Add activity selection new algorithm (#11667)

* Add activity selection new algorithm

* updating DIRECTORY.md

* Rename x to activity

* updating DIRECTORY.md

* updating DIRECTORY.md

* Refactor activity_selection function documentation

Updated docstring and added a check for empty input.

* Fix activity_selection function test cases

---------

Co-authored-by: Hardvan <Hardvan@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: Hardvan

DIRECTORY.md

@@ -671,6 +671,7 @@
   * [Travelling Salesman Problem](graphs/travelling_salesman_problem.py)
 
 ## [Greedy Methods](greedy_methods)
+  * [Activity Selection](greedy_methods/activity_selection.py)
   * [Best Time To Buy And Sell Stock](greedy_methods/best_time_to_buy_and_sell_stock.py)
   * [Fractional Cover Problem](greedy_methods/fractional_cover_problem.py)
   * [Fractional Knapsack](greedy_methods/fractional_knapsack.py)

greedy_methods/activity_selection.py

@@ -0,0 +1,57 @@
+"""
+The Activity Selection Problem is a classic problem in which a set of activities,
+each with a start and end time, needs to be scheduled in such a way that the
+maximum number of non-overlapping activities is selected.
+This is a greedy algorithm where at each step,
+we choose the activity that finishes the earliest
+and does not conflict with previously selected activities.
+
+Wikipedia: https://en.wikipedia.org/wiki/Activity_selection_problem
+"""
+
+
+def activity_selection(activities: list[tuple[int, int]]) -> list[tuple[int, int]]:
+    """
+    Solve the Activity Selection Problem using a greedy algorithm by selecting
+    the maximum number of non-overlapping activities from a list of activities.
+
+    Parameters:
+    activities: A list of tuples where each tuple contains
+                                        the start and end times of an activity.
+
+    Returns:
+    A list of selected activities that are non-overlapping.
+
+    Example:
+    >>> activity_selection([(1, 3), (2, 5), (3, 9), (6, 8)])
+    [(1, 3), (6, 8)]
+
+    >>> activity_selection([(0, 6), (1, 4), (3, 5), (5, 7), (5, 9), (8, 9)])
+    [(1, 4), (5, 7), (8, 9)]
+
+    >>> activity_selection([(1, 2), (2, 4), (3, 5), (0, 6)])
+    [(1, 2), (2, 4)]
+
+    >>> activity_selection([(5, 9), (1, 2), (3, 4), (0, 6)])
+    [(1, 2), (3, 4), (5, 9)]
+
+    >>> all(activity_selection(x) == [] for x in ([], {}, None, False, 0, 0.0))
+    True
+    """
+    if not activities:
+        return []
+
+    # Step 1: Sort the activities by their end time
+    sorted_activities = sorted(activities, key=lambda activity: activity[1])
+
+    # Step 2: Select the first activity (the one that finishes the earliest)
+    # as the initial activity
+    selected_activities = [sorted_activities[0]]
+
+    # Step 3: Iterate through the sorted activities and select the ones
+    # that do not overlap with the last selected activity
+    for i in range(1, len(sorted_activities)):
+        if sorted_activities[i][0] >= selected_activities[-1][1]:
+            selected_activities.append(sorted_activities[i])
+
+    return selected_activities