Exercise 7

Added Exercise 7 to the repository

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