feat: add program to calculate binomial coefficients (#1448)

* Add program to calculate binomial coefficients

* docs: add link to github profile, change cmath to cstdlib

* correction of comments, adding math namespace

* updating DIRECTORY.md

* Adding binomial namespace, rename function and filename, correcting comments

* updating DIRECTORY.md

Co-authored-by: astronmax <astronmax@yandex.ru>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -136,6 +136,7 @@
 ## Math
   * [Armstrong Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/armstrong_number.cpp)
   * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp)
+  * [Binomial Calculate](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binomial_calculate.cpp)
   * [Check Amicable Pair](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_amicable_pair.cpp)
   * [Check Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_factorial.cpp)
   * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_prime.cpp)

math/binomial_calculate.cpp

@@ -0,0 +1,92 @@
+/**
+ * @file
+ * @brief Program to calculate [Binomial
+ * coefficients](https://en.wikipedia.org/wiki/Binomial_coefficient)
+ *
+ * @author [astronmax](https://github.com/astronmax)
+ */
+
+#include <cassert>   /// for assert
+#include <cstdint>   /// for int32_t type
+#include <cstdlib>   /// for atoi
+#include <iostream>  /// for IO operations
+
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * @namespace binomial
+ * @brief Functions for [Binomial
+ * coefficients](https://en.wikipedia.org/wiki/Binomial_coefficient)
+ * implementation
+ */
+namespace binomial {
+/**
+ * @brief Function to calculate binomial coefficients
+ * @param n first value
+ * @param k second value
+ * @return binomial coefficient for n and k
+ */
+size_t calculate(int32_t n, int32_t k) {
+    // basic cases
+    if (k > (n / 2))
+        k = n - k;
+    if (k == 1)
+        return n;
+    if (k == 0)
+        return 1;
+
+    size_t result = 1;
+    for (int32_t i = 1; i <= k; ++i) {
+        result *= n - k + i;
+        result /= i;
+    }
+
+    return result;
+}
+}  // namespace binomial
+}  // namespace math
+
+/**
+ * @brief Test implementations
+ * @returns void
+ */
+static void tests() {
+    // tests for calculate function
+    assert(math::binomial::calculate(1, 1) == 1);
+    assert(math::binomial::calculate(57, 57) == 1);
+    assert(math::binomial::calculate(6, 3) == 20);
+    assert(math::binomial::calculate(10, 5) == 252);
+    assert(math::binomial::calculate(20, 10) == 184756);
+    assert(math::binomial::calculate(30, 15) == 155117520);
+    assert(math::binomial::calculate(40, 20) == 137846528820);
+    assert(math::binomial::calculate(50, 25) == 126410606437752);
+    assert(math::binomial::calculate(60, 30) == 118264581564861424);
+    assert(math::binomial::calculate(62, 31) == 465428353255261088);
+
+    std::cout << "[+] Binomial coefficients calculate test completed"
+              << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @param argc commandline argument count
+ * @param argv commandline array of arguments
+ * @returns 0 on exit
+ */
+int main(int argc, const char* argv[]) {
+    tests();  // run self-test implementations
+
+    if (argc < 3) {
+        std::cout << "Usage ./binomial_calculate {n} {k}" << std::endl;
+        return 0;
+    }
+
+    int32_t n = atoi(argv[1]);
+    int32_t k = atoi(argv[2]);
+
+    std::cout << math::binomial::calculate(n, k) << std::endl;
+    return 0;
+}