added disjoint set application problems.

Data Structures/disjointset/ConnectedComponent/ConnectedComponents.cs

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+/*
+You are given number of nodes  N, and number of edges M of a undirected connected graph.
+After adding each edge, print the size of all the connected components (in increasing order).
+
+Input:
+First line contains two integers N and M ,number of nodes and number of edges.
+Next M lines contains two integers each, 
+X and Y, denoting that there is an edge between X and Y.
+
+Output:
+For each edge, print the size of all the connected components (in increasing order) after adding that edge.
+
+Constraints:
+1<=N<=10^3
+1<=M<=N-1
+1<=X,Y<=N-1
+
+sample input:
+5 4
+1 2
+3 4
+4 5
+1 3
+
+sample output:
+1 1 1 2
+1 2 2
+2 3
+5
+*/
+using System; 
+using System.Numerics;
+class MyClass {
+static void Main(string[] args) {
+    int[] nm = Array.ConvertAll(Console.ReadLine().Split(' '),Int32.Parse);
+    int n = nm[0];
+    int m = nm[1];
+    int[] arr = new int[n];
+    int[] size = new int[n];
+    Intialize(arr,size,n);
+
+    for(int i = 0; i < m; i++)
+    {
+        int[] ver= Array.ConvertAll(Console.ReadLine().Split(' '), Int32.Parse);
+        WeightedUnion(arr,size,ver[0],ver[1]);
+        DisplayConnected(size,n);
+    }
+}
+
+    private static void DisplayConnected(int[] size, int n)
+    {
+        int[] temp=new int[n];
+        Array.Copy(size,temp,n);
+        Array.Sort(temp);
+        for (int j=0; j < n; j++)
+        {
+            if(temp[j]>0)Console.Write(temp[j]+" ");
+        }
+        Console.WriteLine();
+    }
+
+    private static void WeightedUnion(int[] arr, int[] size, int a, int b)
+    {
+        int root_a = root(a,arr);
+        int root_b = root(b,arr);
+        if (arr[root_a] == arr[root_b]) return;
+        else if (size[root_a] < size[root_b])
+        {
+            arr[root_a] = arr[root_b];
+            size[root_b] += size[root_a];
+            size[root_a]=0;
+        }
+        else
+        {
+            arr[root_b] = arr[root_a];
+            size[root_a] += size[root_b];
+            size[root_b]=0;
+        }
+    }
+
+    private static int root(int a,int[] arr)
+    {
+        int i = a - 1;
+        while (arr[i] != i)
+        {
+            i = arr[i];
+        }
+        return i;
+    }
+
+    private static void Intialize(int[] arr,int[] size,int n)
+    {
+        for(int i = 0; i < n; i++)
+        {
+            arr[i] = i;
+            size[i] = 1;
+        }
+    }
+}

Data Structures/disjointset/ExampleProblem_TeachersDilemma.cs

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+/*
+Monk is having a hard time teaching the 2nd standard students.
+He wants to divide the students into small groups so that he can conduct 
+some fun-filled activities for them. But students also want their friends in the same group. So, if student 
+A is a friend of student B, and student B is a friend of student C, then the students 
+A,B and C must be in the same group, otherwise they will start crying.
+After dividing the students, he will choose a leader from each group who will lead their respective groups. 
+Now he wants to know the number of ways he can choose the group leaders from all the groups.
+Print this answer modulo 10^9+7.
+
+Note: Two ways A and B will be considered different if at least 1 person is a leader in group A,
+and is not a leader in group B, or vice-versa.
+
+Input:
+The first line consists of two integers N and M denoting the number of students and the number of relationships respectively.
+The next M lines consists of two integers 
+u and v denoting that student u and student v are friends. 
+u and v can never be equal and relationships are not repeated.
+
+output:
+Print the answer modulo 10^9+7 in a single line.
+*/
+using System; 
+using System.Numerics;
+class MyClass {
+    static void Main(string[] args)
+    {
+        int[] _nm= Array.ConvertAll(Console.ReadLine().Split(' '), Int32.Parse);
+        int n = _nm[0];
+        int m = _nm[1];
+
+        int[] students = new int[n];
+        long[] size = new long[n];
+        Initialize(students,size,n);
+        for(int i = 0; i < m; i++)
+        {
+            int[] ver= Array.ConvertAll(Console.ReadLine().Split(' '), Int32.Parse);
+            WeightedUnion(students,size,ver[0]-1,ver[1]-1);
+        }
+        long product = 1;
+        for(int i = 0; i < n; i++)
+        {
+            if (size[i] != 0) product *= size[i];
+            product %= (long)(Math.Pow(10, 9) + 7);
+        }
+        Console.WriteLine(product);
+    }
+    private static void WeightedUnion(int[] students, long[] size, int a, int b)
+    {
+        int root_a = root(a,students);
+        int root_b = root(b,students);
+        if (students[root_a] == students[root_b]) return;
+        else if (size[root_a] < size[root_b])
+        {
+            students[root_a] = students[root_b];
+            size[root_b] += size[root_a];
+            size[root_a]=0;
+        }
+        else
+        {
+            students[root_b] = students[root_a];
+            size[root_a] += size[root_b];
+            size[root_b] = 0;
+        }
+    }
+    private static int root(int v, int[] students)
+    {
+        int i = v;
+        while (students[i] != i)
+        {
+            i = students[i];
+        }
+        return i;
+    }
+    private static void Initialize(int[] students, long[] size, int n)
+    {
+        for(int i = 0; i < n; i++)
+        {
+            students[i] = i;
+            size[i] = 1;
+        }
+    }
+}