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Find two disjoint good sets of vertices in a given graph
• Last Updated : 02 Nov, 2020

Given an undirected unweighted graph with N vertices and M edges. The task is to find two disjoint good sets of vertices. A set X is called good if for every edge UV in the graph at least one of the endpoint belongs to X(i.e, U or V or both U and V belongs to X).
If it is not possible to make such sets then print -1.
Examples:

Input :

Output : {1 3 4 5} ,{2 6}
One disjoint good set contains vertices {1, 3, 4, 5} and other contains {2, 6}.
Input :

Output : -1

Approach:
One of the observation is that there is no edge UV that U and V are in the same set.The two good sets form a bipartition of the graph, so the graph has to be bipartite. And being bipartite is also sufficient. Read about bipartition here.
Below is the implementation of the above approach :

## C++

 `// C++ program to find two disjoint``// good sets of vertices in a given graph``#include ``using` `namespace` `std;``#define N 100005` `// For the graph``vector<``int``> gr[N], dis[2];``bool` `vis[N];``int` `colour[N];``bool` `bip;` `// Function to add edge``void` `Add_edge(``int` `x, ``int` `y)``{``    ``gr[x].push_back(y);``    ``gr[y].push_back(x);``}` `// Bipartie function``void` `dfs(``int` `x, ``int` `col)``{``    ``vis[x] = ``true``;``    ``colour[x] = col;` `    ``// Check for child vertices``    ``for` `(``auto` `i : gr[x]) {` `        ``// If it is not visited``        ``if` `(!vis[i])``            ``dfs(i, col ^ 1);` `        ``// If it is already visited``        ``else` `if` `(colour[i] == col)``            ``bip = ``false``;``    ``}``}` `// Function to find two disjoint``// good sets of vertices in a given graph``void` `goodsets(``int` `n)``{``    ``// Initially assume that graph is bipartie``    ``bip = ``true``;` `    ``// For every unvisited vertex call dfs``    ``for` `(``int` `i = 1; i <= n; i++)``        ``if` `(!vis[i])``            ``dfs(i, 0);` `    ``// If graph is not bipartie``    ``if` `(!bip)``        ``cout << -1;``    ``else` `{` `        ``// Differentiate two sets``        ``for` `(``int` `i = 1; i <= n; i++)``            ``dis[colour[i]].push_back(i);` `        ``// Print vertices belongs to both sets` `        ``for` `(``int` `i = 0; i < 2; i++) {` `            ``for` `(``int` `j = 0; j < dis[i].size(); j++)``                ``cout << dis[i][j] << ``" "``;``            ``cout << endl;``        ``}``    ``}``}` `// Driver code``int` `main()``{``    ``int` `n = 6, m = 4;` `    ``// Add edges``    ``Add_edge(1, 2);``    ``Add_edge(2, 3);``    ``Add_edge(2, 4);``    ``Add_edge(5, 6);` `    ``// Function call``    ``goodsets(n);``}`

## Java

 `// Java program to find two disjoint``// good sets of vertices in a given graph``import` `java.util.*;` `class` `GFG``{` `    ``static` `int` `N = ``100005``;` `    ``// For the graph``    ``@SuppressWarnings``(``"unchecked"``)``    ``static` `Vector[] gr = ``new` `Vector[N],``                            ``dis = ``new` `Vector[``2``];``    ``static``    ``{``        ``for` `(``int` `i = ``0``; i < N; i++)``            ``gr[i] = ``new` `Vector<>();``        ``for` `(``int` `i = ``0``; i < ``2``; i++)``            ``dis[i] = ``new` `Vector<>();``    ``}``    ``static` `boolean``[] vis = ``new` `boolean``[N];``    ``static` `int``[] color = ``new` `int``[N];``    ``static` `boolean` `bip;` `    ``// Function to add edge``    ``static` `void` `add_edge(``int` `x, ``int` `y)``    ``{``        ``gr[x].add(y);``        ``gr[y].add(x);``    ``}` `    ``// Bipartie function``    ``static` `void` `dfs(``int` `x, ``int` `col)``    ``{``        ``vis[x] = ``true``;``        ``color[x] = col;` `        ``// Check for child vertices``        ``for` `(``int` `i : gr[x])``        ``{` `            ``// If it is not visited``            ``if` `(!vis[i])``                ``dfs(i, col ^ ``1``);` `            ``// If it is already visited``            ``else` `if` `(color[i] == col)``                ``bip = ``false``;``        ``}``    ``}` `    ``// Function to find two disjoint``    ``// good sets of vertices in a given graph``    ``static` `void` `goodsets(``int` `n)``    ``{``        ``// Initially assume that graph is bipartie``        ``bip = ``true``;` `        ``// For every unvisited vertex call dfs``        ``for` `(``int` `i = ``1``; i <= n; i++)``            ``if` `(!vis[i])``                ``dfs(i, ``0``);` `        ``// If graph is not bipartie``        ``if` `(!bip)``            ``System.out.println(-``1``);``        ``else``        ``{` `            ``// Differentiate two sets``            ``for` `(``int` `i = ``1``; i <= n; i++)``                ``dis[color[i]].add(i);` `            ``// Print vertices belongs to both sets` `            ``for` `(``int` `i = ``0``; i < ``2``; i++)``            ``{``                ``for` `(``int` `j = ``0``; j < dis[i].size(); j++)``                    ``System.out.print(dis[i].elementAt(j) + ``" "``);``                ``System.out.println();``            ``}``        ``}``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``6``, m = ``4``;` `        ``// Add edges``        ``add_edge(``1``, ``2``);``        ``add_edge(``2``, ``3``);``        ``add_edge(``2``, ``4``);``        ``add_edge(``5``, ``6``);` `        ``// Function call``        ``goodsets(n);``    ``}``}` `// This code is contributed by``// sanjeev2552`

## Python 3

 `# Python 3 program to find two disjoint``# good sets of vertices in a given graph``N ``=` `100005` `# For the graph``gr ``=` `[[] ``for` `i ``in` `range``(N)]``dis ``=` `[[] ``for` `i ``in` `range``(``2``)]``vis ``=` `[``False` `for` `i ``in` `range``(N)]``colour ``=` `[``0` `for` `i ``in` `range``(N)]``bip ``=` `0` `# Function to add edge``def` `Add_edge(x, y):``    ``gr[x].append(y)``    ``gr[y].append(x)` `# Bipartie function``def` `dfs(x, col):``    ``vis[x] ``=` `True``    ``colour[x] ``=` `col` `    ``# Check for child vertices``    ``for` `i ``in` `gr[x]:``        ` `        ``# If it is not visited``        ``if` `(vis[i] ``=``=` `False``):``            ``dfs(i, col ^ ``1``)` `        ``# If it is already visited``        ``elif` `(colour[i] ``=``=` `col):``            ``bip ``=` `False` `# Function to find two disjoint``# good sets of vertices in a given graph``def` `goodsets(n):``    ` `    ``# Initially assume that``    ``# graph is bipartie``    ``bip ``=` `True` `    ``# For every unvisited vertex call dfs``    ``for` `i ``in` `range``(``1``, n ``+` `1``, ``1``):``        ``if` `(vis[i] ``=``=` `False``):``            ``dfs(i, ``0``)` `    ``# If graph is not bipartie``    ``if` `(bip ``=``=` `0``):``        ``print``(``-``1``)``    ``else``:``        ` `        ``# Differentiate two sets``        ``for` `i ``in` `range``(``1``, n ``+` `1``, ``1``):``            ``dis[colour[i]].append(i)` `        ``# Print vertices belongs to both sets``        ``for` `i ``in` `range``(``2``):``            ``for` `j ``in` `range``(``len``(dis[i])):``                ``print``(dis[i][j], end ``=` `" "``)``            ``print``(``'\n'``, end ``=` `"")` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``n ``=` `6``    ``m ``=` `4` `    ``# Add edges``    ``Add_edge(``1``, ``2``)``    ``Add_edge(``2``, ``3``)``    ``Add_edge(``2``, ``4``)``    ``Add_edge(``5``, ``6``)` `    ``# Function call``    ``goodsets(n)` `# This code is contributed``# by Surendra_Gangwar`

## C#

 `// C# program to find two``// disjoint good sets of``// vertices in a given graph``using` `System;``using` `System.Collections.Generic;``class` `GFG{` `static` `int` `N = 100005;` `// For the graph``static` `List<``int``>[] gr =``            ``new` `List<``int``>[N],``            ``dis = ``new` `List<``int``>[2]; ``static` `bool``[] vis = ``new` `bool``[N];``static` `int``[] color = ``new` `int``[N];``static` `bool` `bip;` `// Function to add edge``static` `void` `add_edge(``int` `x,``                     ``int` `y)``{``  ``gr[x].Add(y);``  ``gr[y].Add(x);``}` `// Bipartie function``static` `void` `dfs(``int` `x,``                ``int` `col)``{``  ``vis[x] = ``true``;``  ``color[x] = col;` `  ``// Check for child vertices``  ``foreach` `(``int` `i ``in` `gr[x])``  ``{``    ``// If it is not visited``    ``if` `(!vis[i])``      ``dfs(i, col ^ 1);` `    ``// If it is already visited``    ``else` `if` `(color[i] == col)``      ``bip = ``false``;``  ``}``}` `// Function to find two disjoint``// good sets of vertices in a``// given graph``static` `void` `goodsets(``int` `n)``{``  ``// Initially assume that``  ``// graph is bipartie``  ``bip = ``true``;` `  ``// For every unvisited``  ``// vertex call dfs``  ``for` `(``int` `i = 1; i <= n; i++)``    ``if` `(!vis[i])``      ``dfs(i, 0);` `  ``// If graph is not bipartie``  ``if` `(!bip)``    ``Console.WriteLine(-1);``  ``else``  ``{``    ``// Differentiate two sets``    ``for` `(``int` `i = 1;``             ``i <= n; i++)``      ``dis[color[i]].Add(i);` `    ``// Print vertices belongs``    ``// to both sets``    ``for` `(``int` `i = 0; i < 2; i++)``    ``{``      ``for` `(``int` `j = 0;``               ``j < dis[i].Count; j++)``        ``Console.Write(dis[i][j] + ``" "``);``      ``Console.WriteLine();``    ``}``  ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``  ``int` `n = 6, m = 4;``  ` `  ``for` `(``int` `i = 0; i < N; i++)``    ``gr[i] = ``new` `List<``int``>();``  ` `  ``for` `(``int` `i = 0; i < 2; i++)``    ``dis[i] = ``new` `List<``int``>();``  ` `  ``// Add edges``  ``add_edge(1, 2);``  ``add_edge(2, 3);``  ``add_edge(2, 4);``  ``add_edge(5, 6);` `  ``// Function call``  ``goodsets(n);``}``}` `// This code is contributed by shikhasingrajput`
Output:
```1 3 4 5
2 6

```

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