Learn and practice Tries, Graphs, Cyclic Sort, and Topological Sort patterns to solve coding interview problems.

Grokking the Blind 75 Problems in Java

In this module, we'll explore some advanced data structures and sorting techniques to help us solve challenging coding interview questions. We'll start by mastering two advanced data structures: graphs and tries. Graphs are versatile data structures that tackle complex interconnected problems, while tries offer an elegant solution for scenarios where standard data structures fall short. Next, we’ll explore two advanced sorting algorithms: Cyclic Sort and Topological Sort. Cyclic Sort is used when specific constraints on the input are met, making it the most efficient sorting algorithm in such cases. Topological Sort leverages graph-based algorithms to handle partially ordered elements. We’ll learn to recognize when these advanced sorting techniques are applicable and how to leverage them effectively to solve complex problems. By completing this module, you’ll enhance your problem-solving toolkit and solidify your status as a standout candidate in technical interviews.

Advanced Data Structures and Sorting Techniques

# Statement

Given `n` as the number of nodes and an array of the `edges` of a graph, find out if the graph is a valid tree. The nodes of the graph are labeled from $0$ to $n - 1$, and $edges[i] = [x, y]$ represents an undirected edge connecting the nodes $x$ and $y$ of the graph.

A graph is a valid tree when all the nodes are connected and there is no cycle between them.

**Constraints:**
- $1 \leq$ `n` $\leq 1000$
- $0 \leq$ `edges.length` $\leq 2000$
- `edges[i].length` $= 2$
- $0 \leq$ $x$, $y$ $<$ `n`
- $x$ $!=$ $y$
- There are no repeated edges.

# Examples

Try to solve the Graph Valid Tree problem.