added data for hacktober fest 2022

01. Mathematics/10_exactly 3 divisors.cpp

@@ -0,0 +1,62 @@
+// { Driver Code Starts
+//Initial Template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// } Driver Code Ends
+//User function Template for C++
+
+class Solution
+{
+public:
+    int exactly3Divisors(int n)
+    {
+     cout << "Numbers with 3 divisors : "<< endl;
+    for(int i = 2; i * i <= n; i++)
+    {        
+        // Checks for prime
+        if (isPrime(i)) //if prime checks if its square is less than or equal to n
+            if (i * i <= n)
+            {                
+                // Print numbers 
+                cout << i * i << " ";
+            }
+        }
+    }
+    return 0;
+    }
+    //method for checking whether number is prime or not
+    bool isPrime(int n)
+{
+    if (n == 0 || n == 1)
+        return false;        
+    for(int i = 2; i * i <= n; i++)
+    {
+        if (n % i == 0)
+            return false;
+    }
+    return true;
+}
+};
+
+// { Driver Code Starts.
+
+int main()
+{
+    int T;
+
+    //taking testcases
+    cin >> T;
+    while (T--)
+    {
+        int N;
+
+        //taking N
+        cin >> N;
+        Solution ob;
+        //calling function exactly3Divisors()
+        cout << ob.exactly3Divisors(N) << endl;
+    }
+    return 0;
+} // } Driver Code Ends

01. Mathematics/11_GPterm.cpp

@@ -0,0 +1,44 @@
+// { Driver Code Starts
+//Initial Template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// } Driver Code Ends
+//User function Template for C++
+
+class Solution
+{
+public:
+    //Complete this function
+    double termOfGP(int A, int B, int N)
+    {
+        //first finding ratio
+        double ratio = double(B)/double(A);
+        //Nth term according to the formula
+        double ans = A*(pow(ratio,N-1));
+        return ans;
+    }
+};
+
+// { Driver Code Starts.
+
+int main()
+{
+    int T;    //testcases total
+    cin >> T; //input the testcases
+
+    for (int i = 0; i < T; i++) //white testcases are not exhausted
+    {
+        int A, B;
+        cin >> A >> B; //input first and second term of gp
+        int N;
+        cin >> N; //input n
+        Solution ob;
+        cout << floor(ob.termOfGP(A, B, N)) << endl;
+    }
+
+    return 0;
+}
+
+// } Driver Code Ends

01. Mathematics/12_Missing-number-in-array.cpp

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+/*
+Given an array of size N-1 such that it only contains distinct integers in the range of 1 to N. Find the missing element.
+
+Example 1:
+
+Input:
+N = 5
+A[] = {1,2,3,5}
+Output: 4
+
+Example 2:
+
+Input:
+N = 10
+A[] = {1,2,3,4,5,6,7,8,10}
+Output: 9
+
+Your Task :
+You don't need to read input or print anything. 
+Complete the function MissingNumber() that takes array and N as input  parameters and returns the value of the missing number.
+
+Expected Time Complexity: O(N)
+Expected Auxiliary Space: O(1)
+
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+class Solution
+{
+public:
+    int MissingNumber(vector<int> &array, int n)
+    {
+       // Your code goes here
+        int i=0,sum=0,missing_num;
+        int sum_of_n=n*(n+1)/2;//sum of first n natural numbers
+        for(i=0;i<n-1;i++)
+            sum+=array[i];//sum of elements present in array.
+        missing_num=sum_of_n-sum;//missing element 
+        return missing_num;
+    }
+};
+
+int main()
+{
+    int t;
+    cin >> t;
+    while (t--)
+    {
+        int n;
+        cin >> n;
+
+        vector<int> array(n - 1);
+        for (int i = 0; i < n - 1; ++i)
+            cin >> array[i];
+        Solution obj;
+        cout << obj.MissingNumber(array, n) << "\n";
+    }
+    return 0;
+}

01. Mathematics/13_ModularMultiplicativeInverse.cpp

@@ -0,0 +1,41 @@
+// { Driver Code Starts
+//Initial Template for C++
+
+#include <iostream>
+using namespace std;
+
+// } Driver Code Ends
+//User function Template for C++
+
+class Solution
+{
+public:
+	//Complete this function
+	int modInverse(int a, int m)
+	{
+		for (int x = 1; x < m; x++)
+        	if (((a%m) * (x%m)) % m == 1)
+            	return x;
+	}
+};
+
+// { Driver Code Starts.
+
+int main()
+{
+	int T;
+
+	//taking testcases
+	cin >> T;
+	while (T--)
+	{
+		int a, m;
+
+		//taking input a and m
+		cin >> a >> m;
+		Solution ob;
+		//calling function modInverse()
+		cout << ob.modInverse(a, m) << endl;
+	}
+	return 0;
+} // } Driver Code Ends

01. Mathematics/14_primalityTest.cpp

@@ -0,0 +1,45 @@
+// { Driver Code Starts
+//Initial Template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// } Driver Code Ends
+//User function Template for C++
+
+class Solution
+{
+public:
+    bool isPrime(int N)
+    {
+        for(int i=2;i<=sqrt(N);i++)
+        {
+            if(N%i==0)
+             return false;
+        }
+        return true;
+        //Your code here
+    }
+};
+
+// { Driver Code Starts.
+
+int main()
+{
+    int T;      //testcases
+    cin >> T;   //input testcases
+    while (T--) //while testcase have not been exhausted
+    {
+        int N;
+        cin >> N; //input n
+        Solution ob;
+        if (ob.isPrime(N))
+            cout << "Yes";
+        else
+            cout << "No";
+
+        cout << endl;
+    }
+    return 0;
+}
+// } Driver Code Ends

01. Mathematics/15_QuadraticEquationRoots.cpp

@@ -0,0 +1,65 @@
+// { Driver Code Starts
+// Initial template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// } Driver Code Ends
+// User function Template for C++
+
+class Solution
+{
+public:
+    vector<int> quadraticRoots(int a, int b, int c)
+    {
+        vector<int> ans;
+        if(a==0)
+        {
+            ans.push_back(-1);
+            return ans;
+        }
+        int d = b*b - 4*a*c;
+        double sqrt_val = sqrt(abs(d));
+        if(d>0)
+        {
+            double root1 = (double)(-b + sqrt_val)/(2*a);
+            double root2 = (double)(-b - sqrt_val)/(2*a);
+            ans.push_back(root1);
+            ans.push_back(root2);
+        }
+        else if(d==0)
+        {
+            double root = -(double)b/(2*a);
+            ans.push_back(root);
+            ans.push_back(root);
+        }
+        else
+        {
+            ans.push_back(-1);
+        }
+        return ans;
+        // code here
+    }
+};
+
+// { Driver Code Starts.
+
+int main()
+{
+    int T;
+    cin >> T;
+    while (T--)
+    {
+        int a, b, c;
+        cin >> a >> b >> c;
+        Solution ob;
+        vector<int> roots = ob.quadraticRoots(a, b, c);
+        if (roots.size() == 1 && roots[0] == -1)
+            cout << "Imaginary";
+        else
+            for (int i = 0; i < roots.size(); i++)
+                cout << roots[i] << " ";
+        cout << endl;
+    }
+    return 0;
+} // } Driver Code Ends

01. Mathematics/16_Smallestdivisiblenumber.cpp

@@ -0,0 +1,36 @@
+// { Driver Code Starts
+//Initial template for C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// } Driver Code Ends
+//User function template for C++
+
+class Solution
+{
+public:
+    long long getSmallestDivNum(long long n)
+    {
+        long long ans = 1;
+        for(long long i=1;i<=n;i++)
+          ans = (ans*i)/(__gcd(ans,i));
+        return ans;
+        // code here
+    }
+};
+
+// { Driver Code Starts.
+int main()
+{
+    int t;
+    cin >> t;
+    while (t--)
+    {
+        int n;
+        cin >> n;
+        Solution ob;
+        cout << ob.getSmallestDivNum(n) << endl;
+    }
+    return 0;
+} //