try to understand some mathematics

src/main/java/workshop/exercises/DeadlockPreventionWorkshop.java

@@ -22,6 +22,8 @@ public class DeadlockPreventionWorkshop {
     public static void useResources(Resource r1, Resource r2) {
         // TODO: Prevent deadlock by enforcing a consistent lock acquisition order
         // Hint: Compare resource IDs and always synchronize on the resource with the smaller ID first.
+        Resource first  = r1.getId() < r2.getId() ? r1 : r2;
+        Resource second = r1.getId() < r2.getId() ? r2 : r1;
 
         System.out.println(Thread.currentThread().getName() + " is attempting to lock " + r1.getName());
         synchronized (r1) {

src/main/java/workshop/exercises/LockWorkshop.java

@@ -7,14 +7,19 @@ public class LockWorkshop {
     public static int counter = 0;
     
     // TODO: Create a ReentrantLock instance to protect the critical section
-
+    static final Lock lock = new ReentrantLock();
     public static class MyRunnable implements Runnable {
         @Override
         public void run() {
             int i;
             for (i = 0; i < 1_000_000; i++) {
                 // TODO: Acquire the lock, increment the counter, and release the lock safely in a finally block
-                counter += 1;
+                lock.lock();
+                try {
+                    counter += 1;
+                } finally {
+                    lock.unlock();
+                }
             }
             System.out.println("Increments completed by " + Thread.currentThread().getName() + ": " + i);
         }

src/main/java/workshop/exercises/SynchronizedWorkshop.java

@@ -4,14 +4,16 @@ public class SynchronizedWorkshop {
     public static int counter = 0;
     
     // TODO: Define a lock object to prevent race condition
-
+    static final Object lock = new Object();
     public static class MyRunnable implements Runnable {
         @Override
         public void run() {
             int i;
             for (i = 0; i < 1_000_000; i++) {
                 // TODO: Use a synchronized block to protect the counter increment
-                counter += 1;
+                synchronized (lock) {
+                    counter += 1;
+                }
             }
             System.out.println("Increments completed by " + Thread.currentThread().getName() + ": " + i);
         }

src/main/java/workshop/exercises/TaylorSeries.java

@@ -24,11 +24,25 @@ public class TaylorSeries {
             // TODO: Calculate the n-th term of the Taylor series for sin(x):
             // term = (-1)^n * (x^(2n+1)) / (2n+1)!
             // Add the term to the global sum ensuring thread-safety.
+            BigDecimal sign = (n % 2 == 0) ? BigDecimal.ONE : BigDecimal.ONE.negate();
+            BigDecimal numerator = x.pow(2 * n + 1, mc);
+            BigDecimal denominator = factorial(2 * n + 1);
+            BigDecimal term = sign.multiply(numerator, mc).divide(denominator, mc);
+
+            synchronized (TaylorSeries.class) {
+                sum = sum.add(term, mc);
+            }
         }
 
         // TODO: Implement factorial(k) using BigDecimal
         private BigDecimal factorial(int k) {
-            return BigDecimal.ZERO;
+            if (k == 0) return BigDecimal.ONE;
+            BigDecimal result = BigDecimal.ONE;
+            for (int i = 2; i <= k; i++) {
+                result = result.multiply(BigDecimal.valueOf(i));
+            }
+            return result;
+          //  return BigDecimal.ZERO;
         }
     }
 
@@ -42,6 +56,7 @@ public class TaylorSeries {
         // Submit tasks to calculate terms
         for (int i = 0; i < 100; i++) {
             // TODO: Submit task to the thread pool
+            threadPool.submit(new CalculateSin(x, i));
         }
 
         threadPool.shutdown();