Euclidean Algorithm for GCD and comparision with Brute force approach.

code/data_structures/Linked_lists/Header_Linked_List.cpp

@@ -0,0 +1,99 @@
+//Part of Cosmos by OpenGenus Foundation
+//Contributed by Tushar Gautam (Tushark21)
+
+#include <iostream>
+#include <conio.h>
+
+using namespace std;
+
+struct node{
+	int info;
+	node *next;
+}*ptr,*head,*start;
+
+
+//Function for creating new node and Inserting data in the node
+struct node* insert(struct node* head,int data){
+	ptr=new node;
+	ptr->next=NULL;
+	ptr->info=data;
+
+	head->next=ptr;
+	cout<<"Data Inserted\n";
+	return ptr;
+}
+
+//Function for searching item in Linked List
+int search(struct node* start,int item){
+	ptr=start->next;
+	int f,k;
+	f=0;
+	k=0;
+	while(ptr!=NULL){
+		k++;
+		if(ptr->info==item){
+			f++;
+			cout<<"Item Found at Node: "<<k<<"\n";
+		}
+		ptr=ptr->next;
+	}
+	return f;
+}
+
+//Function for Printing the Linked List
+void printLL(struct node* start){
+
+	ptr=start->next;
+
+	while(ptr!=NULL){
+		cout<<ptr->info<<"->";
+		ptr=ptr->next;
+	}
+	cout<<"\n";
+
+}
+
+int main(){
+
+int c=1,k=0,item,data;
+
+ptr=new node;
+ptr->next=NULL;
+start=head=ptr;
+
+while(c<4 && c>0){
+	cout<<"1.Insert\n2.Search Item\n3.Link List\n";
+	cin>>c;
+
+	switch(c){
+		case 1:
+			cout<<"Enter Data\n";
+			cin>>data;
+
+			head=insert(head,data);
+		break;
+
+		case 2:
+			cout<<"Enter Item that you want to find\n";
+			cin>>item;
+
+			int f;
+			f=search(start,item);
+			if(f==0){
+				cout<<"Item Not Found\n";
+			}
+		break;
+
+		case 3:
+			printLL(start);
+		break;
+
+		default:
+			cout<<"Wrong Choice\nExiting...\n";
+	}
+
+}
+
+getch();
+return 0;
+}

code/mathematical-algorithms/Coprime.java

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+//Part of Cosmos by OpenGenus Foundation
+
+import java.util.*;
+
+public class coprime{
+
+	public static void main(String args[]){
+
+		Scanner i= new Scanner(System.in);
+                int a,b;
+		System.out.println("Enter 1st Number");
+		a=i.nextInt();
+		System.out.println("Enter 2nd Number");
+		b=i.nextInt();
+
+		while(b!=0) {
+                int x=a;
+                a=b;
+                b=x%b;
+        }
+
+		if(a==1){
+            System.out.println("Coprime");
+		}
+
+        else{
+            System.out.println("Not Coprime");
+        }
+	}
+
+
+}

code/mathematical-algorithms/euclidean_gcd/README.md

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+GCD-Greatest Common Divisor of two numbers is the largest number that divides both numbers with remainder zero.
+
+Euclidean Algorithm:
+Idea behind Euclidean's Algorithm is that GCD(a,b) is same as GCD(b%a,a).

code/mathematical-algorithms/euclidean_gcd/euclidean_gcd.cpp

@@ -0,0 +1,63 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int steps=0;
+
+int min(int x,int y){
+    if(x>y){
+        return x;
+    }
+    return y;
+}
+
+int gcd(int x,int y){
+    if(x==0 && y==0){
+        steps++;
+        return -1;
+    }
+
+    if(x==0 || y==0){
+        steps++;
+        return x==0?y:y;
+    }
+
+    int smallerNum=min(x,y),divisor;
+    for(int i=1;i<=smallerNum;i++){
+        if(x%i==0 && y%i==0){
+            divisor=i;
+        }
+        steps++;
+    }
+
+    return divisor;
+}
+
+int euclideanGCD(int x,int y){
+    steps++;
+    if(x==0 && y==0){
+        return -1;
+    }
+
+    if(x==0){
+        return y;
+    }
+
+    return euclideanGCD(y%x,x);
+}
+
+int main(){
+
+    int a,b;
+    cout<<"Enter 1st Number:";
+    cin>>a;
+    cout<<"Enter 2nd Number:";
+    cin>>b;
+
+    cout<<"GCD of "<<a<<" and "<<b<<" by Brute Force Approach is "<<gcd(a,b)<<"\n";
+    cout<<"Steps Taken by Brute Force Approach: "<<steps<<"\n";
+    steps=0;
+    cout<<"GCD of "<<a<<" and "<<b<<" by Euclidean's Algorithm is "<<euclideanGCD(a,b)<<"\n";
+    cout<<"Steps taken by Euclidean's Algorithm: "<<steps;
+    return 0;
+}