In a town, there are N people labelled from 1 to N. There is a rumor that one of these people is secretly the town judge. If the town judge exists, then: The town judge trusts nobody. Everybody (except for the town judge) trusts the town judge. There is exactly one person that satisfies properties 1 and 2. You are given trust, an array of pairs trust[i] = [a, b] representing that the person labelled a trusts the person labelled b.
There are a total of n courses you have to take, labeled from 0 to n-1. Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1] Given the total number of courses and a list of prerequisite pairs, return the ordering of courses you should take to finish all courses. There may be multiple correct orders, you just need to return one of them.
Given an undirected graph, return true if and only if it is bipartite. Recall that a graph is bipartite if we can split it’s set of nodes into two independent subsets A and B such that every edge in the graph has one node in A and another node in B. The graph is given in the following form: graph[i] is a list of indexes j for which the edge between nodes i and j exists.
Given a non-empty array of unique positive integers A, consider the following graph: There are A.length nodes, labelled A[0] to A[A.length - 1]; There is an edge between A[i] and A[j] if and only if A[i] and A[j] share a common factor greater than 1. Return the size of the largest connected component in the graph. Example 1 Input: [4,6,15,35] Output: 4 Example 2 Input: [20,50,9,63] Output: 2 Example 3 Input: [2,3,6,7,4,12,21,39] Output: 8 Note 1 <= A.
Given a reference of a node in a connected undirected graph, return a deep copy (clone) of the graph. Each node in the graph contains a val (int) and a list (List[Node]) of its neighbors. Example: Input: {"$id":"1","neighbors":[{"$id":"2","neighbors":[{"$ref":"1"},{"$id":"3","neighbors":[{"$ref":"2"},{"$id":"4","neighbors":[{"$ref":"3"},{"$ref":"1"}],"val":4}],"val":3}],"val":2},{"$ref":"4"}],"val":1} Explanation: Node 1's value is 1, and it has two neighbors: Node 2 and 4. Node 2's value is 2, and it has two neighbors: Node 1 and 3. Node 3's value is 3, and it has two neighbors: Node 2 and 4.
Tree: n - 1 edges, all nodes connected, contains no loop.
Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to find the number of connected components in an undirected graph. Example 1 Input: n = 5 and edges = [[0, 1], [1, 2], [3, 4]] 0 3 | | 1 --- 2 4 Output: 2 Example 2 Input: n = 5 and edges = [[0, 1], [1, 2], [2, 3], [3, 4]] 0 4 | | 1 --- 2 --- 3 Output: 1 Note You can assume that no duplicate edges will appear in edges.
Given n nodes labeled from 0 to n-1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree. ###Example 1: Input: n = 5, and edges = [[0,1], [0,2], [0,3], [1,4]] Output: true Example 2 Input: n = 5, and edges = [[0,1], [1,2], [2,3], [1,3], [1,4]] Output: false ###Note: you can assume that no duplicate edges will appear in edges.
There are a total of n courses you have to take, labeled from 0 to n-1. Some courses may have prerequisites, for example to take course 0 you have to first take course 1, which is expressed as a pair: [0,1] Given the total number of courses and a list of prerequisite pairs, is it possible for you to finish all courses? Example 1 Input: 2, [[1,0]] Output: true Explanation: There are a total of 2 courses to take.