fix: fit approximate_pi.cpp to guidelines (TheAlgorithms#2499)

* Update approximate_pi.cpp

* clang-format and clang-tidy fixes for 5a951bd

---------

Co-authored-by: github-actions[bot] <[email protected]>
Co-authored-by: realstealthninja <[email protected]>
Co-authored-by: David Leal <[email protected]>

Author: 4 people

math/approximate_pi.cpp

@@ -1,78 +1,83 @@
 /**
  * @file
- * @brief Implementation to calculate an estimate of the [number π (Pi)](https://en.wikipedia.org/wiki/File:Pi_30K.gif).
+ * @brief
+ * Implementation to calculate an estimate of the [number π
+ * (Pi)](https://en.wikipedia.org/wiki/File:Pi_30K.gif).
  *
  * @details
- * We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. If x² + y² ≤ 1, then the 
- * point is inside the quarter disk of radius 1, otherwise the point is outside.
- * We know that the probability of the point being inside the quarter disk is equal to π/4
- * double approx(vector<Point> &pts) which will use the points pts (drawn at random) to 
- * return an estimate of the number π
- * \note This implementation is better than naive recursive or iterative
+ * We take a random point P with coordinates (x, y) such that 0 ≤ x ≤ 1 and 0 ≤
+ * y ≤ 1. If x² + y² ≤ 1, then the point is inside the quarter disk of radius 1,
+ * else the point is outside. We know that the probability of the point being
+ * inside the quarter disk is equal to π/4 double approx(vector<Point> &pts)
+ * which will use the points pts (drawn at random) to return an estimate of the
+ * number π
+ * @note This implementation is better than naive recursive or iterative
  * approach.
  *
  * @author [Qannaf AL-SAHMI](https://github.com/Qannaf)
  */
 
+#include <cassert>   /// for assert
+#include <cstdlib>   /// for std::rand
 #include <iostream>  /// for IO operations
 #include <vector>    /// for std::vector
-#include <cstdlib>  /// for std::rand
 
 /**
  * @namespace math
  * @brief Mathematical algorithms
  */
 namespace math {
 
-    /**
-     * structure of points containing two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. 
-    */
-    typedef struct {
+/**
+ * @brief structure of points containing two numbers, x and y, such that 0 ≤ x ≤
+ * 1 and 0 ≤ y ≤ 1.
+ */
+using Point = struct {
     double x;
     double y;
-    } Point;
+};
 
-    double  approximate_pi(const std::vector<Point> &pts) {
-    /**
-     * This function use the points pts (drawn at random) to return an estimate of the number π  using the given points
-     * @param pts Each item of pts contains a point. A point is represented by a structure containing exactly 
-     * two numbers, respectively x and y such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. 
-     * pts always contains at least one item
-     * @return  an estimate of the number π
-     */
-        {
-            int count =0;    // Points in cercle
-            for(Point p:pts)
-                if(p.x * p.x + p.y*p.y <= 1)
-                    ++count;
-            
-            return 4.0*count/pts.size();
+/**
+ * @brief This function uses the points in a given vector 'pts' (drawn at
+ * random) to return an approximation of the number π.
+ * @param pts Each item of pts contains a point. A point is represented by the
+ * point structure (coded above).
+ * @return  an estimate of the number π.
+ */
+double approximate_pi(const std::vector<Point> &pts) {
+    double count = 0;  // Points in circle
+    for (Point p : pts) {
+        if ((p.x * p.x) + (p.y * p.y) <= 1) {
+            count++;
         }
     }
+    return 4.0 * count / static_cast<double>(pts.size());
+}
 }  // namespace math
 
 /**
  * @brief Self-test implementations
  * @returns void
  */
-static void test() {
-        std::vector<math::Point> rands;
+static void tests() {
+    std::vector<math::Point> rands;
     for (std::size_t i = 0; i < 100000; i++) {
         math::Point p;
-        p.x = rand() / (double)RAND_MAX; // 0 <= x <= 1
-        p.y = rand() / (double)RAND_MAX; // 0 <= y <= 1
+        p.x = rand() / static_cast<double>(RAND_MAX);  // 0 <= x <= 1
+        p.y = rand() / static_cast<double>(RAND_MAX);  // 0 <= y <= 1
         rands.push_back(p);
     }
-    std::cout << math::approximate_pi(rands) << std::endl;          // ~3.14
+    assert(math::approximate_pi(rands) > 3.135);
+    assert(math::approximate_pi(rands) < 3.145);
+
+    std::cout << "All tests have successfully passed!" << std::endl;
 }
 
 /**
  * @brief Main function
- * @param argc commandline argument count (ignored)
- * @param argv commandline array of arguments (ignored)
  * @returns 0 on exit
  */
-int main(int argc, char *argv[]) {
-    test();  // run self-test implementations
+int main() {
+    tests();  // run self-test implementations
     return 0;
 }