Given a tree check if it is linear or not.
1 / \ 2 3 Linear as we can form a line 2 1 3
1
/ \
2 3
/ \
4 5
Not linear
Examples:
Input : 3 1 2 1 3 Output : YES Explanation: The Tree formed is 2-1-3 which is a linear one. Input : 4 1 2 2 3 4 2 Output : NO
Approach: The given tree would be linear only if n-2 of its nodes have indegree == 2 or number of nodes, n==1.
Implementation:
C++
// A C++ program to check whether a graph is // Linear or not#include<bits/stdc++.h>using namespace std;// This class represents a undirected graph // using adjacency list representationclass Graph{ public: // No. of vertices int V; // Constructor Graph(int v) { V = v; } // Function to add an edge into the graph void addEdge(vector<int> adj[], int v, int w) { adj[v].push_back(w); adj[w].push_back(v); } // Returns true if the graph is linear, // else false. bool isLinear(vector<int> adj[]) { // If the number of vertice is 1 then // the tree is always Linear if (V == 1) return true; int count = 0; // Counting the number of vertices // with indegree 2 for(int i = 0; i < V; i++) { if (adj[i].size() == 2) count++; } if (count == V - 2) return true; else return false; }};// Driver codeint main(){ // Create a graph given in the // above example Graph g1(3); vector<int> adj[g1.V]; g1.addEdge(adj, 0, 1); g1.addEdge(adj, 0, 2); if (g1.isLinear(adj)) cout << "YES"; else cout << "NO"; return 0;}// This code is contributed by pratham76 |
Java
// A Java Program to check whether a graph is // Linear or notimport java.io.*;import java.util.*;// This class represents a undirected graph // using adjacency list representationclass Graph { private int V; // No. of vertices // Adjacency List private LinkedList<Integer> adj[]; // Constructor Graph(int v) { V = v; adj = new LinkedList[v]; for (int i = 0; i < v; ++i) adj[i] = new LinkedList<Integer>(); } // Function to add an edge into the graph void addEdge(int v, int w) { adj[v].add(w); adj[w].add(v); } // Returns true if the graph is linear, // else false. boolean isLinear() { // If the number of vertice is 1 then // the tree is always Linear if (V == 1) return true; int count = 0; // Counting the number of vertices // with indegree 2 for (int i = 0; i < V; i++) { if (adj[i].size() == 2) count++; } if (count == V - 2) return true; else return false; } // Driver method public static void main(String args[]) { // Create a graph given in the above example Graph g1 = new Graph(3); g1.addEdge(0, 1); g1.addEdge(0, 2); if (g1.isLinear()) System.out.println("YES"); else System.out.println("NO"); }} |
Python3
# A Python3 Program to check whether a # graph is Linear or not # This class represents a undirected # graph using adjacency list representationclass Graph: def __init__(self, v): # No. of vertices self.V = v # Adjacency List self.adj = [[] for i in range(v)] # Function to add an edge into # the graph def addEdge(self, v, w): self.adj[v].append(w) self.adj[w].append(v) # Returns true if the graph is # linear, else false. def isLinear(self): # If the number of vertice is # 1 then the tree is always Linear if (self.V == 1): return True count = 0 # Counting the number of vertices # with indegree 2 for i in range(self.V): if (len(self.adj[i]) == 2): count += 1 if (count == self.V - 2): return True else: return False # Driver codeif __name__=='__main__': # Create a graph given in the # above example g1 = Graph(3) g1.addEdge(0, 1) g1.addEdge(0, 2) if (g1.isLinear()): print("YES") else: print("NO") # This code is contributed by rutvik_56 |
C#
// A C# Program to check whether a graph is // Linear or notusing System;using System.Collections.Generic;// This class represents a undirected graph // using adjacency list representationpublic class Graph { private int V; // No. of vertices // Adjacency List private List<int> []adj; // Constructor Graph(int v) { V = v; adj = new List<int>[v]; for (int i = 0; i < v; ++i) adj[i] = new List<int>(); } // Function to add an edge into the graph void addEdge(int v, int w) { adj[v].Add(w); adj[w].Add(v); } // Returns true if the graph is linear, // else false. bool isLinear() { // If the number of vertice is 1 then // the tree is always Linear if (V == 1) return true; int count = 0; // Counting the number of vertices // with indegree 2 for (int i = 0; i < V; i++) { if (adj[i].Count == 2) count++; } if (count == V - 2) return true; else return false; } // Driver Code public static void Main(String []args) { // Create a graph given in the above example Graph g1 = new Graph(3); g1.addEdge(0, 1); g1.addEdge(0, 2); if (g1.isLinear()) Console.WriteLine("YES"); else Console.WriteLine("NO"); }}// This code is contributed by 29AjayKumar |
Javascript
<script>// A Javascript program to check // whether a graph is Linear or notlet V;let adj;// Function to add an edge into the graphfunction addEdge(v, w){ adj[v].push(w); adj[w].push(v);}// Returns true if the graph is linear,// else false.function isLinear(){ // If the number of vertice is 1 then // the tree is always Linear if (V == 1) return true; let count = 0; // Counting the number of vertices // with indegree 2 for(let i = 0; i < V; i++) { if (adj[i].length == 2) count++; } if (count == V - 2) return true; else return false;}// Driver code// Create a graph given in the above exampleV = 3;adj = new Array(V)for(let i = 0; i < V; ++i) adj[i] = []; addEdge(0, 1);addEdge(0, 2);if (isLinear()) document.write("YES");else document.write("NO");// This code is contributed by suresh07</script> |
Output
YES
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