# Nodes with prime degree in an undirected Graph

Given an undirected graph with N vertices and M edges, the task is to print all the nodes of the given graph whose degree is a Prime Number.

Examples:

Input: N = 4, arr[][] = { { 1, 2 }, { 1, 3 }, { 1, 4 }, { 2, 3 }, { 2, 4 }, { 3, 4 } }
Output: 1 2 3 4
Explanation:
Below is the graph for the above information: The degree of the node as per above graph is:
Node -> Degree
1 -> 3
2 -> 3
3 -> 3
4 -> 3
Hence, the nodes with prime degree are 1 2 3 4

Input: N = 5, arr[][] = { { 1, 2 }, { 1, 3 }, { 2, 4 }, { 2, 5 } }
Output: 1

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

Approach:

1. Use Sieve of Eratosthenes to calculate the prime numbers upto 105.
2. For each vertex, the degree can be calculated by the length of Adjacency List of the given graph at corresponding vertex.
3. Print those vertex of the given graph whose degree is a Prime Number.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `int` `n = 10005; ` ` `  `// To store Prime Numbers ` `vector<``bool``> Prime(n + 1, ``true``); ` ` `  `// Function to find the prime numbers ` `// till 10^5 ` `void` `SieveOfEratosthenes() ` `{ ` ` `  `    ``int` `i, j; ` `    ``Prime = Prime = ``false``; ` `    ``for` `(i = 2; i * i <= 10005; i++) { ` ` `  `        ``// Traverse all multiple of i ` `        ``// and make it false ` `        ``if` `(Prime[i]) { ` ` `  `            ``for` `(j = 2 * i; j < 10005; j += i) { ` `                ``Prime[j] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// Function to print the nodes having ` `// prime degree ` `void` `primeDegreeNodes(``int` `N, ``int` `M, ` `                      ``int` `edges[]) ` `{ ` `    ``// To store Adjacency List of ` `    ``// a Graph ` `    ``vector<``int``> Adj[N + 1]; ` ` `  `    ``// Make Adjacency List ` `    ``for` `(``int` `i = 0; i < M; i++) { ` `        ``int` `x = edges[i]; ` `        ``int` `y = edges[i]; ` ` `  `        ``Adj[x].push_back(y); ` `        ``Adj[y].push_back(x); ` `    ``} ` ` `  `    ``// To precompute prime numbers ` `    ``// till 10^5 ` `    ``SieveOfEratosthenes(); ` ` `  `    ``// Traverse each vertex ` `    ``for` `(``int` `i = 1; i <= N; i++) { ` ` `  `        ``// Find size of Adjacency List ` `        ``int` `x = Adj[i].size(); ` ` `  `        ``// If length of Adj[i] is Prime ` `        ``// then print it ` `        ``if` `(Prime[x]) ` `            ``cout << i << ``' '``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// Vertices and Edges ` `    ``int` `N = 4, M = 6; ` ` `  `    ``// Edges ` `    ``int` `edges[M] = { { 1, 2 }, { 1, 3 },  ` `                        ``{ 1, 4 }, { 2, 3 },  ` `                        ``{ 2, 4 }, { 3, 4 } }; ` ` `  `    ``// Function Call ` `    ``primeDegreeNodes(N, M, edges); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` `class` `GFG{ ` ` `  `static` `int` `n = ``10005``; ` ` `  `// To store Prime Numbers ` `static` `boolean` `[]Prime = ``new` `boolean``[n + ``1``]; ` ` `  `// Function to find the prime numbers ` `// till 10^5 ` `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``int` `i, j; ` `    ``Prime[``0``] = Prime[``1``] = ``false``; ` `    ``for` `(i = ``2``; i * i <= ``10005``; i++)  ` `    ``{ ` ` `  `        ``// Traverse all multiple of i ` `        ``// and make it false ` `        ``if` `(Prime[i]) ` `        ``{ ` `            ``for` `(j = ``2` `* i; j < ``10005``; j += i)  ` `            ``{ ` `                ``Prime[j] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// Function to print the nodes having ` `// prime degree ` `static` `void` `primeDegreeNodes(``int` `N, ``int` `M, ` `                              ``int` `edges[][]) ` `{ ` `    ``// To store Adjacency List of ` `    ``// a Graph ` `    ``Vector []Adj = ``new` `Vector[N + ``1``]; ` `    ``for``(``int` `i = ``0``; i < Adj.length; i++) ` `        ``Adj[i] = ``new` `Vector(); ` ` `  `    ``// Make Adjacency List ` `    ``for` `(``int` `i = ``0``; i < M; i++)  ` `    ``{ ` `        ``int` `x = edges[i][``0``]; ` `        ``int` `y = edges[i][``1``]; ` ` `  `        ``Adj[x].add(y); ` `        ``Adj[y].add(x); ` `    ``} ` ` `  `    ``// To precompute prime numbers ` `    ``// till 10^5 ` `    ``SieveOfEratosthenes(); ` ` `  `    ``// Traverse each vertex ` `    ``for` `(``int` `i = ``1``; i <= N; i++)  ` `    ``{ ` ` `  `        ``// Find size of Adjacency List ` `        ``int` `x = Adj[i].size(); ` ` `  `        ``// If length of Adj[i] is Prime ` `        ``// then print it ` `        ``if` `(Prime[x]) ` `            ``System.out.print(i + ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``// Vertices and Edges ` `    ``int` `N = ``4``, M = ``6``; ` ` `  `    ``// Edges ` `    ``int` `edges[][] = { { ``1``, ``2` `}, { ``1``, ``3` `},  ` `                      ``{ ``1``, ``4` `}, { ``2``, ``3` `},  ` `                      ``{ ``2``, ``4` `}, { ``3``, ``4` `} }; ` `    ``Arrays.fill(Prime, ``true``); ` `     `  `    ``// Function Call ` `    ``primeDegreeNodes(N, M, edges); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG{ ` ` `  `static` `int` `n = 10005; ` ` `  `// To store Prime Numbers ` `static` `bool` `[]Prime = ``new` `bool``[n + 1]; ` ` `  `// Function to find the prime numbers ` `// till 10^5 ` `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``int` `i, j; ` `    ``Prime = Prime = ``false``; ` `    ``for``(i = 2; i * i <= 10005; i++)  ` `    ``{ ` `        `  `       ``// Traverse all multiple of i ` `       ``// and make it false ` `       ``if` `(Prime[i]) ` `       ``{ ` `           ``for``(j = 2 * i; j < 10005; j += i)  ` `           ``{ ` `              ``Prime[j] = ``false``; ` `           ``} ` `       ``} ` `    ``} ` `} ` ` `  `// Function to print the nodes having ` `// prime degree ` `static` `void` `primeDegreeNodes(``int` `N, ``int` `M, ` `                             ``int` `[,]edges) ` `{ ` `     `  `    ``// To store Adjacency List of ` `    ``// a Graph ` `    ``List<``int``> []Adj = ``new` `List<``int``>[N + 1]; ` `    ``for``(``int` `i = 0; i < Adj.Length; i++) ` `       ``Adj[i] = ``new` `List<``int``>(); ` ` `  `    ``// Make Adjacency List ` `    ``for``(``int` `i = 0; i < M; i++)  ` `    ``{ ` `       ``int` `x = edges[i, 0]; ` `       ``int` `y = edges[i, 1]; ` `        `  `       ``Adj[x].Add(y); ` `       ``Adj[y].Add(x); ` `    ``} ` `     `  `    ``// To precompute prime numbers ` `    ``// till 10^5 ` `    ``SieveOfEratosthenes(); ` ` `  `    ``// Traverse each vertex ` `    ``for``(``int` `i = 1; i <= N; i++)  ` `    ``{ ` `         `  `       ``// Find size of Adjacency List ` `       ``int` `x = Adj[i].Count; ` `        `  `       ``// If length of Adj[i] is Prime ` `       ``// then print it ` `       ``if` `(Prime[x]) ` `           ``Console.Write(i + ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `     `  `    ``// Vertices and Edges ` `    ``int` `N = 4, M = 6; ` ` `  `    ``// Edges ` `    ``int` `[,]edges = { { 1, 2 }, { 1, 3 },  ` `                     ``{ 1, 4 }, { 2, 3 },  ` `                     ``{ 2, 4 }, { 3, 4 } }; ` `                      `  `    ``for``(``int` `i = 0; i < Prime.Length; i++) ` `       ``Prime[i] = ``true``; ` `     `  `    ``// Function Call ` `    ``primeDegreeNodes(N, M, edges); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```1 2 3 4
```

Time Complexity: O(N + M), where N is the number of vertices and M is the number of edges. My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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