KRUSKAL

 #include <conio.h>

#include <stdlib.h>

#include <stdio.h>

    int i, j, k, a, b, u, v, n, ne = 1;

    int min, mincost = 0, cost[9][9], parent[9];

    int find(int);

    int uni(int, int);

    void main() {

      printf("\n\tImplementation of Kruskal's Algorithm\n");

      printf("\nEnter the no. of vertices:");

      scanf("%d",&n);

      printf("\nEnter the cost adjacency matrix:\n");

      for (i = 1; i<= n; i++) {

        for (j = 1; j <= n; j++) {

          scanf("%d", &cost[i][j]);

          if (cost[i][j] == 0)

            cost[i][j] = 999;

        }

      }

      printf("The edges of Minimum Cost Spanning Tree are\n");

      while (ne < n) {

        for (i = 1, min = 999; i <= n; i++) {

          for (j = 1; j <= n; j++) {

            if (cost[i][j] <min) {

              min = cost[i][j];

              a = u = i;

              b = v = j;

            }

          }

        }

        u = find(u);

        v = find(v);

        if (uni(u, v)) {

          printf("%d edge (%d,%d) =%d\n", ne++, a, b, min);

          mincost += min;

        }

        cost[a][b] = cost[b][a] = 999;

      }

      printf("\n\tMinimum cost = %d\n", mincost);

      getch();

    }

    int find(int i) {

      while (parent[i])

        i = parent[i];

      return i;

    }

    int uni(int i, int j) {

      if (i != j) {

        parent[j] = i;

        return 1;

      }

      return 0;

    }

prims algorithm

 #include<iostream>

using namespace std;

// Number of vertices in the graph  

const int V=6;

// Function to find the vertex with minimum key value 

int min_Key(int key[], bool visited[])  

{ 

    int min = 999, min_index;  // 999 represents an Infinite value

    for (int v = 0; v < V; v++) { 

        if (visited[v] == false && key[v] < min) { 

        // vertex should not be visited

            min = key[v];

min_index = v;  

        }

    }    

    return min_index;  

}  

// Function to print the final MST stored in parent[]  

void print_MST(int parent[], int cost[V][V])  

{  

    int minCost=0;

cout<<"Edge \tWeight\n";  

    for (int i = 1; i< V; i++) {

cout<<parent[i]<<" - "<<i<<" \t"<<cost[i][parent[i]]<<" \n";  

minCost+=cost[i][parent[i]];

    }

cout<<"Total cost is"<<minCost;

}  

// Function to find the MST using adjacency cost matrix representation  

void find_MST(int cost[V][V])  

{  

    int parent[V], key[V];

    bool visited[V];

    // Initialize all the arrays 

    for (int i = 0; i< V; i++) { 

        key[i] = 999;    // 99 represents an Infinite value

        visited[i] = false;

        parent[i]=-1;

    }    

    key[0] = 0;  // Include first vertex in MST by setting its key vaue to 0.  

    parent[0] = -1; // First node is always root of MST  

    // The MST will have maximum V-1 vertices  

    for (int x = 0; x < V - 1; x++) 

    {  

        // Finding the minimum key vertex from the 

        //set of vertices not yet included in MST  

        int u = min_Key(key, visited);  

        visited[u] = true;  // Add the minimum key vertex to the MST  

        // Update key and parent arrays

        for (int v = 0; v < V; v++)  

        {

            // cost[u][v] is non zero only for adjacent vertices of u  

            // visited[v] is false for vertices not yet included in MST  

            // key[] gets updated only if cost[u][v] is smaller than key[v]  

            if (cost[u][v]!=0 && visited[v] == false && cost[u][v] < key[v])

            {  

                parent[v] = u;

                key[v] = cost[u][v];  

            }        

        }

    }

    // print the final MST  

print_MST(parent, cost);  

}  

// main function

int main()  

{  

    int cost[V][V];

cout<<"Enter the vertices for a graph with 6 vetices";

    for (int i=0;i<V;i++)

    {

        for(int j=0;j<V;j++)

        {

cin>>cost[i][j];

        }

    }

find_MST(cost);  

    return 0;  

}  

Twin Prime Number in a range

 

import java.io.*; 

import java.util.*;

 

public class Main

{static boolean checkPrimeNumber(int number) 

    { 

        int i; 

        int m = 0; 

        int flag = 0;       

        m = number/2;       

        if(number == 0 || number == 1){   

            return false;       

        }else{   

            for(i = 2; i <= m ;i++){       

                if(number%i == 0){       

                    flag=1;       

                    return false;       

                }       

            }       

            if(flag == 0)   

            {  

                return true; 

            }   

        } 

        return false; 

    }     

    static boolean checkTwinPrimeNumber(int number1, int number2) 

    { 

        if(checkPrimeNumber(number1) && checkPrimeNumber(number2) && Math.abs(number1 - number2) == 2) 

            return true; 

        else 

            return false; 

    } 

  

    public static void main(String[] args) 

    { 

        int startRange, endRange; 

         

        Scanner sc=new Scanner(System.in);          

      

        System.out.println("Enter start value");            

        startRange = sc.nextInt();            

                System.out.println("Enter last value");            

        endRange = sc.nextInt(); 

         

        System.out.println("The pairs of twin primes between" + startRange + " and " + endRange + "are:"); 

         

        for (int i = startRange; i < endRange; i++) { 

            if (checkTwinPrimeNumber(i, (i + 2))){ 

                System.out.printf("(%d, %d)\n", i, i + 2); 

            } 

        } 

    } 

} 

Neon Number

 import java.util.Scanner;  

import java.lang.Math;  

public class Main

{

    

public static void main(String args[])     

{     

int sum = 0, n;      

Scanner sc = new Scanner(System.in);  

System.out.print("Enter the number to check: ");  

n = sc.nextInt();  

int square = n * n; 

while(square != 0)  

{  

 

int digit = square % 10; 

sum = sum + digit;

square = square / 10;  

}  

if(n == sum)  

System.out.println(n + " is a Neon Number.");  

else  

System.out.println(n + " is not a Neon Number.");  

}  

}  

DecimalToBinary

 

import java.util.Scanner; 

import java.lang.Math; 

public class Main

{

    public static int convertDecimalToBinary(int dec) {

   

      int rem,b1=0;

      int rev = 1;

      while (dec > 0) {

         rem = dec % 2;

         dec = dec / 2;

         b1 = b1 + rem * rev;

         rev = rev * 10;

      }

    return b1;

  }

public static void main(String args[])    

{    

 

 

    Scanner in = new Scanner(System.in); 

System.out.print("Enter a number : "); 

 

int num = in.nextInt(); 

 

    int decimal = convertDecimalToBinary(num);

    System.out.println("Binary to Decimal");

    System.out.println(num + " = " + decimal);

  }

 

 

}

Automorphic Number

 

import java.util.Scanner; 

import java.lang.Math; 

public class Main

{

public static void main(String args[])    

{    

Scanner in = new Scanner(System.in); 

System.out.print("Enter a number to check: "); 

 

int num = in.nextInt(); 

int count=0;

int square = num*num;

int temp = num;

while(temp>0) 

{ 

count++;

temp=temp/10; 

}  

int lastDigit = (int) (square%(Math.pow(10, count)));  

if(num == lastDigit) 

System.out.println(num+ " is an automorphic number."); 

else 

System.out.println(num+ " is not an automorphic number."); 

} 

} 

Armstrong Number

 

import java.util.Scanner; 

import java.lang.Math; 

public class Main

{

     static boolean isArmstrong(int n)  

{  

int temp, digits=0, last=0, sum=0;  

 

temp=n;  

 

while(temp>0)   

{  

temp = temp/10;  

digits++;  

}  

temp = n;  

while(temp>0)  

{

last = temp % 10;  

sum +=  (Math.pow(last, digits));

temp = temp/10;  

} 

 

if(n==sum)

return true;

else return false;  

}  

   

   

 

public static void main(String args[])    

{    

int num;  

Scanner sc= new Scanner(System.in); 

System.out.print("Enter the limit: ");

num=sc.nextInt(); 

if(isArmstrong(num)) 

System.out.print(num+ " is armstrong Number "); 

}  

} 

Fibonacci series

 

import java.util.*;

 

public class Main

{

                public static void main(String[] args) {

                        Scanner sc = new Scanner(System.in); 

                                 System.out.println( " enter a value");

 

                     int n1=0,n2=1,n3,i,count;

                     count = sc.nextInt();   

 

   

 for(i=1;i<=count;++i)//loop starts from 2 because 0 and 1 are already printed   

 {   

  n3=n1+n2;   

  System.out.print(" "+n1);   

  n1=n2;   

  n2=n3;   

 }   

 

}} 

 

Java happy Number

 

import java.util.*;

public class Main

{public static int isHappyNumber(int num){ 

        int rem = 0, sum = 0; 

         

        while(num > 0){ 

            rem = num%10; 

            sum = sum + (rem*rem); 

            num = num/10; 

        } 

        return sum; 

    } 

                public static void main(String[] args) {

                    Scanner sc = new Scanner(System.in); 

                                 System.out.println( " enter a value");

                                 int num = sc.nextInt();   

        int result = num; 

         

        while(result != 1 && result != 4){ 

            result = isHappyNumber(result); 

        } 

         

      

        if(result == 1) 

            System.out.println(num + " is a happy number"); 

        else if(result == 4) 

            System.out.println(num + " is not a happy number");    

    } 

} 

Java Magic Number

 

import java.util.Scanner; 

public class Main

{

                public static void main(String[] args) {

                                int n, remainder = 1, number, sum = 0; 

Scanner sc = new Scanner(System.in); 

System.out.print("Enter a number you want to check: "); 

n = sc.nextInt(); 

number = n; 

while (number > 9)               

{ 

while (number > 0) 

{ 

remainder = number % 10;  

sum = sum + remainder; 

number = number / 10;    

} 

number = sum; 

sum = 0; 

} 

if (number == 1) 

{ 

System.out.println("The given number is a magic number."); 

} 

else 

{ 

System.out.println("The given number is not a magic number."); 

} 

} 

}