Exercise 8

Added Exercise 8 to repository

Informatik_I/Exercise_8/Task_3/README.org

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+#+title: Task 3: All permutations
+
+#+author: JirR02
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+In this exercise, you are going to implement a function which computes
+the set of all permutations of a given string.
+
+Note: This task naturally lends itself to a *recursive implementation*.
+
+** Example
+:PROPERTIES:
+:CUSTOM_ID: example
+:END:
+The string "abc" has the following set of permutations:
+
+{ abc, acb, bac, bca, cab, cba }
+
+** 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 the 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 a string.
+
+Then, the program computes the set of all permutations using the
+function *all_permutations*. Finally, the resulting set is printed to
+the console.
+
+*** Example
+:PROPERTIES:
+:CUSTOM_ID: example-1
+:END:
+#+begin_src shell
+String: abc
+Permutations: 
+{abc,acb,bac,bca,cab,cba}
+#+end_src
+
+Hint: You may find the substr method useful. The method is documented
+here.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+#+begin_src cpp
+#include "pair_sum.h"
+#include <climits>
+
+// PRE:  for any two indices i and j, v[i] + v[j] ≤ INT_MAX
+// POST: returns the number of indices (i,j), i<j of a vector v
+//       that corresponds to the given iterator range such that
+//       v[i] + v[j] == sum.
+int pairs_with_sum(int sum, iterator begin, iterator end) {
+  int count = 0;
+  int size = end - begin;
+
+  for (int i = 0; i < size; ++i) {
+    for (int j = i + 1; j < size; ++j) {
+      iterator cur_begin = begin + i;
+      iterator cur_end = begin + j;
+      if (*cur_begin + *cur_end == sum)
+  ++count;
+    }
+  }
+
+  return count;
+}
+#+end_src
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭