Merge pull request #171 from BrianLusina/feat/algorithms-intervals

feat(algorithms, intervals): most booked meeting rooms

Author: BrianLusina

DIRECTORY.md

@@ -237,6 +237,7 @@
       * [Test Intervals Intersection](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/interval_intersection/test_intervals_intersection.py)
     * Meeting Rooms
       * [Test Min Meeting Rooms](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/meeting_rooms/test_min_meeting_rooms.py)
+      * [Test Most Booked Meeting Rooms](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/meeting_rooms/test_most_booked_meeting_rooms.py)
     * Merge Intervals
       * [Test Merge Intervals](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/merge_intervals/test_merge_intervals.py)
     * Non Overlapping Intervals
@@ -451,9 +452,11 @@
     * [Test My Hashset](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/hashset/test_my_hashset.py)
   * Linked Lists
     * Circular
+      * [Circular Linked List Utils](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/circular/circular_linked_list_utils.py)
       * [Node](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/circular/node.py)
       * [Test Circular Linked List](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/circular/test_circular_linked_list.py)
       * [Test Circular Linked List Split](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/circular/test_circular_linked_list_split.py)
+      * [Test Circular Linked List Utils](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/circular/test_circular_linked_list_utils.py)
     * Doubly Linked List
       * [Node](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/doubly_linked_list/node.py)
       * [Test Doubly Linked List](https://github.com/BrianLusina/PythonSnips/blob/master/datastructures/linked_lists/doubly_linked_list/test_doubly_linked_list.py)
@@ -911,6 +914,8 @@
     * [Test Reverse Integer](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/reverse_integer/test_reverse_integer.py)
   * Self Crossing
     * [Test Is Self Crossing](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/self_crossing/test_is_self_crossing.py)
+  * Sum Of Multiples
+    * [Test Sum Of Multiples](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/sum_of_multiples/test_sum_of_multiples.py)
   * Super Size
     * [Test Super Size](https://github.com/BrianLusina/PythonSnips/blob/master/pymath/super_size/test_super_size.py)
   * Triangles
@@ -942,6 +947,8 @@
     * [Test First Occurrence](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/first_occurrence/test_first_occurrence.py)
   * Greatest Common Divisor
     * [Test Greatest Common Divisor](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/greatest_common_divisor/test_greatest_common_divisor.py)
+  * Integer To English
+    * [Test Integer To English](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/integer_to_english/test_integer_to_english.py)
   * Inttostr
     * [Test Int To Str](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/inttostr/test_int_to_str.py)
   * Is Prefix
@@ -1207,7 +1214,6 @@
     * [Test Sieve Of Erastothenes](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_sieve_of_erastothenes.py)
     * [Test Split Even Numbers](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_split_even_numbers.py)
     * [Test Sum Between](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_sum_between.py)
-    * [Test Sum Of Multiples](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_sum_of_multiples.py)
     * [Test Sum Same](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_sum_same.py)
     * [Test Summation](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_summation.py)
     * [Test Tank Truck](https://github.com/BrianLusina/PythonSnips/blob/master/tests/pymath/test_tank_truck.py)

algorithms/intervals/meeting_rooms/README.md

@@ -114,3 +114,156 @@ becomes O(n log(n)) + O(n log(n)) = O(n log(n)).
 
 The space complexity of this solution is O(n). This is because we are building a min-heap that, in the worst case, 
 can have all the input elements. Therefore, the space required to compute this solution would be O(n).
+
+---
+# Meeting Rooms III
+
+Given an integer, rooms, which represents the total number of rooms, where each room is numbered from 0 to rooms - 1.
+Additionally, you are given a 2D integer array called meetings, where each element meetings[i] = 
+[starti, endi] indicates that a meeting will be held in the half-closed interval [starti, endi). Each starti is unique.
+
+Meetings are allocated to rooms in the following manner:
+
+1. Each meeting will take place in the unused room with the lowest number.
+2. If there are no available rooms, the meeting will be delayed until a room becomes free. The delayed meeting should
+   have the same duration as the original meeting.
+3. When a room is vacated, the meeting with the earliest original start time is given priority for that room.
+
+Your task is to determine the room number that hosted the most meetings. If there are multiple rooms, return the room
+with the lowest number.
+
+> Note: A half-closed interval [a, b) is the interval between a and b, including a and not including b.
+
+## Constraints
+
+- 1 ≤ rooms ≤ 100
+- 1 ≤ meetings.length ≤ 1000
+- meetings[i].length == 2
+- 0 ≤ starti < endi ≤ 10000
+- All the values of `starti` are unique
+
+## Examples
+
+![Example 1](./images/examples/meeting_rooms_3_example_1.png)
+![Example 2](./images/examples/meeting_rooms_3_example_3.png)
+![Example 3](./images/examples/meeting_rooms_3_example_3.png)
+![Example 4](./images/examples/meeting_rooms_3_example_4.png)
+
+Example 5:
+```text
+Input: n = 2, meetings = [[0,10],[1,5],[2,7],[3,4]]
+Output: 0
+Explanation:
+- At time 0, both rooms are not being used. The first meeting starts in room 0.
+- At time 1, only room 1 is not being used. The second meeting starts in room 1.
+- At time 2, both rooms are being used. The third meeting is delayed.
+- At time 3, both rooms are being used. The fourth meeting is delayed.
+- At time 5, the meeting in room 1 finishes. The third meeting starts in room 1 for the time period [5,10).
+- At time 10, the meetings in both rooms finish. The fourth meeting starts in room 0 for the time period [10,11).
+Both rooms 0 and 1 held 2 meetings, so we return 0. 
+```
+
+Example 6:
+```text
+Input: n = 3, meetings = [[1,20],[2,10],[3,5],[4,9],[6,8]]
+Output: 1
+Explanation:
+- At time 1, all three rooms are not being used. The first meeting starts in room 0.
+- At time 2, rooms 1 and 2 are not being used. The second meeting starts in room 1.
+- At time 3, only room 2 is not being used. The third meeting starts in room 2.
+- At time 4, all three rooms are being used. The fourth meeting is delayed.
+- At time 5, the meeting in room 2 finishes. The fourth meeting starts in room 2 for the time period [5,10).
+- At time 6, all three rooms are being used. The fifth meeting is delayed.
+- At time 10, the meetings in rooms 1 and 2 finish. The fifth meeting starts in room 1 for the time period [10,12).
+Room 0 held 1 meeting while rooms 1 and 2 each held 2 meetings, so we return 1. 
+```
+
+## Topics
+
+- Array
+- Hash Table
+- Sorting
+- Heap (Priority Queue)
+- Simulation
+
+## Hints
+
+- Sort meetings based on start times.
+- Use two min heaps, the first one keeps track of the numbers of all the rooms that are free. The second heap keeps
+  track of the end times of all the meetings that are happening and the room that they are in.
+- Keep track of the number of times each room is used in an array.
+- With each meeting, check if there are any free rooms. If there are, then use the room with the smallest number.
+  Otherwise, assign the meeting to the room whose meeting will end the soonest.
+
+## Solution
+
+We use a two-heap approach for optimal scheduling to determine which room hosts the most meetings. One min heap keeps
+track of available rooms, ordered by room number, while the other tracks rooms currently in use, ordered by their next
+availability (i.e., meeting end time). This setup ensures we always have quick access to the room that becomes free the
+earliest or the lowest-numbered available room.
+
+As all meeting start times are unique, we sort the meetings by their start time to process them chronologically. For
+each meeting:
+
+- **Freeing up rooms**: Before scheduling the current meeting, we remove entries from the in-use heap whose end times
+  are less than or equal to the current meeting’s start time. Each freed room is pushed back into the available heap.
+- **Assigning a room**:
+  - If the available heap is not empty, we pop the room with the lowest number and assign the meeting to it. 
+  - If no room is available, we pop the room from the in-use heap with the earliest end time. We delay the meeting to
+    start at the room’s available time, then reassign it back into the in-use heap with the new end time.
+- **Tracking usage**: Each time a room is assigned, we increment its usage counter.
+
+After processing all meetings, we scan the counters and return the room with the highest count. The room with the lowest
+number is selected in case of a tie.
+
+The steps of the algorithm are as follows:
+1. Initialize a count array of size equal to the number of rooms to track the number of meetings held by each room.
+2. Create two min heaps:
+   - `available`: Contains free room numbers. 
+   - `used_rooms`: Contains pairs of (end time, room number) for rooms currently in use.
+3. Populate the `available` min heap with all room numbers [0, 1, 2, ..., rooms-1].
+4. Sort the `meetings` list by their `start_time` to process them in chronological order.
+5. For each meeting interval `(start_time, end_time)`:
+   - Free up rooms: While the top room in `used_rooms` has an `end_time` ≤ `start_time`, remove it from `used_rooms` and
+     add the room back to available.
+   - If no rooms are available, pop the room that will be free soonest from `used_rooms`. As the meeting must be delayed,
+     calculate its new `end_time` by extending the duration starting from the previous room’s `end_time`.
+   - Allocate the smallest available room (pop from `available`) and push its new (`end_time`, `room`) into `used_rooms`.
+   - Increment that room’s meeting count in the `count` array.
+6. After all meetings are processed, return the room’s index with the maximum meeting count. In case of a tie, return
+   the smallest index.
+
+![Solution 1](./images/solutions/meeting_rooms_3_solution_1.png)
+![Solution 2](./images/solutions/meeting_rooms_3_solution_2.png)
+![Solution 3](./images/solutions/meeting_rooms_3_solution_3.png)
+![Solution 4](./images/solutions/meeting_rooms_3_solution_4.png)
+![Solution 5](./images/solutions/meeting_rooms_3_solution_5.png)
+![Solution 6](./images/solutions/meeting_rooms_3_solution_6.png)
+![Solution 7](./images/solutions/meeting_rooms_3_solution_7.png)
+![Solution 8](./images/solutions/meeting_rooms_3_solution_8.png)
+![Solution 9](./images/solutions/meeting_rooms_3_solution_9.png)
+![Solution 10](./images/solutions/meeting_rooms_3_solution_10.png)
+![Solution 11](./images/solutions/meeting_rooms_3_solution_11.png)
+![Solution 12](./images/solutions/meeting_rooms_3_solution_12.png)
+![Solution 13](./images/solutions/meeting_rooms_3_solution_13.png)
+![Solution 14](./images/solutions/meeting_rooms_3_solution_14.png)
+![Solution 15](./images/solutions/meeting_rooms_3_solution_15.png)
+![Solution 16](./images/solutions/meeting_rooms_3_solution_16.png)
+
+### Time Complexity
+
+There are mainly two factors contributing toward the time complexity of a problem:
+
+- **Sorting**: The sorting of the given intervals takes `O(m log(m))` where m is the number of meetings or intervals.
+- **Heap operations**: We perform multiple push and pop operations for each room. Therefore, we have `O(log n)` time
+  complexity for each operation where n is the number of rooms. As the heap operations are done for all the given
+  meetings, the time complexity leads to `O(m log(n))`.
+
+Hence, the total complexity becomes `O(m log(m) + m log(n))`.
+
+### Space Complexity
+
+The space complexity of this solution will mainly be contributed by the `counter` array, i.e., O(n) where 
+n is the number of rooms, and the two min-heaps `used_rooms` and `available` i.e., O(n+n)
+as in the worst-case scenario, either of these two heaps can have n elements. Hence, the overall space complexity will
+lead up to `O(n+n+n)`, which is `O(n)`.

algorithms/intervals/meeting_rooms/__init__.py

@@ -1,4 +1,4 @@
-from typing import List
+from typing import List, Tuple
 import heapq
 
 
@@ -68,3 +68,46 @@ def find_minimum_meeting_rooms_priority_queue(meetings: List[List[int]]) -> int:
 
     # The size of the heap tells us the number of rooms allocated
     return len(rooms)
+
+
+def most_booked(meetings: List[List[int]], rooms: int) -> int:
+    # A counter array that keeps track of the number of meetings held in each room
+    counter = [0] * rooms
+    # Min heap to keep track of free rooms
+    available = [i for i in range(rooms)]
+    # Min heap for rooms currently in use
+    used_rooms: List[Tuple[int, int]] = []
+
+    # Sort the meetings by their start times to process them in chronological order. This uses additional space as we
+    # don't want to mutate the input meetings list. In addition, incurs time complexity of O(n log(n)) due to sorting
+    sorted_meetings = sorted(meetings, key=lambda x: x[0])
+
+    # For each meeting, free up rooms that have finished their meetings by moving them from used_rooms to available
+    for meeting in sorted_meetings:
+        current_start_time, current_end_time = meeting
+
+        # If a room is free, assign it to the current meeting. If no rooms are fre, delay the meeting until the earliest
+        # available room is free, then schedule it
+
+        # Free up rooms that have finished their meetings by their current start time
+        while used_rooms and used_rooms[0][0] <= current_start_time:
+            used_room = heapq.heappop(used_rooms)
+            end_time, room_number = used_room
+            heapq.heappush(available, room_number)
+
+        # If no rooms are available, delay the meeting until a room becomes free
+        if not available:
+            used_room = heapq.heappop(used_rooms)
+            used_room_end_time, used_room_number = used_room
+            current_end_time = used_room_end_time + (
+                current_end_time - current_start_time
+            )
+            heapq.heappush(available, used_room_number)
+
+        # Allocate the meeting to the available room with the lowest number
+        available_room = heapq.heappop(available)
+        heapq.heappush(used_rooms, (current_end_time, available_room))
+        counter[available_room] += 1
+
+    # Once all meetings are processed, return the room with the highest number of meetings from the counter array
+    return counter.index(max(counter))