6.2

Uebung 6/Uebung6_2/ExtendedBinaryTree.cpp

@@ -0,0 +1,164 @@
+#include "ExtendedBinaryTree.h"
+#include <iostream>
+
+ExtendedBinaryTree::ExtendedBinaryTree(Ware *rootNodeKey, int priority) {
+  ExtendedBinaryTreeNode *root =
+      new ExtendedBinaryTreeNode(rootNodeKey, priority);
+  this->rootNode = root;
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTree::insert(Ware *key, int priority) {
+  return this->rootNode->insert(key, priority);
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTree::search(int value) {
+  ExtendedBinaryTreeNode *node = this->rootNode;
+  while (value != node->key->getVerkaufspreis() && node != nullptr) {
+    if (value > node->key->getVerkaufspreis()) {
+      node = node->right;
+    } else {
+      node = node->left;
+    }
+  }
+  return node;
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTree::deleteItem(Ware *key) {
+  return this->rootNode->deleteItem(key);
+}
+
+ExtendedBinaryTreeNode *
+ExtendedBinaryTree::findMin(ExtendedBinaryTreeNode *node) {
+  while (node->left != nullptr) {
+    node = node->left;
+  }
+  return node;
+}
+
+ExtendedBinaryTreeNode *
+ExtendedBinaryTree::findMax(ExtendedBinaryTreeNode *node) {
+  while (node->right != nullptr) {
+    node = node->right;
+  }
+  return node;
+}
+
+// function to print a tree in pre-order: (sub)root, left (sub)tree, right
+// (sub)tree
+std::string ExtendedBinaryTree::printPreorder(ExtendedBinaryTreeNode *node) {
+  std::stringstream output;
+  output << *(node->key) << " " << node->priority << std::endl;
+
+  if (node->left != nullptr) {
+    output << this->printPreorder(node->left);
+  }
+  if (node->right != nullptr) {
+    output << this->printPreorder(node->right);
+  }
+  return output.str();
+}
+
+std::string ExtendedBinaryTree::printPreorder() {
+  return this->printPreorder(this->rootNode);
+}
+
+std::string ExtendedBinaryTree::printPostorder() {
+  return this->printPostorder(this->rootNode);
+}
+
+std::string ExtendedBinaryTree::printPostorder(ExtendedBinaryTreeNode *node) {
+  std::stringstream output;
+
+  if (node->left != nullptr) {
+    output << this->printPreorder(node->left);
+  }
+  if (node->right != nullptr) {
+    output << this->printPreorder(node->right);
+  }
+  output << *(node->key) << std::endl;
+  return output.str();
+}
+
+std::string ExtendedBinaryTree::printInorder() {
+  return this->printInorder(this->rootNode);
+}
+
+std::string ExtendedBinaryTree::printInorder(ExtendedBinaryTreeNode *node) {
+  std::stringstream output;
+
+  if (node->left != nullptr) {
+    output << this->printPreorder(node->left);
+  }
+  output << *(node->key) << std::endl;
+
+  if (node->right != nullptr) {
+    output << this->printPreorder(node->right);
+  }
+  return output.str();
+}
+
+std::string ExtendedBinaryTree::printPriority() {
+  return this->printPriority(this->rootNode, INT_MAX);
+}
+
+std::string ExtendedBinaryTree::printPriority(ExtendedBinaryTreeNode *node,
+                                              int max) {
+  std::stringstream output;
+
+  // Print the node
+  if (node->priority < max) {
+    output << *(node->key) << " Priority: " << node->priority << std::endl;
+  }
+
+  // find out which of the children has lower priority
+  ExtendedBinaryTreeNode *bigger = nullptr;
+  ExtendedBinaryTreeNode *smaller = nullptr;
+
+  if (node->left != nullptr) {
+    if (node->right != nullptr) {
+      smaller = node->left->priority < node->right->priority ? node->left
+                                                             : node->right;
+      bigger = node->left->priority > node->right->priority ? node->left
+                                                            : node->right;
+    } else {
+      smaller = node->left;
+    }
+  } else if (node->right != nullptr) {
+    smaller = node->right;
+  }
+
+  if (smaller != nullptr) {
+    int prio;
+    if (bigger != nullptr) {
+      if (bigger->priority < max) {
+
+        prio = bigger->priority;
+      } else {
+        prio = max;
+      }
+    } else {
+      prio = INT_MAX;
+    }
+    output << printPriority(smaller, prio);
+  }
+  if (bigger != nullptr) {
+    output << printPriority(bigger, INT_MAX);
+  }
+  return output.str();
+}
+std::string ExtendedBinaryTree::printPriorityBruteForce() {
+  // return ExtendedBinaryTree::printPriorityBruteForce(this->rootNode,
+  // INT_MAX);
+  int maxprinted = 0;
+  ExtendedBinaryTreeNode *maxprintedNode = nullptr;
+  while (true) {
+  }
+}
+
+std::string
+ExtendedBinaryTree::printPriorityBruteForce(ExtendedBinaryTreeNode *key,
+                                            int max) {
+  int currentMin = max;
+  while (true) {
+  }
+}

Uebung 6/Uebung6_2/ExtendedBinaryTree.h

@@ -0,0 +1,33 @@
+#include "ExtendedBinaryTreeNode.h"
+#include <sstream>
+#include <string>
+
+#pragma once
+
+class ExtendedBinaryTree {
+public:
+  ExtendedBinaryTreeNode *rootNode;
+
+  ExtendedBinaryTree(Ware *rootNodeKey, int priority);
+
+  ExtendedBinaryTreeNode *search(int value);
+  ExtendedBinaryTreeNode *insert(Ware *key, int priority);
+  ExtendedBinaryTreeNode *deleteItem(Ware *key);
+  ExtendedBinaryTreeNode *findMin(ExtendedBinaryTreeNode *node);
+  ExtendedBinaryTreeNode *findMax(ExtendedBinaryTreeNode *node);
+  std::string printPreorder(ExtendedBinaryTreeNode *node);
+  std::string printPreorder();
+  std::string printPostorder(ExtendedBinaryTreeNode *node);
+  std::string printPostorder();
+  std::string printInorder(ExtendedBinaryTreeNode *node);
+  std::string printInorder();
+  std::string printPriority();
+  std::string printPriority(ExtendedBinaryTreeNode *node, int max);
+  std::string printPriorityBruteForce();
+  std::string printPriorityBruteForce(ExtendedBinaryTreeNode *node, int max);
+};
+
+// std::string printPreorder(BinaryTreeNode* node);
+// /*  --  Your TODO   --  */
+// std::string printPostorder(BinaryTreeNode* node);
+// std::string printInorder(BinaryTreeNode* node);

Uebung 6/Uebung6_2/ExtendedBinaryTreeNode.cpp

@@ -0,0 +1,86 @@
+#include "ExtendedBinaryTreeNode.h"
+
+#include <iostream>
+
+ExtendedBinaryTreeNode::ExtendedBinaryTreeNode(Ware *key, int priority) {
+  this->key = key;
+  this->left = nullptr;
+  this->right = nullptr;
+  this->priority = priority;
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTreeNode::insert(Ware *key,
+                                                       int priority) {
+  if (key->getVerkaufspreis() > this->key->getVerkaufspreis()) {
+    if (this->right == nullptr) {
+      ExtendedBinaryTreeNode *temp = new ExtendedBinaryTreeNode(key, priority);
+      this->right = temp;
+      return this->right;
+    }
+    this->right->insert(key, priority);
+  } else {
+    if (this->left == nullptr) {
+      ExtendedBinaryTreeNode *temp = new ExtendedBinaryTreeNode(key, priority);
+      this->left = temp;
+      return this->left;
+    }
+    this->left->insert(key, priority);
+  }
+  return this;
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTreeNode::deleteItem(Ware *key) {
+  ExtendedBinaryTreeNode *node = this;
+
+  if (node == nullptr) {
+    return this;
+  } else if (key->getVerkaufspreis() < node->key->getVerkaufspreis()) {
+    node->left = node->left->deleteItem(key);
+  } else if (key->getVerkaufspreis() > node->key->getVerkaufspreis()) {
+    node->right = node->right->deleteItem(key);
+  } else {
+    if (node->left == nullptr && node->right == nullptr) {
+      delete node;
+      node = nullptr;
+    } else if (node->left == nullptr) { // only children in right subtree
+      ExtendedBinaryTreeNode *temp = node;
+      node = node->right;
+      delete temp;
+    } else if (this->right == nullptr) { // only children in left subtree
+      ExtendedBinaryTreeNode *temp = node;
+      node = node->left;
+      delete temp;
+    } else { // we have to keep the BST structure, here, we look for the minimum
+             // in the right subtree (see lecture)
+      ExtendedBinaryTreeNode *temp = node->right;
+      while (temp->left != nullptr) {
+        temp = temp->left;
+      }
+      node->key = temp->key;
+      node->right = node->right->deleteItem(temp->key);
+    }
+  }
+  return node;
+}
+
+ExtendedBinaryTreeNode *ExtendedBinaryTreeNode::leftRotation() {
+  // std::cout << "Do a left rotation on node " << this->key << "\n";
+  ExtendedBinaryTreeNode *rightNode = this->right;
+  ExtendedBinaryTreeNode *leftOfRightNode = rightNode->left;
+
+  rightNode->left = this;
+  this->right = leftOfRightNode;
+  return rightNode;
+}
+
+// perform a right rotation (see lecture)
+ExtendedBinaryTreeNode *ExtendedBinaryTreeNode::rightRotation() {
+  // std::cout << "Do a right rotation on node " << this->key << "\n";
+  ExtendedBinaryTreeNode *leftNode = this->left;
+  ExtendedBinaryTreeNode *rightOfLeftNode = leftNode->right;
+
+  leftNode->right = this;
+  this->left = rightOfLeftNode;
+
+  return leftNode;
+}

Uebung 6/Uebung6_2/ExtendedBinaryTreeNode.h

@@ -0,0 +1,17 @@
+#pragma once
+#include "Ware.h"
+
+class ExtendedBinaryTreeNode {
+public:
+  Ware *key;
+  int priority;
+  ExtendedBinaryTreeNode *left;
+  ExtendedBinaryTreeNode *right;
+
+  ExtendedBinaryTreeNode(Ware *key, int priority);
+
+  ExtendedBinaryTreeNode *insert(Ware *key, int priority);
+  ExtendedBinaryTreeNode *deleteItem(Ware *key);
+  ExtendedBinaryTreeNode *leftRotation();
+  ExtendedBinaryTreeNode *rightRotation();
+};

Uebung 6/Uebung6_2/Makefile

@@ -0,0 +1,51 @@
+
+# Name of the binary for Development
+BINARY = main
+# Name of the binary for Release
+FINAL = prototyp
+# Object files
+OBJS   = Ware.o ExtendedBinaryTreeNode.o ExtendedBinaryTree.o main.o
+# Compiler flags
+CFLAGS = -Werror -Wall -std=c++17 -g -fsanitize=address,undefined
+# Linker flags
+LFLAGS = -fsanitize=address,undefined
+#Which Compiler to use
+COMPILER = c++
+
+
+# all target: builds all important targets
+all: binary
+
+final : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${FINAL} ${OBJS}
+
+binary : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+# Links the binary
+${BINARY} : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+
+# Compiles a source-file (any file with file extension .c) into an object-file
+#
+# "%" is a wildcard which matches every file-name (similar to * in regular expressions)
+# Such a rule is called a pattern rule (because it matches a pattern, see https://www.gnu.org/software/make/manual/html_node/Pattern-Rules.html),
+# which are a form of so called implicit rules (see https://www.gnu.org/software/make/manual/html_node/Implicit-Rules.html)
+# "$@" and "$<" are so called automatic variables (see https://www.gnu.org/software/make/manual/html_node/Automatic-Variables.html)
+%.o : %.cpp
+	${COMPILER} -c ${CFLAGS} -o $@ $<
+
+
+# Rules can not only be used for compiling a program but also for executing a program
+run: ${BINARY}
+	./${BINARY}
+
+
+# Delete all build artifacts
+clean :
+	rm -rf ${BINARY} ${OBJS}
+
+
+# all  and clean are a "phony" targets, meaning they are no files
+.PHONY : all clean

Uebung 6/Uebung6_2/Ware.cpp

@@ -0,0 +1,9 @@
+#include "Ware.h"
+
+std::ostream &operator<<(std::ostream &out, const Ware &ware) {
+  out << "Name: " << ware.getBezeichnung() << ", SN: " << ware.getSeriennummer()
+      << ", Gewicht: " << ware.getGewicht()
+      << ", EK: " << ware.getEinkaufspreis()
+      << ", VK: " << ware.getVerkaufspreis();
+  return out;
+}

Uebung 6/Uebung6_2/Ware.h

@@ -0,0 +1,46 @@
+#pragma once
+#include <iostream>
+#include <string>
+
+class Ware {
+private:
+  std::string bezeichnung;
+  int seriennummer;
+  double gewicht;
+  double einkaufspreis;
+  double verkaufspreis;
+
+public:
+  std::string getBezeichnung() const { return this->bezeichnung; }
+
+  void setBezeichnung(std::string bezeichnung) {
+    this->bezeichnung = bezeichnung;
+  }
+
+  int getSeriennummer() const { return this->seriennummer; }
+
+  void setSeriennummer(int seriennummer) { this->seriennummer = seriennummer; }
+
+  double getGewicht() const { return this->gewicht; }
+
+  void setGewicht(double gewicht) { this->gewicht = gewicht; }
+
+  double getEinkaufspreis() const { return this->einkaufspreis; }
+
+  void setEinkaufspreis(double einkaufspreis) {
+    this->einkaufspreis = einkaufspreis;
+  }
+
+  double getVerkaufspreis() const { return this->verkaufspreis; }
+
+  void setVerkaufspreis(double verkaufspreis) {
+    this->verkaufspreis = verkaufspreis;
+  }
+
+  Ware(std::string bezeichnung, int seriennummer, double gewicht,
+       double einkaufspreis, double verkaufspreis)
+      : bezeichnung(bezeichnung), seriennummer(seriennummer), gewicht(gewicht),
+        einkaufspreis(einkaufspreis), verkaufspreis(verkaufspreis) {}
+};
+
+std::ostream &operator<<(std::ostream &out, const Ware &ware);

Uebung 6/Uebung6_2/main.cpp

@@ -0,0 +1,58 @@
+#include "ExtendedBinaryTree.h"
+#include "ExtendedBinaryTreeNode.h"
+#include "Ware.h"
+#include <iostream>
+
+void generateRandomIntArray(int *array, int arrayLength) {
+  std::srand(time(NULL));
+  for (int i = 0; i < arrayLength; i++) {
+    array[i] = rand() % 100000 + 1;
+  }
+}
+
+int main() {
+
+  // bez, sn, gw, ek, vk
+  Ware ware1("S", 1, 5.12, 10.37, 13.0);
+  Ware ware2("L", 2, 6.12, 1.37, 29.0);
+  Ware ware3("A", 3, 4.12, 9.37, 10.0);
+  Ware ware4("Z", 12, 1.12, 18.37, 19.0);
+  Ware ware5("LA", 27, 0.12, 13.37, 17.0);
+  Ware ware6("LC", 13, 13.12, 15.37, 16.0);
+  Ware ware7("ABC", 4, 7.12, 27.37, 35.0);
+  Ware ware8("C", 123, 9.12, 2.37, 4.0);
+
+  int randInts[8];
+  generateRandomIntArray(randInts, 8);
+
+  // Händisch sortierte Prioritäten, um die Waren ihren Prioritäten entsprechend
+  // einzusortieren, damit die Heapbedingung nicht verletzt werden kann.
+  std::sort(randInts, randInts + 8);
+
+  ExtendedBinaryTree tree(&ware1, randInts[0]);
+  //  std::cout << tree.printPreorder() << std::endl << std::flush;
+  tree.insert(&ware2, randInts[1]);
+  // std::cout << tree.printPreorder() << std::endl << std::flush;
+  tree.insert(&ware3, randInts[2]);
+  // std::cout << tree.printPreorder() << std::endl << std::flush;
+  tree.insert(&ware4, randInts[3]);
+  // std::cout << tree.printPreorder() << std::endl << std::flush;
+  tree.insert(&ware5, randInts[4]);
+  // std::cout << tree.printPreorder() << std::endl << std::flush;
+  tree.insert(&ware6, randInts[5]);
+  // std::cout << tree.printInorder() << std::endl << std::flush;
+  tree.insert(&ware7, randInts[6]);
+  // std::cout << tree.printInorder() << std::endl << std::flush;
+  tree.insert(&ware8, randInts[7]);
+  std::cout << tree.printPreorder() << std::endl << std::flush;
+
+  // std::cout << ware1 << std::endl;
+  // std::cout << tree.printPreorder() << std::endl;
+  // std::cout << tree.printPostorder() << std::endl;
+  // std::cout << tree.printPreorder() << "\n" << std::endl;
+  // std::cout << tree.printPostorder() << "\n" << std::endl;
+  // std::cout << tree.printInorder();
+  std::cout << tree.printPriority() << std::endl;
+
+  return 0;
+}

Uebung 6/Uebung6_3/Makefile

@@ -0,0 +1,52 @@
+
+# Name of the binary for Development
+BINARY = main
+# Name of the binary for Release
+FINAL = prototyp
+# Object files
+OBJS   = main.o
+# Compiler flags
+CFLAGS = -Werror -Wall -std=c++17 -g -fsanitize=address,undefined -g
+# Linker flags
+LFLAGS = -fsanitize=address,undefined
+#Which Compiler to use
+COMPILER = g++
+
+
+# all target: builds all important targets
+all: binary
+
+final : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${FINAL} ${OBJS}
+	rm ${OBJS}
+
+binary : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+# Links the binary
+${BINARY} : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+
+# Compiles a source-file (any file with file extension .c) into an object-file
+#
+# "%" is a wildcard which matches every file-name (similar to * in regular expressions)
+# Such a rule is called a pattern rule (because it matches a pattern, see https://www.gnu.org/software/make/manual/html_node/Pattern-Rules.html),
+# which are a form of so called implicit rules (see https://www.gnu.org/software/make/manual/html_node/Implicit-Rules.html)
+# "$@" and "$<" are so called automatic variables (see https://www.gnu.org/software/make/manual/html_node/Automatic-Variables.html)
+%.o : %.cpp
+	${COMPILER} -c ${CFLAGS} -o $@ $<
+
+
+# Rules can not only be used for compiling a program but also for executing a program
+run: ${BINARY}
+	./${BINARY}
+
+
+# Delete all build artifacts
+clean :
+	rm -rf ${BINARY} ${OBJS}
+
+
+# all  and clean are a "phony" targets, meaning they are no files
+.PHONY : all clean

Uebung 6/Uebung6_3/main.cpp

@@ -0,0 +1,92 @@
+#include <cmath>
+#include <iostream>
+
+// Konstanten aus der Angabe
+#define n 12
+#define k 6
+#define L 15
+
+// Liste der Primzahlen. Durch die oben angeführten Konstanten ist
+// sichergestellt dass diese eindeutig sind
+uint16_t listofPrimes[L];
+
+// Random n-bits Zahl generieren. MSB ist immer 1
+uint16_t createRandomNumber(uint8_t bits) {
+
+  // äquivalent zu:
+  // return rand() % pow(2,bits-1) + pow(2,bits-1);
+
+  uint16_t result = 1;
+  for (uint8_t i = 0; i < bits - 1; i++) {
+    result <<= 1;
+    result |= rand() % 2;
+  }
+  return result;
+}
+
+// Check ob eine Zahl Prim ist
+bool checkPrime(int number) {
+  for (int i = 2; i < sqrt(number); i++) {
+    if (number % i == 0) {
+
+      return false;
+    }
+  }
+  return true;
+}
+
+// Schreibe "length" primzahlen größer als "start" in "array"
+void findPrimesBiggerThan(uint16_t *array, int length, int start) {
+  for (int i = 0; i < length; i++) {
+    while (!checkPrime(start)) {
+      start++;
+    }
+    array[i] = start;
+    start++;
+  }
+}
+
+// die zwei Zahlen die Alice und Bob aussuchen werden
+int xAlice;
+int xBob;
+
+// Daten die an Bob übermittelt werden. j = x_A mod p_i. Bob antwortet mit Bool
+bool transmitToBob(int i, int j) {
+
+  if (j != (xBob % listofPrimes[i])) {
+    return false;
+  }
+  return true;
+}
+
+int main() {
+  // rand() mit timestamp seeden
+  srand(time(NULL));
+
+  // Primzahlen für Alice und Bob initialisieren
+  findPrimesBiggerThan(listofPrimes, L, pow(2, k));
+
+  // Alice sucht ein i zw. 1 und L aus
+  int iAlice = rand() % (L - 1) + 1;
+
+  // Counter für false positives
+  int falseCounter = 0;
+
+  long long iterations = 1000000;
+  for (int i = 0; i < iterations; i++) {
+    // Alice und Bob suchen 2 Zahlen aus
+    xAlice = createRandomNumber(n);
+    xBob = createRandomNumber(n);
+
+    // false positive, wenn Bob behauptet die Zahlen wären gleich, sie es aber
+    // nicht sind
+    if (transmitToBob(iAlice, xAlice % listofPrimes[iAlice]) &&
+        xAlice != xBob) {
+      falseCounter++;
+    }
+  }
+
+  // false-positive rate in Prozent. Empirisch: ca. 1%
+  std::cout << "False positivity rate: "
+            << 100 * (float)(falseCounter) / iterations << "%" << std::endl;
+}

Uebung 6/Uebung6_3/theorie.txt

@@ -0,0 +1,4 @@
+da ein L = 10^6 * n/k eine false Positive Wahrscheinlichkeit von 10^-6 ergibt, nehme ich stark an, dass man eine false Positive Wahrscheinlichkeit von 10^-15 duch ein L = 10^15 * n/k erreichen kann.
+
+Ich schätze in der Angabe ist ein Tippfehler drinnen.
+Da jede Wahrscheinlichkeit per Definition kleiner oder gleich 1 ist, ist auch die Wahrscheinlichkeit eines falschen Ergebnisses zwangsläufig kleiner als 10^15.