Merge pull request #227 from Mukulbaid63/pf_3

N digit prime added

Author: yashaswibiyahut

Diff for: Java/NthDigitMaxPrime/MaxPrime.java

@@ -0,0 +1,54 @@
+imjort java.util.*; 
+
+class MaxPrime
+{ 
+static int limit = 100000000; 
+static boolean[] sieve = new boolean[limit + 1]; 
+
+/*The Sieve of Eratosthenes marks all the no.s except 
+primes to false in the bool arr in most optimal way.*/
+static void SieveOfEratosthenes() 
+{ 
+	for (int i=0;i<limit+1;i++) 
+	{ //setting all values to true 
+		sieve[i]=true; 
+	} 
+	for (int j=2;j*j<=limit;j++) 
+	{ 
+		if(sieve[j]==true) 
+		{   //setting all the multiples of j as false
+			for (int i=j*j;i<=limit;i+=j) 
+				sieve[i]=false; 
+		} 
+	} 
+} 
+
+static int maxPrime(int d) 
+{ 
+	int l=(int)Math.pow(10,d-1); //lowest d digit number 
+	int r=(int)Math.pow(10,d)-1; //highest d digit number
+	for (int i=r;i>=l;i--) 
+	{   /**The first index with true value in sieve[] will be 
+        the answer as we are traversing in decreasing order */
+		if(sieve[i]) 
+		{ 
+			return i; 
+		} 
+	} 
+    
+	return -1; 
+} 
+
+
+public static void main(String[] args) 
+{ 
+	SieveOfEratosthenes(); 
+
+    Scanner sc=new Scanner(System.in);
+    int n=sc.nextInt();//Input
+    
+	System.out.println(maxPrime(n)); //Output
+	
+} 
+} 
+ 

Diff for: Java/NthDigitMaxPrime/README.md

@@ -0,0 +1,35 @@
+# Sample Input:
+
+2
+
+  
+
+# Sample Output:
+
+97
+
+  
+
+# Sample Input:
+
+6
+
+  
+
+# Sample Output:
+
+999983
+
+  
+
+# Explaination:
+TC 1:         
+l=10^(2-1)=10
+r=10^2-1=99
+
+After checking in the sieve[] in decreasing order,the first time comes out to be 97
+
+
+# Time Complexity:
+
+<h3>O(limit log(log limit))</h3>,where limit is the size of the sieve[].This is the most optimal way to find out the  required solution.