Update openmp Cdoe

integral.c

 #include <stdio.h>
+#include <stdlib.h>
 #include <math.h>
 #include <omp.h>
 
@@ -7,37 +8,128 @@ double lnFunction(double x) {
     return log(x) / x; 
 }
 
-double calculate_integral(int num_rectangles, double start, double end) {
-    double width = (end - start) / num_rectangles;
-    double total_area = 0.0;
+// this is the first approach 
+double calculateIntegral(int numRectangles, int start, int end) {
+    
+    // the width of  aa single rectangle
+    double width = (end - start ) /( numRectangles * 1.0 );
+    
+    // total area
+    double totalArea = 0.0;
+
+    #pragma omp parallel for reduction(+:totalArea)
+    for (int i = 0; i < numRectangles; i++) {
 
-    #pragma omp parallel for reduction(+:total_area)
-    for (int i = 0; i < num_rectangles; i++) {
         // Midpoint for rectangle
-        double x = start + (i + 0.5) * width;  
-        double area = lnFunction(x) * width;
-        total_area += area;
+        double xMid = start + (i + 0.5) * width;  
+        // calcute F (x)
+        double area = lnFunction(xMid) * width;
+
+        totalArea += area;
     }
 
-    return total_area;
+    return totalArea;
 }
+// anpother appraoch to calc the itegral using openmp 
+// by using an atomic operation for the (+=)
+double calculateIntegralTrapezoidal(int numRectangles, int start, int end) {
+    double width = (end - start) / (numRectangles * 1.0);
+    double totalArea = 0.0;
+
+    // Calculate the area using the in parallel
+    #pragma omp parallel
+    {
+        double localSum = 0.0;
+
+        #pragma omp for
+        for (int i = 0; i < numRectangles; i++) {
+            // Midpoint for rectangle
+            double xMid = start + (i + 0.5) * width;  
+            // calcute F (x)
+            double area = lnFunction(xMid) * width;
+            localSum += area;
+        }
+
+        // Reduce local sums into total area
+        #pragma omp atomic
+        totalArea += localSum;
+    }
+
+    return totalArea;
+}
+
 
 int main(int argc, char *argv[]) {
+
+    // * note => ( 
+    //          the two parameter nume of threads and num of rectangle 
+    //          we read them from the argument of the program    
+    // )
+
     // Adjust for higher precision
-    int num_rectangles = 1000000;  
+    int numRectangles = 1000000;  
+    // number of threads 
+    int numThreads = 2;
 
     // integration interval
-    double start = 1.0, end = 10.0;
+    int  start = 1, end = 10;
+    
+    // read the number of threads and rectangles from argument if it passed  
+    if (argc < 3) {
+        printf("+ Usage: %s <num_threads> <num_rectangles>\n", argv[0]);
+        printf("+ Using default values: %d threads, %d rectangles.\n", numThreads, numRectangles);
+      
+    } else {
+        // Convert command line argument to integer for threads
+        numThreads = atoi(argv[1]); 
+        // Convert command line argument to integer for rectangles
+        numRectangles = atoi(argv[2]);
+    }
+    
+    // Set the number o threads
+    omp_set_num_threads(numThreads);
+
+    // start the timer 
+    double startTime = omp_get_wtime();
+    double result = calculateIntegral(numRectangles, start, end);
+    // stop the timer 
+    double endTime = omp_get_wtime();
+
+    // Print results in a good way
+    printf("\n+----------------------------------------+\n");
+    printf("+\tResult\t\t\n");
+    printf("+------------------------------------------+\n");
+    printf("[+] Calculated integral:    %.10f\n", result);
+    printf("[+] Execution time:         %.4f seconds\n", endTime - startTime);
+    printf("[+] Number of threads:      %d\n", numThreads);
+    printf("[+] Number of rectangles:   %d\n", numRectangles);
+    printf("+------------------------------------------+\n");
+
+ // this is an old code for the main 
+/*
+    int ad ;
+
+    int numThreads;    //number of threads
+
+    printf("Enter the number of threads: ");
+    ad =scanf("%d", &numThreads);
+
+    // Set the number of threads for OpenMP
+    omp_set_num_threads(numThreads);
+
+    // Start timing the execution
+    double startTime = omp_get_wtime();
     
-    // Start time for performance measurement
-    double start_time = omp_get_wtime(); 
-    double total_area = calculate_integral(num_rectangles, start, end);
+    // Calculate the integral
+    double result = calculateIntegral(numRectangles , start , end );
 
-    // End time for performance measurement
-    double end_time = omp_get_wtime(); 
+    // End timing the execution
+    double endTime = omp_get_wtime();
 
-    printf("Calculated integral: %.10f\n", total_area);
-    printf("Execution time: %.4f seconds\n", end_time - start_time);
+    // Output the results
+    printf("Calculated integral: %.10f\n", result);
+    printf("Execution time: %.4f seconds with %d threads\n", endTime - startTime, numThreads);
+ */
 
     return 0;
 }

mandlebrot.c

-#include "iostream"
+#include <stdio.h>
+#include <stdlib.h>
 #include <complex>
 #include <omp.h>
-#include <cstdlib>
 
-bool isInMandelbrotSet(double real, double imag, int max_iterations) {
-    std::complex<double> c(real, imag);
-    std::complex<double> z = 0;
-    for (int i = 0; i < max_iterations; ++i) {
+using namespace std ;
+// global varibles 
+
+// define the interval for the complex plane region 
+const double REAL_MIN = -2.5;
+const double REAL_MAX = 1.0;
+const double IMAG_MIN = -1.0;
+const double IMAG_MAX = 1.0;
+
+
+// define the max iteration for check the mandlebrot set 
+const int MAXITERATION = 3000;
+
+// function to check if a point is in the Mandelbrot set
+bool isInMandelbrotSet(double real, double imag) {
+    complex<double> c(real, imag);
+    complex<double> z = 0;
+    
+    // iterate to check if the point diverges
+    for (int i = 0; i < MAXITERATION; ++i) {
         z = z * z + c;
-        if (std::abs(z) > 2.0) return false;
+        
+        // if the magnitude of z exceeds 2, it escapes the set
+        if (abs(z) > 2.0) return false;
     }
+    
+    // if max_iterations reached without escaping, it s not  in the set
     return true;
 }
 
-double calculateMandelbrotArea(int num_points, int max_iterations, bool parallel) {
-    int in_set_count = 0;
+// function to estimate the area of the Mandelbrot set
+//  using Monte Carlo method
+double calculateMandelbrotArea(int numIteration) {
+    int inSetCount = 0;
     double real, imag;
 
-    #pragma omp parallel for reduction(+:in_set_count) private(real, imag) if (parallel)
-    for (int i = 0; i < num_points; ++i) {
-        real = (rand() / (double)RAND_MAX) * 3.5 - 2.5;  // Real part in range [-2.5, 1]
-        imag = (rand() / (double)RAND_MAX) * 2.0 - 1.0;  // Imaginary part in range [-1, 1]
-        if (isInMandelbrotSet(real, imag, max_iterations)) {
-            in_set_count++;
+    // Parallelize the loop
+    #pragma omp parallel for reduction(+:inSetCount) private(real, imag) 
+    for (int i = 0; i < numIteration; ++i) {
+        
+        // generate a random point within the specified complex plane region
+
+        // Real part in range [REAL_MIN, REAL_MAX]
+        real = (rand() / (double)RAND_MAX) * (REAL_MAX - REAL_MIN) + REAL_MIN;
+
+        // Imagina part in range [IMAG_MIN, IMAG_MAX]
+        imag = (rand() / (double)RAND_MAX) * (IMAG_MAX - IMAG_MIN) + IMAG_MIN;  
+
+        // check if the point is within the mandelbrot set
+        if (isInMandelbrotSet(real, imag)) {
+            inSetCount++;  
         }
     }
 
-    double area = (3.5 * 2.0) * (in_set_count / (double)num_points);
+    // calculate the estimated area based on the fraction of points in the set
+
+    double area = ((REAL_MAX - REAL_MIN) * (IMAG_MAX - IMAG_MIN)) * (inSetCount / (double)numIteration);
+    
     return area;
 }
 
-int main() {
-    int num_points = 1000000;         // Number of random points for Monte Carlo
-    int max_iterations = 5000;        // Maximum iterations for Mandelbrot check
-
-    // Sequential run
-    double start_time = omp_get_wtime();
-    double area_seq = calculateMandelbrotArea(num_points, max_iterations, false);
-    double end_time = omp_get_wtime();
-    std::cout << "Sequential Mandelbrot area: " << area_seq << std::endl;
-    std::cout << "Sequential time: " << end_time - start_time << " seconds\n";
-
-    // Parallel run
-    start_time = omp_get_wtime();
-    double area_par = calculateMandelbrotArea(num_points, max_iterations, true);
-    end_time = omp_get_wtime();
-    std::cout << "Parallel Mandelbrot area: " << area_par << std::endl;
-    std::cout << "Parallel time: " << end_time - start_time << " seconds\n";
+int main(int argc, char *argv[]) {
+    // 
+    double startTime, endTime ;
+    
+    // number of iteration  for Monte Carlo method
+    int numIteration = 1000000;     
+    // default number of threads
+    int numThreads = 4;            
+
+    // check if the number of threads is provided as a command line argument
+    if (argc > 1) {
+        // Convert argument to integer
+        numThreads = atoi(argv[1]);  
+    }
+
+    // set the number of threads for OpenMP
+    omp_set_num_threads(numThreads);
+
+    // execution
+    
+    // Start timer
+    startTime = omp_get_wtime();                   
+    // Calculate area
+    double area_par = calculateMandelbrotArea(numIteration);   
+    // End timer
+    endTime = omp_get_wtime();                
+    
+    printf("[+] Mandelbrot area: %.10f\n", area_par);
+    printf("[+] time: %.4f seconds with %d threads\n", endTime - startTime, numThreads);
 
     return 0;
 }