feat: add sum_of_binomial_coefficients (#1363)

* Add files via upload

* update sum_of_binomial_coefficients

* Update math/sum_of_binomial_coefficient.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update math/sum_of_binomial_coefficient.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* clang-format and clang-tidy fixes for e7ac2255

* Update math/sum_of_binomial_coefficient.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update sum_of_binomial_coefficient.cpp

* Update math/sum_of_binomial_coefficient.cpp

Co-authored-by: Ayaan Khan <ayaankhan98@gmail.com>

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Ayaan Khan <ayaankhan98@gmail.com>

DIRECTORY.md

@@ -156,6 +156,7 @@
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sieve_of_eratosthenes.cpp)
   * [Sqrt Double](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sqrt_double.cpp)
   * [String Fibonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/string_fibonacci.cpp)
+  * [Sum Of Binomial Coefficient](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_binomial_coefficient.cpp)
   * [Sum Of Digits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/sum_of_digits.cpp)
 
 ## Numerical Methods

math/sum_of_binomial_coefficient.cpp

@@ -0,0 +1,67 @@
+/**
+ * @file
+ * @brief Algorithm to find sum of binomial coefficients of a given positive integer.
+ * @details Given a positive integer n, the task is to find the sum of binomial coefficient i.e
+ * nC0 + nC1 + nC2 + ... + nCn-1 + nCn
+ * By induction, we can prove that the sum is equal to 2^n
+ * @see more on https://en.wikipedia.org/wiki/Binomial_coefficient#Sums_of_the_binomial_coefficients
+ * @author [muskan0719](https://github.com/muskan0719)
+ */
+#include <iostream> /// for std::cin and std::cout
+#include <cassert>  /// for assert
+
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+
+	/** 
+	 * Function to calculate sum of binomial coefficients
+	 * @param n number
+	 * @return Sum of binomial coefficients of number 
+	 */
+	uint64_t binomialCoeffSum(uint64_t n) 
+	{ 
+	    // Calculating 2^n  
+		return (1 << n); 
+	}
+}  // namespace math
+
+/**
+ * Function for testing binomialCoeffSum function.
+ * test cases and assert statement.
+ * @returns `void`
+*/
+static void test()
+{
+	int test_case_1 = math::binomialCoeffSum(2);
+	assert(test_case_1==4);
+	std::cout<<"Test_case_1 Passed!"<<std::endl;
+	
+	int test_case_2 = math::binomialCoeffSum(3);
+	assert(test_case_2==8);
+	std::cout<<"Test_case_2 Passed!"<<std::endl;
+	
+	int test_case_3 = math::binomialCoeffSum(4);
+	assert(test_case_3==16);
+	std::cout<<"Test_case_3 Passed!"<<std::endl;
+	
+	int test_case_4 = math::binomialCoeffSum(5);
+	assert(test_case_4==32);
+	std::cout<<"Test_case_4 Passed!"<<std::endl;
+	
+	int test_case_5 = math::binomialCoeffSum(7);
+	assert(test_case_5==128);
+	std::cout<<"Test_case_5 Passed!"<<std::endl;
+ } 
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() 
+{ 
+    test(); // execute the tests
+	return 0; 
+}