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+# Problem 8.1: Compare `ForkJoinPool` to `ThreadPoolExecutor`
+
+According to the lecture, the two types of Java thread pools are optimized for different application
+scenarios:
+
+- `ForkJoinPool` for task that are mutually dependent, created by other tasks, short, rarely blocking (i.e. computation-intensive)
+- `ThreadPoolExecutor` for tasks that are mutually independent, submitted "from the
+outside", long, sometimes blocking
+
+Can you give justifications for these five differences (many vs. few tasks, dependent vs. independent
+tasks, created by the application vs. created by other tasks, short vs. long tasks, rarely vs. frequently
+blocking tasks) when considering the different queuing behavior and also the `join()` operation of
+the ForkJoinTask? Formulate one sentence for each of the five differences, e.g. "`ForkJoinPool`
+is better suited to independent tasks because ...".
+
+## Answer:
+
+`ForkJoinPool` is better suited for mutually dependent tasks because the `join()` allows for efficient execution of child tasks without blocking the thread
+
+`ThreadPoolExecutor` is better suited for tasks which can block because blocking threads can make `ForkJoinPool`s much more inefficient.
+
+`ThreadPoolExecutor` is better suited for long running tasks, because `join()` executes another task while waiting for the current one to finish, therefore possibly waiting longer than strictly necessary.
+
+`ForkJoinPool` is better suited for short running tasks because it creates less synchronization overhead than `ThreadPoolExecutor` and it uses a stack instead of a FiFo Queue to allow the newest tasks to be executed first (which also makes it better suited for mutually dependent tasks, since the waiting time for `join()`ing tasks is minimized)
+
+Tasks usually create other tasks if they are dependent on that task, so since `ForkJoinPool` is better suited for mutually dependent tasks, it is also better suited for tasks that create other tasks.
+
diff --git a/u08-2/README.md b/u08-2/README.md
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+# Problem 8.2: Recursive counting using Callable vs. ForkJoinTask
+
+Class `TreeSumSequential` in the source code folder on the server builds a binary tree with a
+random structure with each node containing a random number. Then it sequentially computes for each
+node the number of prime numbers up to the number in this node (this computation is performed in
+two parts in order to simulate that it may become clear only during the processing of a node that some
+further computation effort is necessary – see method `countPrimesInTree`). Finally, the total
+number of prime numbers over all nodes it printed.
+
+Extend this program by two more implementations of this tree-wide prime number counting:
+
+- a concurrent one that uses a `Callable` for each node and a `ThreadPoolExecutor`
+- a concurrent one that uses a `ForkJoinTask` for each node and the `ForkJoinPool.commonPool()`
+
+The tasks for child nodes should be created and submitted about in the middle of processing the parent
+node, quite as in `countPrimesInTree`.
+
+Compare the run times of the three implementations – if you like, also for different values of the
+configuration constants `MAX_NUMBER_IN_NODE` (corresponds to the size of a task) und
+`MAX_NODES` (an upper limit for the number of tasks which is reached provided that
+`SUBTREE_THRESHOLD_PERCENT` is large enough). The run time of a task depends on the depth
+of its node in the tree.
+
+Since all three implementations compute the sum for the same tree, all three must print the same total
+number; you may thus use a comparison to the sequentially computed number as a correctness check
+of your concurrent implementations.
\ No newline at end of file
diff --git a/u08-2/TreeSumSequential.java b/u08-2/TreeSumSequential.java
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+import java.io.FileInputStream;
+import java.io.FileOutputStream;
+import java.io.ObjectInputStream;
+import java.io.ObjectOutputStream;
+import java.io.Serializable;
+import java.util.ArrayDeque;
+import java.util.Queue;
+import java.util.concurrent.Callable;
+import java.util.concurrent.ExecutionException;
+import java.util.concurrent.ExecutorService;
+import java.util.concurrent.Executors;
+import java.util.concurrent.ForkJoinPool;
+import java.util.concurrent.ForkJoinTask;
+import java.util.concurrent.Future;
+import java.util.concurrent.RecursiveAction;
+import java.util.concurrent.RecursiveTask;
+import java.util.concurrent.ThreadPoolExecutor;
+
+/**
+ *  Construct a binary tree and compute the sum over all tree nodes 
+ *  of the number of primes between 2 and each node's number
+ *  using a sequential implementation.
+ *  
+ * @author Holger.Peine@hs-hannover.de
+ */
+@SuppressWarnings("serial")
+public class TreeSumSequential {
+
+	/**
+	 * Probability for a node to have a child node. If this is low, a small tree often results;
+	 * if this is high, then the tree often has the maximum allowed number of nodes. 
+	 */
+	private static final int SUBTREE_THRESHOLD_PERCENT = 70; 
+	
+	/**
+	 * Each node contains a random number between 1 and this: 
+	 * Must count the number of primes in that range
+	 */
+	private static final int MAX_NUMBER_IN_NODE = 300;
+	
+	private static final int MAX_NODES = 300_000;
+
+	/*
+	 * Number of repetitions of the test
+	 */
+	private static final int N_TESTS = 5;
+
+	/**
+	 * A simple binary tree node, holding a random int between 0 and MAX_NUMBER_IN_NODE,
+	 * the level/height of this node, and references to up to two child nodes.
+	 */
+	static final class Node  implements Serializable {
+		Node(int level) {
+			this.number = (int)(Math.random()*MAX_NUMBER_IN_NODE);
+			this.level = level;
+			left = null;
+			right = null;
+			++nNodes;
+		}
+		Node left, right;
+		int number, level;
+	}
+
+	private static int nNodes;
+	private static int maxLevel;
+
+	/**
+	 * Create a random binary tree where each node has children with a certain probability.
+	 * Create the tree breadth-first by taking a node from the front of a work queue of nodes,
+	 * possibly creating child nodes for this node and adding those at the back of the queue, 
+	 * and repeating this until the queue is empty or MAX_NODES nodes have been created.
+	 * 
+	 * Note that nodes removed from the queue do not vanish, but are still linked with their
+	 * ancestor nodes higher up in the tree. At any time, the queue contains the leaves of the
+	 * current tree.
+	 */
+	private static void createTree(Queue<Node> queue) {
+		Node current, leftChild, rightChild;
+		
+		nNodes = 0;
+		maxLevel = 0;
+
+		while (!queue.isEmpty() && nNodes < MAX_NODES) {
+			current = queue.remove();
+			int level = current.level;
+			if (level > maxLevel) {
+				maxLevel = level;
+			}
+			if ( (int)(Math.random()*100) < SUBTREE_THRESHOLD_PERCENT) {
+				leftChild = new Node(level+1);
+				current.left = leftChild;
+				queue.add(leftChild);
+			}
+			if ( (int)(Math.random()*100) < SUBTREE_THRESHOLD_PERCENT) {
+				rightChild = new Node(level+1);
+				current.right = rightChild;
+				queue.add(rightChild);
+			}
+		}
+	}
+	/**
+	 * @return the number of primes between from and to
+	 * using a deliberately inefficient implementation
+	 */
+	private static int countPrimes(int from, int to) {
+		int nPrimes = 0, t;
+		for (int n = from; n < to; n++) {
+			// check if n is prime (using a deliberately inefficient test)
+			for (t = 2; t < n; t++) {
+				if (n % t == 0) {
+					break;
+				}
+			}
+			if (t == n) {  // n is prime
+				++nPrimes;
+			}
+		}
+		return nPrimes;
+	}
+
+	/**
+	 * The prime counting method used by the sequential implementation
+	 * @param node the tree
+	 * @return sum over all tree nodes of the number of primes between 2 and each node's number
+	 * 
+	 * Note that the recursive calls occur after half of the work for this node has been completed.
+	 * (Half of the work is about 70% of the numbers, since the amount of work for a number increases
+	 * with the square of the number.) This is to sort of simulate the situation that the need for 
+	 * further work to be done becomes clear only during the work for this node. While this does not 
+	 * really make a difference in the sequential case here, the time when recursive tasks are submitted 
+	 * does make a difference for the overall behavior in the parallel case.
+	 */
+	public static int countPrimesInTree(Node node) {
+		int leftResult = 0, rightResult = 0;
+		int nPrimesFirstPart = countPrimes(2, (int)(0.7*node.number));
+		if (node.left != null)
+			leftResult = countPrimesInTree(node.left);
+		if (node.right != null)
+			rightResult = countPrimesInTree(node.right);
+		int nPrimesSecondPart = countPrimes((int)(0.7*node.number), node.number+1);
+		return nPrimesFirstPart + nPrimesSecondPart + leftResult + rightResult;
+	}
+
+	static final class TreeSumTaskThreadPool implements Callable<Integer> {
+		private Node node;
+		private ExecutorService executorService;
+
+		public TreeSumTaskThreadPool(Node node, ExecutorService executorService) {
+			this.node = node;
+			this.executorService = executorService;
+		}
+
+		@Override
+		public Integer call() throws InterruptedException, ExecutionException {
+			Future<Integer> leftFuture = null;
+			Future<Integer> rightFuture = null;
+			int nPrimesFirstPart = countPrimes(2, (int)(0.7*node.number));
+			if (node.left != null) {
+				leftFuture = executorService.submit(new TreeSumTaskThreadPool(node.left, executorService));
+			}
+			if (node.right != null) {
+				rightFuture = executorService.submit(new TreeSumTaskThreadPool(node.right, executorService));
+			}
+
+			int nPrimesSecondPart = countPrimes((int)(0.7*node.number), node.number+1);
+
+			int leftResult = leftFuture == null ? 0 : leftFuture.get();
+			int rightResult = rightFuture == null ? 0 : rightFuture.get();
+
+			return nPrimesFirstPart + nPrimesSecondPart + leftResult + rightResult;
+		}
+	}
+
+	static final class TreeSumTaskForkJoin extends RecursiveTask<Integer> {
+		private Node node;
+
+		public TreeSumTaskForkJoin(Node node) {
+			this.node = node;
+		}
+
+		@Override
+		protected Integer compute() {
+			int nPrimesFirstPart = countPrimes(2, (int)(0.7*node.number));
+
+			TreeSumTaskForkJoin leftTask = null, rightTask = null;
+			if (node.left != null) {
+				leftTask = new TreeSumTaskForkJoin(node.left);
+				leftTask.fork();
+			}
+			if (node.right != null) {
+				rightTask = new TreeSumTaskForkJoin(node.right);
+				rightTask.fork();
+			}
+
+			if (leftTask != null) leftTask.join();
+			if (rightTask != null) rightTask.join();
+
+			int leftResult = 0;
+			int rightResult = 0;
+
+			try {
+				leftResult = leftTask == null ? 0 : leftTask.get();
+				rightResult = rightTask == null ? 0 : rightTask.get();
+			} catch (Exception e) {}
+
+			int nPrimesSecondPart = countPrimes((int)(0.7*node.number), node.number+1);
+
+			return nPrimesFirstPart + nPrimesSecondPart + leftResult + rightResult;
+		}
+	}
+
+	public static int countPrimesInTree_ThreadPoolExecutor(Node node) throws InterruptedException, ExecutionException {
+		ExecutorService ecs = Executors.newCachedThreadPool(); // fixed size causes deadlock
+
+		Future<Integer> result = ecs.submit(new TreeSumTaskThreadPool(node, ecs));
+		return result.get();
+	}
+
+	public static int countPrimesInTree_ForkJoinTask(Node node) {
+		ForkJoinPool fjp = ForkJoinPool.commonPool();
+		TreeSumTaskForkJoin task = new TreeSumTaskForkJoin(node);
+		return fjp.invoke(task);
+	}
+
+
+	/**
+	 * @param args: args[0] may hold the name of file holding the serialized tree to be used for benchmarking
+	 */
+	public static void main(String[] args) throws InterruptedException, ExecutionException {
+		long startTime, endTime;
+		long totalSeqRuntime = 0;
+		Node tree = null;
+
+		for (int testRound = 0; testRound < N_TESTS; ++testRound) {
+
+			// Construct tree: Either read it from a file, or create a new one
+			if (args.length > 0) {  // 1st argument is name of file with serialized tree
+				ObjectInputStream ois;
+				try {
+					ois = new ObjectInputStream(new FileInputStream(args[0]));
+					tree = (Node)ois.readObject();
+					ois.close();
+				} catch (Exception e) {
+					System.out.println(e);
+				}
+			}
+			else { // Create a new tree
+				tree = new Node(0);  // the root node (at level 0)
+				Queue<Node> queue = new ArrayDeque<>();
+				queue.add(tree);
+				createTree(queue);
+				System.out.println("Built binary tree with " + nNodes + " nodes, height " + maxLevel);
+			}
+			// Write the tree to file "tree.ser", no matter how it was constructed:
+			try {
+				ObjectOutputStream oos = new ObjectOutputStream(new FileOutputStream("tree.ser"));
+				oos.writeObject(tree);
+				oos.close();
+			} catch (Exception e) {
+				System.out.println(e);
+			}
+
+			// Count sequentially
+			startTime = System.currentTimeMillis();
+			int sequentialResult = countPrimesInTree(tree);
+			endTime = System.currentTimeMillis();
+			totalSeqRuntime += endTime - startTime;
+			System.out.println("Sequential result: Found  " + sequentialResult
+					+ " primes in " +  (double)(endTime - startTime)/1000 + " sec");
+
+			startTime = System.currentTimeMillis();
+			int threadPoolExecutorResult = countPrimesInTree_ThreadPoolExecutor(tree);
+			endTime = System.currentTimeMillis();
+			totalSeqRuntime += endTime - startTime;
+			System.out.println("ThreadPoolExecutor result: Found  " + threadPoolExecutorResult
+					+ " primes in " +  (double)(endTime - startTime)/1000 + " sec");
+
+			startTime = System.currentTimeMillis();
+			int forkJoinResult = countPrimesInTree_ForkJoinTask(tree);
+			endTime = System.currentTimeMillis();
+			totalSeqRuntime += endTime - startTime;
+			System.out.println("ForkJoin result: Found  " + forkJoinResult
+					+ " primes in " +  (double)(endTime - startTime)/1000 + " sec");
+			
+		} // for testRound
+		System.out.println();
+		System.out.println("Average SEQ time after " + N_TESTS + " tests = " + ((double)totalSeqRuntime)/(1000*N_TESTS) + " sec");
+	}
+}
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