# Check if a given tree graph is linear or not

Given a tree check if it is linear or not.

```    1
/    \
2      3
Linear as we can
form a lime 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:The given tree would be linear only if n-2 of its nodes have indegree == 2 or number of nodes, n==1.

## Java

 `// A Java Program to check whether a graph is  ` `// Linear or not ` `import` `java.io.*; ` `import` `java.util.*; ` ` `  `// This class represents a undirected graph  ` `// using adjacency list representation ` `class` `Graph { ` `    ``private` `int` `V; ``// No. of vertices ` ` `  `    ``// Adjacency List ` `    ``private` `LinkedList adj[]; ` ` `  `    ``// Constructor ` `    ``Graph(``int` `v) ` `    ``{ ` `        ``V = v; ` `        ``adj = ``new` `LinkedList[v]; ` `        ``for` `(``int` `i = ``0``; i < v; ++i) ` `            ``adj[i] = ``new` `LinkedList(); ` `    ``} ` ` `  `    ``// 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"``); ` `    ``} ` `} `

## C#

 `// A C# Program to check whether a graph is  ` `// Linear or not ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `// This class represents a undirected graph  ` `// using adjacency list representation ` `public` `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 `

Output :

```YES
```

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