Exercise 8

Added Exercise 8 to repository

Informatik_I/Exercise_8/Task_2/README.org

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+#+title: Task 2: Set Product
+
+#+author: JirR02
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+In this exercise, you are going to implement a function which computes
+the /n-fold Cartesian product/ for sets. The n-fold Cartesian product is
+a way to combine multiple sets of items. Imagine you have multiple sets,
+denoted as \(A_1, A_2, ..., A_n\). The n-fold Cartesian product is like
+taking one item from each set and combining them into a new set.
+
+For example, let's say you have two sets:
+
+\[
+A_1 = \{a,b,c\} \text{ and } A_2 = \{ x, y, z \}
+\]
+
+The Cartesian product of these two sets would be a new set that contains
+all possible combinations of one item from \(A_1\) and one item from
+\(A_2\):
+
+\[
+A_1 \times A_2 = \{(a,x),(a,y),(a,z),(b,x),(b,y),(b,z),(c,x),(c,y),(c,z)\}
+\]
+
+In general, for any two sets \(A\) and \(B\), the Cartesian product
+\(A times B\) is defined as:
+
+\[
+A \times B \{(a,b) | a \in A \text{ and } b \in B\}
+\]
+
+This can be generalized to the n-fold Cartesian product. For any \(n\)
+sets \(A_1, A_2, ... , A_n\), the n-fold Cartesian product is defined
+as:
+
+\[
+A_1 \times A_2 \times ... \times A_n = \{(a_1, a_2, ..., a_n) | a_i \in A_i \text{ for all } i = 1, 2, ... , n\}
+\]
+
+Note: This task naturally lends itself to a *recursive implementation*.
+
+** The Set class
+:PROPERTIES:
+:CUSTOM_ID: the-set-class
+:END:
+A set class is implemented in =set.h= and =set.ipp=. This class
+implements a number of useful operations on sets. *For an overview of
+its functionalities, please refer to this week's Power Set code
+example*. Note that you do not need to understand any of the code in
+=set.h= and =set.ipp= in order to use it!
+
+* Input & Output
+:PROPERTIES:
+:CUSTOM_ID: input-output
+:END:
+When the program starts, you are first prompted to enter the number of
+sets. Then, you are prompted to enter each set. Sets are entered on a
+single line using the format
+=<number of char elements> <elements separated by spaces>=.
+
+Once all sets are entered, the set product is computed using the
+=set_product= function. Finally, the resulting set is printed to the
+console.
+
+*** Example
+:PROPERTIES:
+:CUSTOM_ID: example
+:END:
+#+begin_src shell
+Number of sets: 2
+Set 0: 3 a b c
+Set 1: 2 x y
+Product Set:
+{ax,ay,bx,by,cx,cy}
+#+end_src
+
+*Note*: Each input set is a set of char elements. At least 1 set must be
+inputted.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src cpp
+#include <iterator>
+#include <string>
+#include <vector>
+
+#include "set.h"
+#include "solution.h"
+
+StringSet set_product(const std::vector<CharSet> &sets) {
+  StringSet res;
+  StringSet ram;
+  if (sets.size() == 1) {
+    for (int i = 0; i < sets[0].size(); ++i) {
+      std::string j(1, sets[0][i]);
+    res.insert(j);
+    }
+  return res;
+  }
+
+  CharSet first_subset = sets[0];
+  std::vector<CharSet> remaining_set(sets.begin() + 1, sets.end());
+
+  StringSet res_subset = set_product(remaining_set);
+
+  for (char char_first_subset : first_subset.elements()) {
+    for (std::string str_res_subset : res_subset.elements()) {
+    res.insert(std::string(1, char_first_subset) + str_res_subset);
+    }
+  }
+
+  return res;
+}
+#+end_src
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭