n - 1. The tree is represented by a 0-indexed array parent of size n, where parent[i] is the parent of node i. Since node 0 is the root, parent[0] == -1. You are also given a string s of length n, where s[i] is the character assigned to node i. Return the length of the longest path in the tree such that no pair of adjacent nodes on the path have the same character assigned to them. Constraints: n == parent.length == s.length 1 <= n <= 10^5 0 <= parent[i] <= n - 1 for all i >= 1 parent[0] == -1 parent represents a valid tree. s consists of only lowercase English letters. Analysis For this question, we need to construct a graph, or more specifically, a n-nary tree. How to construct the graph/tree? What we only know is the parent array. So we need to go through the parent array and constr...
Post a Comment
Read more