chore(Java): add factorial of a number using Big Integer (#339)

algorithms/Java/Maths/factorial_using_big_integer.java

@@ -0,0 +1,67 @@
+// Calculating Factorial Using Big Integer
+// https://www.hackerearth.com/practice/notes/factorial-of-large-number/
+import java.math.BigInteger;
+import java.util.*;
+import java.io.*;
+import java.lang.*;
+
+class FactorialUsingBigInteger
+{
+    //Main Method
+    public static void main(String[] args) throws IOException
+    {
+        Scanner sc = new Scanner(System.in);
+        System.out.println("Enter the number of times you want to calculate Factorial:");
+        int t = sc.nextInt();
+        HashMap<Integer,BigInteger> hashmap = new HashMap<>();
+        int maxKey = -1;
+        for(int i=0;i<t;i++){
+            System.out.println("Enter the value of N:");
+            int N = sc.nextInt();
+            if(N>=0)
+            {
+                BigInteger f = new BigInteger("1"); // Or BigInteger assigned to ONE
+                // Multiply f with number till N
+                int initial = 2;
+		//Checking if inputted number exists in map or not
+                if (hashmap.containsKey(N)){
+                    f = hashmap.get(N);
+                } else {
+		    // For a given number, Checking whether any sub factorial has some element present in hashmap
+                    if (maxKey!=-1){
+                        initial = maxKey;
+                    }
+                    for (int j = initial; j <= N; j++) {
+                        if (hashmap.containsKey(j)) {
+                            f = f.multiply(hashmap.get(j));
+                        } else {
+                            f = f.multiply(BigInteger.valueOf(j));
+                            maxKey = j;
+                            hashmap.put(j, f);
+                        }
+                    }
+                }
+                System.out.println("Factorial of given number is :"+f);
+            }else{
+                System.out.println("Number Should be greater than 0");
+            }
+        }
+    }
+} 
+/*
+Time Complexity:O(t*N)
+Space Complexity:O(1)
+Input:
+Enter the number of times you want to calculate Factorial:
+3
+Enter the value of N:
+20   //O(N) ==>20*19*18.....*1
+Enter the value of N:
+80  // O(N) ==>80*79*78.....*21*hashmap[20]
+Enter the value of N:
+10  // O(1) ==>hashmap[10]
+Output:
+Factorial of given number is : 2432902008176640000
+Factorial of given number is : 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000
+Factorial of given number is : 3628800
+*/

algorithms/Java/README.md

@@ -20,6 +20,9 @@
 5. [Singly](linked-lists/singly.java)
 6. [Fold Linked List](linked-lists/fold-linked-list.java)
 
+## Maths
+1. [Factorial](Maths/factorial_using_big_integer.java)
+
 ## Queues
 
 1. [Circular Queue using Linked List](queues/circular-queue-linked-list.java)