Added Count-Primes tutorials

tutorials/basic-topics/Count-primes.md

@@ -0,0 +1,115 @@
+---
+title: 'Count Primes'
+description: 'Prime numbers are numbers that have only 2 factors: 1 and themselves.'
+hide_table_of_contents: true
+keywords:
+  - leetcode
+  - tutorial
+  - count primes
+  - Sieve of Eratosthenes 
+  - algorithm
+---
+
+<TutorialAuthors names="@M-Rahul1"/>
+
+## Overview
+In this we are given an integer, N. The goal is to count how numbers less than N, are primes. The integer is constrained to be non-negative.
+
+## Explanation
+Primes less than 10 are 2, 3, 5 and 7. So, the count is 4.
+
+## Approach(Brute Force)
+The general approach is to check for every integer less than N and increment the result if they are prime. For example, consider N = 10. Now, we can run a check from 2 to N – 1 to find how many primes lie in this range.
+
+### Algorithm
+We can check if each number is a prime or not. To check if the number 'i' is prime we will traverse all the numbers till[2,sqrt(i)] can check if they divide N or not.
+Similarly, we do this for all the N numbers.
+
+### C++ Program
+``` C++
+
+#include <bits/stdc++.h>
+using namespace std;
+
+//Function to check whether number is prime or not
+
+bool isPrime(int N)
+{
+    for(int i = 2 ; i * i <= N ; i++)
+        if(N % i == 0)
+            return false;
+    return true;
+}
+//Function to count number of primes upto N
+void primeSieve(int N){
+    int count=0;
+    for(int i=2;i<=n;i++){
+        if(isPrime(i)){
+            count++;
+        }
+    }
+    return count;
+}
+
+int main()
+{
+    int N = 10;
+    cout << primeSieve(N) << '\n';
+}
+```
+```
+Output:
+4
+```
+#### Time Complexity: 
+We run a loop for N/2 times. In every check, a time of complexity O(N / 2) (taking average as N / 2) is spent. So, the time complexity of this algorithm is O(N√N).
+
+#### Auxiliary Space: 
+O(1), Only constant space is used for constant variables.
+
+## Approach(Optimal Method)
+#### Sieve of Eratosthenes
+
+### Algorithm
+We start from 2, and on each encounter of a prime number, we mark its multiples as composite.
+### Time Complexity: O(n log log n)
+### Space Complexity: O(n)
+
+## Implementation
+
+``` C++ Program
+#include <bits/stdc++.h>
+using namespace std;
+
+int primeSieve(int N)
+{
+    int count = 0;
+    int prime[N]={0};
+    for(int i = 2 ; i <= N ; i++)
+    {
+        if(prime[i]==0)
+            for(int j = i * i ; j < N ; j += i)
+                prime[j] = 1;
+    }
+
+    for(int i = 2 ; i <= N ; i++)
+        if(prime[i]==0)
+            count++;
+
+    return count;
+}
+
+int main()
+{
+    int N = 10;
+    cout << primeSieve(N) ;
+}
+```
+```
+Output:
+4
+```
+
+### Suggested Problems 
+https://leetcode.com/problems/count-primes/
+