Long factorial (#1277)

* Added the c++ code

* Added the description of the question

Commented the description of the question and explained various parts of the code.

* added the changes

Co-authored-by: Tarun Yadav <[email protected]>

Author: Saviour1001

Array/readme.md

@@ -22,9 +22,11 @@ The syntax is:
 
 To create an array, you need to known the length (or size) of the array in advance, and allocate accordingly. Once an array is created, its length is fixed and cannot be changed. At times, it is hard to ascertain the length of an array. Nonetheless, you need to estimate the length and allocate an upper bound. This is probably the major drawback of using an array.
 
+
 ##Questions
 
  * Counting rotations in a sorted array ---> [Python](/Code/Python/Count_of_rotations.py)
+ * Factorials of big numbers ----> [C++](/Code/C++/long_factorial.cpp)
  * Find duplicate in array ----> [C++](/Code/C++/Duplicate_in_array.cpp) | [Java](/Code/Java/dublicate.java)
  * Finding All subset ----> [C++](/Code/C++/Finding_all_subset.cpp)
  * Insertion_at_start ----> [C++](/Code/C++/insertion_at_start.cpp) | [Java](/Code/Java/insertion_at_start.java) | [Python](/Code/Python/insertion_at_start.py)
@@ -51,4 +53,6 @@ To create an array, you need to known the length (or size) of the array in advan
  * Union of two Unsorted Arrays ----> [C++](/Code/C++/Union_of_two_unsorted_array.cpp) 
  * Unsorted Zig-Zag Array ----> [C++](/Code/C++/unsorted_zig_zag_array.cpp) 
  * Kth Minimum in array ---->[Python](/Code/Python/Kth_Minimum_in_Array.py)
-
+ * Insertion_at_start ----> [C++](/Code/C++/insertion_at_start.cpp) | [Java](/Code/Java/insertion_at_start.java) | [Python](/Code/Python/insertion_at_start.py)
+ * Kadane's Algorithm ----> [C++](/Code/C++/kadane_algo.cpp)
+ 

Code/C++/long_factorial.cpp

@@ -0,0 +1,57 @@
+/*Finding huge factorials such as !100, !1000 is sometimes required but in languages such as C++
+the datatypes are not even capable of storing such a big number. We could achieve calculation of
+such a number via going back to the basis of how we used to muiltiply two numbers back in school. 
+We used to muiltiply numbers and would add the summation and get the final result. 
+This program here uses a vector to store each particular digit in a single index of the vector. 
+The carry is forwarded as basic maths and in the end the complete result gets stored in the vector*/
+
+#include <vector>
+#include <iostream>
+
+using namespace std;
+
+
+int main() {
+    int val;
+    int carry = 0;       //Input the number whose factorial is to be calculated 
+    cin >> val;
+    vector <int> arr(10000, 0);  //The size of the vector should be more than the digits present 
+    arr[0] = 1;                  //in the factorial of the number.  
+    int k = 0;                         
+
+    for(int i = 1; i <= val; i++) {
+        for(int j = 0;j <= k; j++) {      
+            arr[j] = arr[j] * i + carry;
+            carry = arr[j] / 10;
+            arr[j] = arr[j] % 10;
+        }
+        while(carry) {        //The carries are forwarded in order to get the final result
+            k++;
+            arr[k] = carry % 10;
+            carry /= 10;
+        }   
+    }
+    for(int i = k; i >= 0; i--) {  //Each digit of the final answer is stored in a single index 
+        cout << arr[i];            //of the vector    
+    }
+    cout << "\n";
+    return 0;
+}
+
+/*
+    Test Cases : 
+
+  1)Input  : 10
+    Output : 3628800
+
+  2)Input  : 20
+    Output : 2432902008176640000
+
+  3)Input  : 30
+    Output : 265252859812191058636308480000000
+
+    Time Complexity: O ( N ) (where N is the number which is the input)
+    Space Complexity: O ( N ) (where N is the number of digits present in the final answer)
+
+
+*/