diff --git a/DIRECTORY.md b/DIRECTORY.md
index d2957aa6..eae3cf76 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -101,6 +101,8 @@
     * [Decoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/decoding.py)
     * [Encoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/encoding.py)
   * Intervals
+    * Count Days
+      * [Test Count Days Without Meetings](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/count_days/test_count_days_without_meetings.py)
     * Insert Interval
       * [Test Insert Interval](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/insert_interval/test_insert_interval.py)
     * Interval Intersection
diff --git a/algorithms/intervals/count_days/README.md b/algorithms/intervals/count_days/README.md
new file mode 100644
index 00000000..668fc1b3
--- /dev/null
+++ b/algorithms/intervals/count_days/README.md
@@ -0,0 +1,65 @@
+# Count Days Without Meetings
+
+You are given a positive integer, `days`, which represents the total number of days an employee is available for work, 
+starting from day 1. You are also given a 2D array, `meetings`, where each entry meetings[i] = [starti, endi] indicates 
+that a meeting is scheduled from day starti to day endi (both inclusive).
+
+Your task is to count the days when the employee is available for work but has no scheduled meetings.
+
+> Note: The meetings may overlap.
+
+## Constraints
+
+- 1 <= days <= 10^5
+- 1 <= meetings.length <= 10^3
+- meetings[i].length == 2
+- 1 <= `meetings[i][0]` <= `meetings[i][1]` <= days
+
+## Examples
+
+![Example 1](./images/examples/count_days_without_meetings_example_1.png)
+![Example 2](./images/examples/count_days_without_meetings_example_2.png)
+![Example 3](./images/examples/count_days_without_meetings_example_3.png)
+
+## Solution
+
+The core idea of this solution is to merge overlapping meetings into continuous intervals to efficiently track the 
+occupied days. We begin by sorting the meetings to process them sequentially. As we iterate, we merge overlapping 
+meetings while counting the occupied days whenever gaps appear. Finally, subtracting the total occupied days from the 
+available days gives the number of free days.
+
+Using the intuition above, we implement the algorithm as follows:
+
+1. First, sort the meetings based on their start time to process them in order.
+2. Initialize a variable, occupied, with 0 to count the days when the employee has scheduled meetings.
+3. Initialize two variables, start and end, with the first meeting’s start and end times. These variables define the 
+   beginning and end of the merged meeting interval to efficiently track continuously occupied periods.
+4. Iterate through the remaining meetings:
+   - If a meeting overlaps with the current merged meeting, extend the end time to merge it into the existing interval.
+   - Otherwise, add the days of the merged meeting to occupied as `occupied = occupied + (end - start + 1)`. Then, update
+     the start and end for the next interval.
+5. After the loop, add the days of the last merged interval to occupied.
+6. Return the difference between days and occupied (`days−occupied`), representing the number of days when the employee 
+   is available for work but has no scheduled meetings.
+
+![Solution 1](./images/solutions/count_days_without_meetings_solution_1.png)
+![Solution 2](./images/solutions/count_days_without_meetings_solution_2.png)
+![Solution 3](./images/solutions/count_days_without_meetings_solution_3.png)
+![Solution 4](./images/solutions/count_days_without_meetings_solution_4.png)
+![Solution 5](./images/solutions/count_days_without_meetings_solution_5.png)
+![Solution 6](./images/solutions/count_days_without_meetings_solution_6.png)
+![Solution 7](./images/solutions/count_days_without_meetings_solution_7.png)
+![Solution 8](./images/solutions/count_days_without_meetings_solution_8.png)
+![Solution 9](./images/solutions/count_days_without_meetings_solution_9.png)
+![Solution 10](./images/solutions/count_days_without_meetings_solution_10.png)
+![Solution 11](./images/solutions/count_days_without_meetings_solution_11.png)
+![Solution 12](./images/solutions/count_days_without_meetings_solution_12.png)
+
+### Time Complexity
+
+The algorithm’s time complexity is O(nlogn), where n is the size of the meetings array. This is due to the sorting step, 
+which dominates the overall complexity while merging the intervals runs in O(n).
+
+### Space Complexity
+
+The algorithm’s space complexity is constant, O(1).
diff --git a/algorithms/intervals/count_days/__init__.py b/algorithms/intervals/count_days/__init__.py
new file mode 100644
index 00000000..a820db5e
--- /dev/null
+++ b/algorithms/intervals/count_days/__init__.py
@@ -0,0 +1,110 @@
+from typing import List
+
+
+def count_days(days: int, meetings: List[List[int]]) -> int:
+    """
+    Counts the number of days the employee is available for work but has no scheduled meetings.
+
+    Complexity:
+
+    Standard time complexity for sorting is O(n log(n)). The loop is O(n). The part that dominates the overall time
+    complexity is the sorting and the loop. It amounts to O(n log(n)) as the overall. The overall space complexity for
+    this approach is O(1) without accounting for the in place sorting that is taking place which is O(n) using timsort
+    in Python.
+
+    Summary of Performance
+    ---
+    Metric	Complexity	Reason
+    ---
+    Time	O(nlogn)	Dominated by the initial sort of n meetings.
+    Space	O(n)	Required by Timsort for internal temporary storage.
+
+    Args:
+        days (int): The total number of days the employee is available for work
+        meetings (List[List[int]]): A list of meetings, where each meeting is represented as a list of two integers [start, end]
+    Returns:
+        int: The number of days the employee is available for work but has no scheduled meetings
+    """
+    # sort meetings by start in place, incurs O(n log(n)) time complexity
+    meetings.sort(key=lambda x: x[0])
+
+    # keep track of free days
+    free_days = 0
+
+    # a pointer that keeps track of the current day
+    last_busy_day = 0
+
+    # iterate through the meetings, for each meeting we might have a gap
+    for meeting in meetings:
+        # get the start and end of the meeting
+        start, end = meeting
+
+        # calculate gaps, if the meeting starts at start and our last_busy_day is less than start - 1, the days in
+        # between are free
+        if start > last_busy_day + 1:
+            free_days += (start - 1) - last_busy_day
+
+        # update the last busy day to the maximum of the last busy day and the end of the meeting
+
+        # This ensures that if a meeting is completely contained within a previous busy block, the boundary doesn't move
+        # backward, which handles overlaps perfectly.
+        last_busy_day = max(last_busy_day, end)
+
+    # add the remaining days to the free days
+    return free_days + (days - last_busy_day)
+
+
+def count_days_2(days: int, meetings: List[List[int]]) -> int:
+    """
+    Counts the number of days the employee is available for work but has no scheduled meetings.
+    
+    This implementation merges overlapping meetings and counts total occupied days.
+    
+    Time Complexity: O(n log n) due to sorting
+    Space Complexity: O(1) excluding sort overhead
+    
+    Args:
+        days (int): The total number of days the employee is available for work
+        meetings (List[List[int]]): A list of meetings, where each meeting is represented as a list of two integers [start, end]
+            Note: This function modifies the input list by sorting it in place.
+    Returns:
+        int: The number of days the employee is available for work but has no scheduled meetings
+    """
+    # Sort the meetings based on their start time to process them in order
+    meetings.sort()
+
+    # Initialize a variable with 0 to count the number of days when the employee has meetings scheduled
+    occupied = 0
+
+    # Initialize two variables with the first meeting’s start and end times
+    # Sort the meetings based on their start time to process them in order
+    meetings.sort()
+
+    # Handle edge case of empty meetings
+    if not meetings:
+        return days
+
+    # Initialize a variable with 0 to count the number of days when the employee has meetings scheduled
+    occupied = 0
+
+    # Initialize two variables with the first meeting's start and end times
+    start, end = meetings[0]
+
+    # Iterate through the remaining meetings
+    for i in range(1, len(meetings)):
+        # If a meeting overlaps with the current merged meeting
+        if meetings[i][0] <= end:
+            # Extend the end time to merge it
+            end = max(end, meetings[i][1])
+        else:
+            # Add the days of the merged meeting
+            occupied += end - start + 1
+
+            # Update start and end for the next interval
+            start, end = meetings[i]
+
+    # Add the days of the last merged meeting
+    occupied += end - start + 1
+
+    # Return the free days
+    return days - occupied
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diff --git a/algorithms/intervals/count_days/test_count_days_without_meetings.py b/algorithms/intervals/count_days/test_count_days_without_meetings.py
new file mode 100644
index 00000000..f2548b20
--- /dev/null
+++ b/algorithms/intervals/count_days/test_count_days_without_meetings.py
@@ -0,0 +1,525 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.intervals.count_days import count_days, count_days_2
+
+TEST_CASES = [
+    (10, [[7, 9], [3, 6]], 3),
+    (100, [[1, 100]], 0),
+    (12, [[10, 12], [1, 5], [4, 8]], 1),
+    (12, [[5, 6], [9, 11], [1, 3]], 4),
+    (6, [[2, 4], [5, 5]], 2),
+    (100000, [[1, 100000]], 0),
+    (3136, [[361, 570], [420, 1225], [72, 144], [987, 1444]], 1979),
+    (786, [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]], 774),
+    (
+        54474,
+        [
+            [1646, 1745],
+            [8226, 8322],
+            [350, 457],
+            [27725, 27748],
+            [14424, 14509],
+            [31944, 32009],
+            [8971, 9017],
+            [684, 772],
+            [21549, 21619],
+            [31929, 31971],
+            [23892, 23955],
+            [19487, 19526],
+            [22921, 22957],
+            [17253, 17308],
+            [18454, 18535],
+            [20151, 20154],
+            [3183, 3285],
+            [20204, 20254],
+            [15794, 15879],
+            [9624, 9653],
+            [20922, 21004],
+            [20841, 20871],
+            [26184, 26265],
+            [8312, 8373],
+            [20521, 20621],
+            [21159, 21206],
+            [33908, 33970],
+            [7775, 7798],
+            [13420, 13476],
+            [18464, 18537],
+            [1780, 1805],
+            [33435, 33531],
+            [7344, 7347],
+            [20990, 21102],
+            [23930, 23987],
+            [33244, 33351],
+            [8764, 8766],
+            [25020, 25053],
+            [5043, 5101],
+            [8575, 8621],
+            [11443, 11526],
+            [1960, 2061],
+            [15120, 15225],
+            [19825, 19857],
+            [22747, 22754],
+            [5122, 5210],
+            [10072, 10087],
+            [28172, 28284],
+            [6259, 6359],
+            [28800, 28812],
+            [21174, 21271],
+            [17472, 17529],
+            [30661, 30755],
+            [25555, 25654],
+            [3942, 4050],
+            [15547, 15627],
+            [33434, 33486],
+            [13205, 13221],
+            [28666, 28738],
+            [16682, 16751],
+            [30500, 30524],
+            [16278, 16290],
+            [29038, 29061],
+            [21498, 21503],
+            [6467, 6530],
+            [25366, 25410],
+            [15900, 16008],
+            [18221, 18299],
+            [30929, 30957],
+            [4568, 4609],
+            [30462, 30522],
+            [34492, 34526],
+            [2259, 2270],
+            [19369, 19452],
+            [1888, 1989],
+            [12254, 12260],
+            [17861, 17914],
+            [31687, 31710],
+            [32534, 32576],
+            [22006, 22031],
+            [25541, 25622],
+            [22168, 22257],
+            [12733, 12832],
+            [8226, 8226],
+            [9279, 9313],
+            [26989, 27086],
+            [10495, 10523],
+            [10509, 10618],
+            [11623, 11723],
+            [12437, 12500],
+            [662, 746],
+            [28486, 28596],
+            [8987, 9087],
+            [23676, 23710],
+            [6104, 6159],
+            [31947, 31997],
+            [3502, 3561],
+            [5550, 5617],
+            [17326, 17341],
+            [10278, 10285],
+            [4291, 4323],
+            [34537, 34644],
+            [4742, 4844],
+            [27462, 27566],
+            [8274, 8288],
+            [2160, 2196],
+            [3645, 3746],
+            [3805, 3848],
+            [21291, 21354],
+            [12913, 13004],
+            [7303, 7383],
+            [32195, 32300],
+            [27748, 27777],
+            [1579, 1592],
+            [8442, 8475],
+            [34076, 34163],
+            [23251, 23325],
+            [31714, 31735],
+            [31004, 31012],
+            [1720, 1744],
+            [31266, 31321],
+            [6903, 7008],
+            [19604, 19610],
+            [34505, 34508],
+            [1579, 1655],
+            [1279, 1294],
+            [13407, 13429],
+            [33781, 33807],
+            [27537, 27604],
+            [25418, 25528],
+            [5044, 5097],
+            [15345, 15391],
+            [19108, 19150],
+            [13736, 13759],
+            [16366, 16368],
+            [12600, 12698],
+            [9897, 9905],
+            [20693, 20747],
+            [22241, 22242],
+            [2113, 2169],
+            [10777, 10796],
+            [10637, 10716],
+            [9424, 9506],
+            [22735, 22774],
+            [22305, 22414],
+            [32819, 32870],
+            [27991, 27993],
+            [13558, 13618],
+            [7561, 7610],
+            [31890, 31900],
+            [7933, 7943],
+            [18311, 18403],
+            [622, 657],
+            [967, 1025],
+            [9176, 9236],
+            [31271, 31292],
+            [5484, 5511],
+            [5122, 5159],
+            [1280, 1329],
+            [30883, 30901],
+            [30532, 30542],
+            [8202, 8227],
+            [21300, 21333],
+            [32066, 32114],
+            [11062, 11153],
+            [33006, 33043],
+            [24669, 24777],
+            [8082, 8149],
+            [27415, 27471],
+            [24098, 24189],
+            [23155, 23257],
+            [27019, 27126],
+            [6007, 6018],
+            [28811, 28917],
+            [4431, 4492],
+            [19729, 19815],
+            [16326, 16367],
+            [18592, 18682],
+            [16466, 16575],
+            [32400, 32499],
+            [1109, 1189],
+            [163, 242],
+            [30273, 30385],
+            [22694, 22737],
+            [9701, 9774],
+            [9410, 9455],
+            [15177, 15193],
+            [14074, 14156],
+            [23316, 23399],
+            [10939, 10983],
+            [23774, 23855],
+            [18728, 18836],
+            [16967, 17075],
+            [11256, 11357],
+            [16580, 16584],
+            [14766, 14829],
+            [24622, 24726],
+            [15456, 15521],
+            [5675, 5710],
+            [19496, 19606],
+            [28766, 28767],
+            [7344, 7412],
+            [2556, 2563],
+            [27267, 27349],
+            [13397, 13450],
+            [31124, 31145],
+            [21373, 21480],
+            [18192, 18237],
+            [7734, 7774],
+            [31010, 31115],
+            [30500, 30511],
+            [14876, 14877],
+            [27441, 27509],
+            [32671, 32693],
+            [10576, 10657],
+            [27960, 28070],
+            [22233, 22249],
+            [8592, 8701],
+            [18084, 18188],
+            [28076, 28162],
+            [22125, 22177],
+            [6599, 6700],
+            [31924, 31937],
+            [4564, 4674],
+            [15445, 15479],
+            [12098, 12198],
+            [6996, 7097],
+            [14720, 14819],
+            [25840, 25940],
+            [3325, 3388],
+            [11431, 11474],
+            [25746, 25814],
+            [10781, 10844],
+            [9860, 9872],
+            [856, 877],
+            [15574, 15659],
+            [2010, 2075],
+            [33072, 33122],
+            [31878, 31882],
+            [29982, 30078],
+            [11921, 11954],
+            [26590, 26631],
+            [290, 396],
+            [8495, 8582],
+            [2172, 2230],
+            [10275, 10372],
+            [20688, 20735],
+            [31161, 31217],
+            [32674, 32716],
+            [10643, 10677],
+            [4865, 4973],
+            [14237, 14318],
+            [18938, 18984],
+            [34649, 34722],
+            [17167, 17267],
+            [29915, 29921],
+            [22967, 22984],
+            [13061, 13123],
+            [26630, 26671],
+            [457, 531],
+            [10193, 10221],
+            [7245, 7249],
+            [13869, 13969],
+            [9071, 9117],
+            [21480, 21507],
+            [27993, 28055],
+            [33244, 33244],
+            [27256, 27329],
+            [34481, 34562],
+            [14557, 14592],
+            [27858, 27964],
+            [10319, 10418],
+            [7634, 7638],
+            [12861, 12942],
+            [30558, 30648],
+            [26123, 26174],
+            [27535, 27623],
+            [34347, 34374],
+            [31847, 31935],
+            [20253, 20351],
+            [29172, 29260],
+            [15069, 15110],
+            [26040, 26044],
+            [22506, 22571],
+            [11831, 11890],
+            [17997, 18040],
+            [17640, 17735],
+            [14877, 14980],
+            [23477, 23494],
+            [34359, 34378],
+            [20086, 20109],
+            [33138, 33155],
+            [10651, 10703],
+            [24402, 24461],
+            [17743, 17823],
+            [6798, 6860],
+            [18346, 18398],
+            [32846, 32931],
+            [25306, 25320],
+            [4060, 4144],
+            [20417, 20427],
+            [2915, 3005],
+            [4271, 4302],
+            [34707, 34717],
+            [26340, 26414],
+            [33061, 33075],
+            [1335, 1386],
+            [6684, 6754],
+            [19197, 19218],
+            [19918, 20004],
+            [22117, 22157],
+            [33642, 33754],
+            [31505, 31583],
+            [25835, 25889],
+            [17333, 17376],
+            [32734, 32782],
+            [29272, 29347],
+            [20859, 20880],
+            [5260, 5318],
+            [31335, 31411],
+            [13260, 13269],
+            [30105, 30185],
+            [23400, 23447],
+            [7940, 7961],
+            [3064, 3167],
+            [14071, 14090],
+            [14873, 14899],
+            [1432, 1499],
+            [13009, 13081],
+            [17882, 17988],
+            [32529, 32531],
+            [2249, 2266],
+            [28386, 28468],
+            [9076, 9137],
+            [29457, 29524],
+            [639, 656],
+            [10142, 10198],
+            [8853, 8923],
+            [29748, 29843],
+            [7508, 7582],
+            [34222, 34317],
+            [29001, 29042],
+            [21638, 21696],
+            [4031, 4131],
+            [31334, 31334],
+            [7188, 7262],
+            [7956, 8024],
+            [16368, 16459],
+            [16202, 16216],
+            [26706, 26733],
+            [22027, 22096],
+            [11954, 12036],
+            [6101, 6129],
+            [12691, 12736],
+            [2056, 2074],
+            [26363, 26414],
+            [18362, 18434],
+            [5840, 5892],
+            [24460, 24560],
+            [26987, 27018],
+            [9195, 9289],
+            [26529, 26556],
+            [25185, 25281],
+            [15571, 15668],
+            [6462, 6487],
+            [23547, 23554],
+            [27225, 27243],
+            [2852, 2854],
+            [15695, 15756],
+            [8464, 8535],
+            [3392, 3434],
+            [1310, 1338],
+            [16282, 16283],
+            [16164, 16252],
+            [22751, 22847],
+            [20645, 20754],
+            [33141, 33146],
+            [31754, 31863],
+            [3143, 3246],
+            [25156, 25161],
+            [24235, 24323],
+            [33011, 33061],
+            [18345, 18346],
+            [23482, 23511],
+            [11537, 11538],
+            [1731, 1777],
+            [15110, 15171],
+            [2636, 2678],
+            [30687, 30791],
+            [27425, 27504],
+            [13612, 13702],
+            [32529, 32565],
+            [15574, 15634],
+            [14103, 14165],
+            [21646, 21731],
+            [9155, 9215],
+            [16524, 16539],
+            [5882, 5934],
+            [12861, 12896],
+            [25297, 25344],
+            [6680, 6685],
+            [5308, 5376],
+            [9623, 9624],
+            [5281, 5296],
+            [7778, 7826],
+            [4570, 4647],
+            [6154, 6162],
+            [13291, 13377],
+            [24863, 24944],
+            [24411, 24456],
+            [5467, 5498],
+            [34165, 34226],
+            [21796, 21828],
+            [12379, 12487],
+            [24397, 24471],
+            [23440, 23502],
+            [19050, 19124],
+            [5790, 5854],
+            [29299, 29338],
+            [33816, 33901],
+            [4138, 4187],
+            [19125, 19165],
+            [9994, 10080],
+            [27622, 27714],
+            [29698, 29752],
+            [16833, 16880],
+            [13, 55],
+            [12292, 12367],
+            [18667, 18741],
+            [6328, 6399],
+            [19110, 19130],
+            [34073, 34184],
+            [33185, 33291],
+            [2746, 2856],
+            [26441, 26469],
+            [471, 535],
+            [29627, 29737],
+            [396, 456],
+            [791, 856],
+            [9643, 9687],
+            [19206, 19271],
+            [15067, 15147],
+            [4729, 4743],
+            [11996, 12041],
+            [15176, 15227],
+            [32384, 32413],
+            [10282, 10307],
+            [33014, 33071],
+            [1421, 1436],
+            [29743, 29751],
+            [4213, 4296],
+            [255, 261],
+            [16004, 16106],
+            [14567, 14637],
+            [7858, 7954],
+            [651, 656],
+            [9482, 9520],
+            [23610, 23715],
+            [6733, 6821],
+            [25395, 25475],
+            [26811, 26907],
+            [15745, 15832],
+            [2845, 2953],
+            [10975, 11051],
+            [4411, 4432],
+            [6847, 6876],
+            [29441, 29469],
+            [12546, 12569],
+            [19604, 19665],
+            [5566, 5597],
+            [28250, 28326],
+            [24449, 24461],
+            [21913, 21940],
+            [30532, 30536],
+            [5886, 5948],
+            [651, 746],
+            [14960, 15057],
+            [22973, 23055],
+            [15263, 15296],
+            [33710, 33752],
+            [22667, 22694],
+            [27322, 27374],
+            [2378, 2455],
+            [2914, 2918],
+        ],
+        32323,
+    ),
+]
+
+
+class CountDaysWithoutMeetingsTestCase(unittest.TestCase):
+    @parameterized.expand(TEST_CASES)
+    def test_count_days_without_meetings(
+        self, days: int, meetings: List[List[int]], expected: int
+    ):
+        actual = count_days(days, meetings)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(TEST_CASES)
+    def test_count_days_without_meetings_2(
+        self, days: int, meetings: List[List[int]], expected: int
+    ):
+        actual = count_days_2(days, meetings)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/algorithms/intervals/merge_intervals/__init__.py b/algorithms/intervals/merge_intervals/__init__.py
index 1bfa7bdc..9e4bab73 100644
--- a/algorithms/intervals/merge_intervals/__init__.py
+++ b/algorithms/intervals/merge_intervals/__init__.py
@@ -22,12 +22,18 @@ def merge(intervals: List[List[int]]) -> List[List[int]]:
     merged = []
 
     for interval in closed_intervals:
+        current_interval_start_time = interval[0]
+        current_interval_end_time = interval[1]
+        last_merged_interval_end_time = merged[-1][1] if merged else float("-inf")
+
         # if the merged array is empty or the last interval in the merged array does not overlap with the current interval
-        if not merged or merged[-1][1] < interval[0]:
+        if not merged or last_merged_interval_end_time < current_interval_start_time:
             # add it to the merged list
             merged.append(interval)
         else:
             # else we merge the intervals, by updating the max end time of the last interval in the merged list
-            merged[-1][1] = max(merged[-1][1], interval[1])
+            merged[-1][1] = max(
+                last_merged_interval_end_time, current_interval_end_time
+            )
 
     return merged