Exercise 7

Added Exercise 7 to Repository

.gitignore

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+*.norg
+*.md

Informatik_I/Exercise_7/Task_1/README.org

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+#+title: Task 1: Recursive function analysis
+
+#+author: JirR02
+/This task is a text based task. You do not need to write any program or C++ file: the answer should be written in main.md (and might include code fragments if questions ask for them)./
+
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+For each of the following recursive functions:
+
+1. 
+
+#+begin_src cpp
+bool f(const int n) {
+if (n == 0) return false;
+return !f(n - 1);
+}
+#+end_src
+
+2. [@2] 
+
+#+begin_src cpp
+void g(const int n) {
+if (n == 0) {
+std::cout << "*";
+return;
+}
+g(n - 1);
+g(n - 1);
+}
+#+end_src
+
+1) Formulate pre- and post conditions.
+
+2) Show that the function terminates. *Hint*: No proof expected, proceed
+   similar as with the lecture example of the factorial function.
+
+3) Determine the number of functions calls as mathematical function of
+   parameter n. *Note*: include the first non-recursive function call.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src markdown
+1. i) Pre- and post conditions
+
+```c++
+// PRE: n is a positive integer
+// POST: returns true if n is even and false if n is odd.
+```
+
+ii) The function =plain|f= terminates because it has a termination
+   condition. It will terminate once n reaches 0. If the number is
+   negative, it will be in an infinite loop.
+
+iii) $\text{Calls}_{f}(n) = n$
+
+2. i) Pre- and post conditions
+
+```cpp
+// PRE: n is a positive integer
+// POST: print 2^n *
+```
+
+ii) The function =plain|g= terminates because it has a termination condition. It will terminate once n reaches 0. If the number is negative, it will be in an infinite loop.
+
+iii) $\text{Calls}_{g}(n) = 2^n$
+
+#+end_src

Informatik_I/Exercise_7/Task_2/README.org

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+#+title: Task 2: Bitstrings up to n
+
+#+author: JirR02
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+Your task is implementing the function =all_bitstrings_up_to_n= in
+=solution.cpp= which generates all bitstrings up to length \(n\) in
+ascending order. The generated bitstrings are returned in a
+=std::vector<std::string>=.
+
+*Note*: It is *mandatory* to use *recursive implementation* for this
+task.
+
+* Input & Output
+:PROPERTIES:
+:CUSTOM_ID: input-output
+:END:
+The program first prompts you to enter the bitstring length \(n\). It
+then calls the function =all_bitstrings_up_to_n= and prints the returned
+bitstrings to the console.
+
+** Example
+:PROPERTIES:
+:CUSTOM_ID: example
+:END:
+#+begin_src sh
+Bitstring length: 2
+Bitstrings up to length 2
+
+0
+1
+00
+01
+10
+11
+#+end_src
+
+*Note*: The empty line after Bitstrings up to length 2 is actually the
+bitstring of length \(0\).
+
+*Note*: The autograder will only accept output that exactly matches the
+expected result. Therefore, do not output anything with =std::cout= in
+the =all_bitstrings_up_to_n= function. For debugging messages, use
+=std::cerr= as in:
+
+#+begin_src cpp
+std::cerr << "This is a test message." << std::endl;
+#+end_src
+
+Those will be ignored by the autograder.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src cpp
+#include "solution.h"
+using vec = std::vector<std::string>;
+using str = std::string;
+
+void bitstring(vec &res, str ram, int l) {
+  if (l == 0) {
+    res.push_back(ram);
+    return;
+  }
+
+  bitstring(res, ram + "0", l - 1);
+  bitstring(res, ram + "1", l - 1);
+}
+
+void recursion(int count, int n, vec &res) {
+  if (count > n)
+  return;
+
+  bitstring(res, "", count);
+  recursion(count + 1, n, res);
+}
+
+vec all_bitstrings_up_to_n(int n) {
+  vec res;
+
+  recursion(0, n, res);
+
+  return res;
+}
+#+end_src

Informatik_I/Exercise_7/Task_3/README.org

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+#+title: Task 3: [Hidden tests] Trapezoid printing
+
+#+author: JirR02
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+In this exercise, you are going to print trapezoids. A trapezoid is
+defined by the width of its base and its height. A trapezoid can also
+either be rightsideup or upsidedown.
+
+*Note*: It is *mandatory* to use *recursive implementation* for this
+task.
+
+** Examples
+:PROPERTIES:
+:CUSTOM_ID: examples
+:END:
+*** Rightsideup trapezoid with height and width \(3\) (aka a triangle)
+:PROPERTIES:
+:CUSTOM_ID: rightsideup-trapezoid-with-height-and-width-3-aka-a-triangle
+:END:
+#+begin_src sh
+  0
+ 0 0
+0 0 0
+#+end_src
+
+Upsidedown trapezoid with height and width \(3\) (aka an upsidedown
+triangle)
+
+#+begin_src sh
+0 0 0
+ 0 0
+  0
+#+end_src
+
+*** Rightsideup trapezoid with base width 5 and height 2
+:PROPERTIES:
+:CUSTOM_ID: rightsideup-trapezoid-with-base-width-5-and-height-2
+:END:
+#+begin_src sh
+ 0 0 0 0
+0 0 0 0 0
+#+end_src
+
+** Subtask 1: print_trapezoid
+:PROPERTIES:
+:CUSTOM_ID: subtask-1-print_trapezoid
+:END:
+Implement the function print_trapezoid. The function takes three
+arguments:
+
+- =int base_width=: The width of the trapezoid's base
+- =int height=: The height of the trapezoid
+- =int offset_left=: The number of spaces between the left edge of the
+  trapezoid's base and the left edge of the console.
+- =bool upsidedown=: Boolean indicating whether or not the trapezoid is
+  upsidedown or rightsideup.
+
+When called, the function should print the specified trapezoid to the
+console.
+
+** Subtask 2: print_diamond:
+:PROPERTIES:
+:CUSTOM_ID: subtask-2-print_diamond
+:END:
+Implement the function =print_diamond=.
+
+The function prints a diamond with a given center width to the console.
+A diamond is a rightsideup trapezoid on top of an upsidedown trapezoid.
+
+For example, a diamond of width \(5\) looks as follows:
+
+#+begin_src sh
+    0
+   0 0
+  0 0 0
+ 0 0 0 0
+0 0 0 0 0
+ 0 0 0 0
+  0 0 0
+   0 0
+    0
+#+end_src
+
+** Subtask 3: print_hourglass:
+:PROPERTIES:
+:CUSTOM_ID: subtask-3-print_hourglass
+:END:
+Implement the function =print_hourglass=.
+
+The function prints an hourglass with a given base width to the console.
+A hourglass is an upsidedown trapezoid on top of a rightsideup
+trapezoid.
+
+For example, an hourglass of width \(5\) looks as follows:
+
+#+begin_src sh
+0 0 0 0 0
+ 0 0 0 0
+  0 0 0
+   0 0
+    0
+   0 0
+  0 0 0
+ 0 0 0 0
+0 0 0 0 0
+#+end_src
+
+*Note*: The autograder will only accept output that exactly matches the
+expected result. Therefore, do not output anything with std::cout beyond
+what is strictly required (i.e., ” ","=0=", and =std::endl= /"=n=“). For
+debugging messages, use =std::cerr= as in:
+
+#+begin_src cpp
+std::cerr << "This is a test message." << std::endl;
+#+end_src
+
+Those will be ignored by the autograder.
+
+* Hidden test cases
+:PROPERTIES:
+:CUSTOM_ID: hidden-test-cases
+:END:
+This exercise has some hidden test cases. You will see whether these
+tests passed or failed, but you will not see the test input or the
+expected output.
+
+** Persistent input
+:PROPERTIES:
+:CUSTOM_ID: persistent-input
+:END:
+To help you in testing your code, you can enter your custom test input
+in =input.txt=. When running the program, you can let CodeExpert read
+the input from the file.
+
+Write some program input in input.txt. Run the program as usual. Type f
+(no spaces) in the terminal window and press Enter. The program will use
+the contents of input.txt as input. Using this feature is entirely
+optional and does not affect your score.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src cpp
+#include <assert.h>
+
+#include <iostream>
+
+#include "solution.h"
+
+void print_row(int n_bricks, int offset_left) {
+  // print spaces for offset
+  for (int i = 0; i < offset_left; ++i) {
+    std::cout << " ";
+  }
+
+  // print bricks
+  for (int i = 0; i < n_bricks; ++i) {
+    if (i != 0) {
+      std::cout << " ";
+    }
+    std::cout << "0";
+  }
+  std::cout << std::endl;
+}
+
+void print_trapezoid(int base_width, int height, int offset_left,
+                     bool upsidedown) {
+  assert(base_width >= height);
+
+  if (upsidedown == true) {
+    if (height == 0)
+    return;
+
+    print_row(base_width, offset_left);
+    print_trapezoid(base_width - 1, height - 1, offset_left + 1, upsidedown);
+  } else if (upsidedown == false) {
+    if (height == 0)
+    return;
+
+    print_row(base_width - height + 1, offset_left + height - 1);
+    print_trapezoid(base_width, height - 1, offset_left, upsidedown);
+}
+}
+
+void print_diamond(int center_width) {
+  print_trapezoid(center_width, center_width, 0, false);
+  print_trapezoid(center_width - 1, center_width - 1, 0, true);
+}
+
+void print_hourglass(int base_width) {
+  print_trapezoid(base_width, base_width, 0, true);
+  print_trapezoid(base_width, base_width - 1, 0, false);
+#+end_src

Informatik_I/Exercise_7/Task_4/README.org

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+#+title: Task 4: [Exam 2022.08 (ITET/MATH/PHYS/RW)] Mini-Knapsack
+
+#+author: JirR02
+* Note
+:PROPERTIES:
+:CUSTOM_ID: note
+:END:
+I don't know if we have to solve this task recursively or not. It is in
+the topic of week but the task does not state this explicitly.
+
+* Task Description
+:PROPERTIES:
+:CUSTOM_ID: task-description
+:END:
+As part of a promotion of the local supermarket, you are allowed to get
+exactly two items for free. You want to maximize the value of the items
+you take, but you need to take the weight limit of your backpack into
+account.
+
+You get two integer vectors, one with the value of every item, and one
+with its weight. Return the maximum value that you can get by choosing
+exactly 2 different items from the supermarket.
+
+* Function
+:PROPERTIES:
+:CUSTOM_ID: function
+:END:
+Implement the function =best_two_elements= in =functions.h= according to
+its pre- and postconditions.
+
+*Rules*:
+
+- The functions must satisfy their respective postconditions.
+- You are not allowed to change the function signatures.
+- You are not allowed to use additional libraries.
+
+*Hint*:
+
+- You do not need to check the pre- and postconditions (no asserts
+  necessary).
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src cpp
+#pragma once
+
+#include <vector>
+
+using vec = std::vector<int>;
+
+// PRE:   The vector "weights" at position i contains the weight of element
+// i.
+//        The vector "values" at position i contains the value of element i.
+//        The vectors have the same size and always contain at least two
+//        items. The value and weight of every item is > 0.
+//
+// POST:  Returns the sum of the value of the two items that have the most
+// value,
+//        while the sum of their weight is at most `weight_limit`.
+//        It is not allowed to pick only one item.
+//        It is also not allowed to pick an item twice, but two different
+//        items must be chosen. If there are no two items that can be chosen
+//        (due to exceeding weight), return 0.
+//
+// Example:
+//  * weights: [1, 2, 2], values: [3, 1, 9], weight_limit: 3  ~~> 12;
+
+void recursion1(int &value, int count1, int count2, const vec &values,
+                const vec &weights, int weight_limit) {
+  if (count2 == int(values.size()))
+  return;
+
+  if (int((values.at(count1)) + int(values.at(count2))) >= value &&
+    (int(weights.at(count1)) + int(weights.at(count2))) <= weight_limit)
+  value = int(values.at(count1)) + int(values.at(count2));
+
+  recursion1(value, count1, count2 + 1, values, weights, weight_limit);
+}
+
+void recursion2(int &value, int count1, const vec &values, const vec &weights,
+                int weight_limit) {
+  if (count1 == (int(values.size()) - 1))
+  return;
+
+  recursion1(value, count1, count1 + 1, values, weights, weight_limit);
+  recursion2(value, count1 + 1, values, weights, weight_limit);
+}
+
+int best_two_elements(const vec &values, const vec &weights, int weight_limit) {
+  int value = 0;
+
+  if (values.size() == weights.size() && values.size() >= 2 &&
+    weights.size() >= 2) {
+    recursion2(value, 0, values, weights, weight_limit);
+  }
+
+  return value;
+}
+#+end_src

README.org

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-#+TITLE: ETH Computer Science Projects
+#+title: ETH Computer Science Projects
-#+AUTHOR: JirR02
 
-In this respository the computer science project of the ETH of D-ITET 2024 are managed. They can be used for inspiration.
+#+author: JirR02
+In this respository the computer science project of the ETH of D-ITET
+2024 are managed. They can be used for inspiration.
 
-The projects are uploaded on [[https://expert.ethz.ch/enrolled/AS24/itet0/exercises][Code Expert]].
+The projects are uploaded on
+[[https://expert.ethz.ch/enrolled/AS24/itet0/exercises][Code Expert]].
 
 * DISCLAIMER!!!
-
+:PROPERTIES:
-I assume no liability for possible errors in the code (it certainly has a few in it, since I write it myself).
+:CUSTOM_ID: disclaimer
+:END:
+I assume no liability for possible errors in the code (it certainly has
+a few in it, since I write it myself).
 
 Bugs can be reported via Discord, WhatsApp, Mail and Moodle.
 
------
+--------------
 
 Made by JirR02 in Switzerland 🇨🇭