diff --git a/DIRECTORY.md b/DIRECTORY.md
index 60ece2b8..caaa5692 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -138,8 +138,24 @@
     * Spread Stones
       * [Test Minimum Moves To Spread Stones](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/greedy/spread_stones/test_minimum_moves_to_spread_stones.py)
   * Heap
+    * Longest Happy String
+      * [Test Longest Happy String](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/longest_happy_string/test_longest_happy_string.py)
+    * Maximal Score After K Operations
+      * [Test Maximal Score](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/maximal_score_after_k_operations/test_maximal_score.py)
+    * Maximum Subsequence Score
+      * [Test Max Subsequence Score](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/maximum_subsequence_score/test_max_subsequence_score.py)
+    * Min Cost Hire K Workers
+      * [Test Min Cost To Hire Workers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py)
+    * Min Cost To Connect Sticks
+      * [Test Min Cost Connect Sticks](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py)
     * Schedule Tasks
       * [Test Schedule Tasks On Minimum Machines](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/schedule_tasks/test_schedule_tasks_on_minimum_machines.py)
+    * Topkclosesttoorigin
+      * [Test Top K Closest To Origin](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/topkclosesttoorigin/test_top_k_closest_to_origin.py)
+    * Topklargest
+      * [Test Top K Largest Elements](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/topklargest/test_top_k_largest_elements.py)
+    * Total Cost Hire K Workers
+      * [Test Total Cost Hire K Workers](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py)
   * Huffman
     * [Decoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/decoding.py)
     * [Encoding](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/huffman/encoding.py)
@@ -173,6 +189,9 @@
       * [Test Task Scheduler](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/intervals/task_scheduler/test_task_scheduler.py)
   * Josephus Circle
     * [Test Josephus Circle](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/josephus_circle/test_josephus_circle.py)
+  * Matrix
+    * Isvalidsudoku
+      * [Test Is Valid Sudoku](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/matrix/isvalidsudoku/test_is_valid_sudoku.py)
   * Memoization
     * [Fibonacci](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/memoization/fibonacci.py)
   * [Petethebaker](https://github.com/BrianLusina/PythonSnips/blob/master/algorithms/petethebaker.py)
@@ -670,17 +689,6 @@
       * [Test Find Difference](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/hashmap/find_difference_of_two_arrays/test_find_difference.py)
     * Unique Number Of Occurrences
       * [Test Unique Occurrences](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/hashmap/unique_number_of_occurrences/test_unique_occurrences.py)
-  * Heap
-    * Maximal Score After K Operations
-      * [Test Maximal Score](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/heap/maximal_score_after_k_operations/test_maximal_score.py)
-    * Maximum Subsequence Score
-      * [Test Max Subsequence Score](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/heap/maximum_subsequence_score/test_max_subsequence_score.py)
-    * Min Cost Hire K Workers
-      * [Test Min Cost To Hire Workers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py)
-    * Min Cost To Connect Sticks
-      * [Test Min Cost Connect Sticks](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py)
-    * Total Cost Hire K Workers
-      * [Test Total Cost Hire K Workers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py)
   * Hidden Cubic Numbers
     * [Hidden Cubic Numbers](https://github.com/BrianLusina/PythonSnips/blob/master/puzzles/hidden_cubic_numbers/hidden_cubic_numbers.py)
   * Matrix In Spiral Form
@@ -861,8 +869,6 @@
     * [Test Longest Common Prefix](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/longest_common_prefix/test_longest_common_prefix.py)
   * Longest Common Suffix Queries
     * [Test Longest Common Suffix Queries](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/longest_common_suffix_queries/test_longest_common_suffix_queries.py)
-  * Longest Happy String
-    * [Test Longest Happy String](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/longest_happy_string/test_longest_happy_string.py)
   * Longest Self Contained Substring
     * [Test Longest Self Contained Substring](https://github.com/BrianLusina/PythonSnips/blob/master/pystrings/longest_self_contained_substring/test_longest_self_contained_substring.py)
   * Look And Say Sequence
diff --git a/puzzles/heap/__init__.py b/algorithms/dfs/__init__.py
similarity index 100%
rename from puzzles/heap/__init__.py
rename to algorithms/dfs/__init__.py
diff --git a/pystrings/longest_happy_string/README.md b/algorithms/heap/longest_happy_string/README.md
similarity index 72%
rename from pystrings/longest_happy_string/README.md
rename to algorithms/heap/longest_happy_string/README.md
index 49cd3b83..633505c4 100644
--- a/pystrings/longest_happy_string/README.md
+++ b/algorithms/heap/longest_happy_string/README.md
@@ -22,9 +22,9 @@ strings, return any one of them. If no such string can be formed, return an empt
 
 ## Examples
 
-![Example 1](./images/examples/longest_happy_string_example_1.png)
-![Example 2](./images/examples/longest_happy_string_example_2.png)
-![Example 3](./images/examples/longest_happy_string_example_3.png)
+![Example 1](images/examples/longest_happy_string_example_1.png)
+![Example 2](images/examples/longest_happy_string_example_2.png)
+![Example 3](images/examples/longest_happy_string_example_3.png)
 
 
 ## Solution
@@ -55,21 +55,21 @@ Note: In Python, strings are immutable, so we construct the result as a list and
 
 Let’s look at the following illustration to get a better understanding of the solution:
 
-![Longest Happy String Solution 1](./images/solutions/longest_happy_string_solution_1.png)
-![Longest Happy String Solution 2](./images/solutions/longest_happy_string_solution_2.png)
-![Longest Happy String Solution 3](./images/solutions/longest_happy_string_solution_3.png)
-![Longest Happy String Solution 4](./images/solutions/longest_happy_string_solution_4.png)
-![Longest Happy String Solution 5](./images/solutions/longest_happy_string_solution_5.png)
-![Longest Happy String Solution 6](./images/solutions/longest_happy_string_solution_6.png)
-![Longest Happy String Solution 7](./images/solutions/longest_happy_string_solution_7.png)
-![Longest Happy String Solution 8](./images/solutions/longest_happy_string_solution_8.png)
-![Longest Happy String Solution 9](./images/solutions/longest_happy_string_solution_9.png)
-![Longest Happy String Solution 10](./images/solutions/longest_happy_string_solution_10.png)
-![Longest Happy String Solution 11](./images/solutions/longest_happy_string_solution_11.png)
-![Longest Happy String Solution 12](./images/solutions/longest_happy_string_solution_12.png)
-![Longest Happy String Solution 13](./images/solutions/longest_happy_string_solution_13.png)
-![Longest Happy String Solution 14](./images/solutions/longest_happy_string_solution_14.png)
-![Longest Happy String Solution 15](./images/solutions/longest_happy_string_solution_15.png)
+![Longest Happy String Solution 1](images/solutions/longest_happy_string_solution_1.png)
+![Longest Happy String Solution 2](images/solutions/longest_happy_string_solution_2.png)
+![Longest Happy String Solution 3](images/solutions/longest_happy_string_solution_3.png)
+![Longest Happy String Solution 4](images/solutions/longest_happy_string_solution_4.png)
+![Longest Happy String Solution 5](images/solutions/longest_happy_string_solution_5.png)
+![Longest Happy String Solution 6](images/solutions/longest_happy_string_solution_6.png)
+![Longest Happy String Solution 7](images/solutions/longest_happy_string_solution_7.png)
+![Longest Happy String Solution 8](images/solutions/longest_happy_string_solution_8.png)
+![Longest Happy String Solution 9](images/solutions/longest_happy_string_solution_9.png)
+![Longest Happy String Solution 10](images/solutions/longest_happy_string_solution_10.png)
+![Longest Happy String Solution 11](images/solutions/longest_happy_string_solution_11.png)
+![Longest Happy String Solution 12](images/solutions/longest_happy_string_solution_12.png)
+![Longest Happy String Solution 13](images/solutions/longest_happy_string_solution_13.png)
+![Longest Happy String Solution 14](images/solutions/longest_happy_string_solution_14.png)
+![Longest Happy String Solution 15](images/solutions/longest_happy_string_solution_15.png)
 
 ### Time complexity
 
diff --git a/pystrings/longest_happy_string/__init__.py b/algorithms/heap/longest_happy_string/__init__.py
similarity index 94%
rename from pystrings/longest_happy_string/__init__.py
rename to algorithms/heap/longest_happy_string/__init__.py
index 7da0fde4..c06f2e6a 100644
--- a/pystrings/longest_happy_string/__init__.py
+++ b/algorithms/heap/longest_happy_string/__init__.py
@@ -20,8 +20,8 @@ def longest_diverse_string(a: int, b: int, c: int) -> str:
     # Process the heap until it's empty or no valid character can be added
     while max_heap:
         # Pop the character with the highest remaining frequency
-        count, character = heappop(max_heap)
-        count = -count  # Convert back to positive
+        negative_count, character = heappop(max_heap)
+        count = -negative_count  # Convert back to positive
 
         # Check if adding this character violates the "no three consecutive" rule
         if len(result) >= 2 and result[-1] == character and result[-2] == character:
diff --git a/pystrings/longest_happy_string/images/examples/longest_happy_string_example_1.png b/algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_1.png
similarity index 100%
rename from pystrings/longest_happy_string/images/examples/longest_happy_string_example_1.png
rename to algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_1.png
diff --git a/pystrings/longest_happy_string/images/examples/longest_happy_string_example_2.png b/algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_2.png
similarity index 100%
rename from pystrings/longest_happy_string/images/examples/longest_happy_string_example_2.png
rename to algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_2.png
diff --git a/pystrings/longest_happy_string/images/examples/longest_happy_string_example_3.png b/algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_3.png
similarity index 100%
rename from pystrings/longest_happy_string/images/examples/longest_happy_string_example_3.png
rename to algorithms/heap/longest_happy_string/images/examples/longest_happy_string_example_3.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_1.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_1.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_1.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_1.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_10.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_10.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_10.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_10.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_11.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_11.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_11.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_11.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_12.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_12.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_12.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_12.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_13.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_13.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_13.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_13.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_14.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_14.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_14.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_14.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_15.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_15.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_15.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_15.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_2.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_2.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_2.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_2.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_3.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_3.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_3.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_3.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_4.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_4.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_4.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_4.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_5.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_5.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_5.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_5.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_6.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_6.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_6.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_6.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_7.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_7.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_7.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_7.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_8.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_8.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_8.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_8.png
diff --git a/pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_9.png b/algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_9.png
similarity index 100%
rename from pystrings/longest_happy_string/images/solutions/longest_happy_string_solution_9.png
rename to algorithms/heap/longest_happy_string/images/solutions/longest_happy_string_solution_9.png
diff --git a/pystrings/longest_happy_string/test_longest_happy_string.py b/algorithms/heap/longest_happy_string/test_longest_happy_string.py
similarity index 90%
rename from pystrings/longest_happy_string/test_longest_happy_string.py
rename to algorithms/heap/longest_happy_string/test_longest_happy_string.py
index 17975251..edb4bbba 100644
--- a/pystrings/longest_happy_string/test_longest_happy_string.py
+++ b/algorithms/heap/longest_happy_string/test_longest_happy_string.py
@@ -1,6 +1,6 @@
 import unittest
 from parameterized import parameterized
-from pystrings.longest_happy_string import longest_diverse_string
+from algorithms.heap.longest_happy_string import longest_diverse_string
 
 
 class LongestHappyStringTestCase(unittest.TestCase):
diff --git a/puzzles/heap/maximal_score_after_k_operations/README.md b/algorithms/heap/maximal_score_after_k_operations/README.md
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/README.md
rename to algorithms/heap/maximal_score_after_k_operations/README.md
diff --git a/puzzles/heap/maximal_score_after_k_operations/__init__.py b/algorithms/heap/maximal_score_after_k_operations/__init__.py
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/__init__.py
rename to algorithms/heap/maximal_score_after_k_operations/__init__.py
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_1.png b/algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_1.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_1.png
rename to algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_1.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_2.png b/algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_2.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_2.png
rename to algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_2.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_3.png b/algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_3.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_3.png
rename to algorithms/heap/maximal_score_after_k_operations/images/examples/maximal_score_after_k_operations_example_3.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_1.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_1.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_1.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_1.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_10.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_10.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_10.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_10.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_11.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_11.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_11.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_11.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_12.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_12.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_12.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_12.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_13.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_13.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_13.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_13.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_14.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_14.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_14.png
rename to algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_14.png
diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_15.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_15.png
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_15.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_3.png
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diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_4.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_4.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_4.png
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diff --git a/puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_5.png b/algorithms/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_5.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_5.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_6.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_7.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_8.png
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rename from puzzles/heap/maximal_score_after_k_operations/images/solution/maximal_score_after_k_operations_solution_9.png
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diff --git a/puzzles/heap/maximal_score_after_k_operations/test_maximal_score.py b/algorithms/heap/maximal_score_after_k_operations/test_maximal_score.py
similarity index 100%
rename from puzzles/heap/maximal_score_after_k_operations/test_maximal_score.py
rename to algorithms/heap/maximal_score_after_k_operations/test_maximal_score.py
diff --git a/puzzles/heap/maximum_subsequence_score/README.md b/algorithms/heap/maximum_subsequence_score/README.md
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rename to algorithms/heap/min_cost_hire_k_workers/__init__.py
diff --git a/puzzles/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py b/algorithms/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py
similarity index 100%
rename from puzzles/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py
rename to algorithms/heap/min_cost_hire_k_workers/test_min_cost_to_hire_workers.py
diff --git a/puzzles/heap/min_cost_to_connect_sticks/README.md b/algorithms/heap/min_cost_to_connect_sticks/README.md
similarity index 70%
rename from puzzles/heap/min_cost_to_connect_sticks/README.md
rename to algorithms/heap/min_cost_to_connect_sticks/README.md
index a13d3acf..4ecdbc50 100644
--- a/puzzles/heap/min_cost_to_connect_sticks/README.md
+++ b/algorithms/heap/min_cost_to_connect_sticks/README.md
@@ -16,7 +16,7 @@ Constraints:
 
 ## Examples
 
-![Example 1](./images/examples/min_cost_to_connect_sticks_1.png)
-![Example 2](./images/examples/min_cost_to_connect_sticks_2.png)
-![Example 3](./images/examples/min_cost_to_connect_sticks_3.png)
-![Example 4](./images/examples/min_cost_to_connect_sticks_4.png)
+![Example 1](images/examples/min_cost_to_connect_sticks_1.png)
+![Example 2](images/examples/min_cost_to_connect_sticks_2.png)
+![Example 3](images/examples/min_cost_to_connect_sticks_3.png)
+![Example 4](images/examples/min_cost_to_connect_sticks_4.png)
diff --git a/puzzles/heap/min_cost_to_connect_sticks/__init__.py b/algorithms/heap/min_cost_to_connect_sticks/__init__.py
similarity index 100%
rename from puzzles/heap/min_cost_to_connect_sticks/__init__.py
rename to algorithms/heap/min_cost_to_connect_sticks/__init__.py
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rename from puzzles/heap/min_cost_to_connect_sticks/images/examples/min_cost_to_connect_sticks_1.png
rename to algorithms/heap/min_cost_to_connect_sticks/images/examples/min_cost_to_connect_sticks_1.png
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rename from puzzles/heap/min_cost_to_connect_sticks/images/examples/min_cost_to_connect_sticks_2.png
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rename from puzzles/heap/min_cost_to_connect_sticks/images/examples/min_cost_to_connect_sticks_4.png
rename to algorithms/heap/min_cost_to_connect_sticks/images/examples/min_cost_to_connect_sticks_4.png
diff --git a/puzzles/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py b/algorithms/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py
similarity index 100%
rename from puzzles/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py
rename to algorithms/heap/min_cost_to_connect_sticks/test_min_cost_connect_sticks.py
diff --git a/algorithms/heap/topkclosesttoorigin/README.md b/algorithms/heap/topkclosesttoorigin/README.md
new file mode 100644
index 00000000..4fd707d0
--- /dev/null
+++ b/algorithms/heap/topkclosesttoorigin/README.md
@@ -0,0 +1,104 @@
+# K Closest Points to Origin
+
+Given a list of points in the form [[x1, y1], [x2, y2], ... [xn, yn]] and an integer k, find the k closest points to the
+origin (0, 0) on the 2D plane.
+
+The distance between two points (x, y) and (a, b) is calculated using the formula:
+
+√(x1 - a2)2 + (y1 - b2)2
+
+Return the k closest points in any order.
+
+## Examples
+
+```text
+Input:
+
+points = [[3,4],[2,2],[1,1],[0,0],[5,5]]
+k = 3
+
+Output:
+[[2,2],[1,1],[0,0]]
+
+Also Valid:
+
+[[2,2],[0,0],[1,1]]
+[[1,1],[0,0],[2,2]]
+[[1,1],[2,2],[0,0]]
+...
+[[0,0],[1,1],[2,2]]
+```
+
+![Example 1](./images/examples/top_k_closest_to_origin_example_1.png)
+
+```text
+Input: points = [[3,3],[5,-1],[-2,4]], k = 2
+Output: [[3,3],[-2,4]]
+Explanation: The answer [[-2,4],[3,3]] would also be accepted.
+```
+
+```text
+Input: points = [[1,3],[-2,2]], k = 1
+Output: [[-2,2]]
+
+Explanation:
+The distance between (1, 3) and the origin is sqrt(10).
+The distance between (-2, 2) and the origin is sqrt(8).
+Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin.
+We only want the closest k = 1 points from the origin, so the answer is just [[-2,2]].
+```
+
+## Solution
+
+- [Approach 1](#approach-1-sorting)
+- [Approach 2](#approach-2-max-heap)
+
+### Approach 1: Sorting
+
+The simplest approach is to sort calculate the distance of each point from the origin and sort the points based on their
+distance. This approach has a time complexity of O(n log n) where n is the number of points in the array, and a space
+complexity of O(n) (to store the sorted array of distances).
+
+### Approach 2: Max Heap
+
+This problem can be solved using a similar approach to the one used to solve [Kth Largest Element in an Array](../topklargest/README.md). The key
+difference is that we need to store the k closest points to the origin, rather than the k largest elements. Since we are
+looking for the k smallest elements, we need a max-heap, rather than a min-heap.
+
+By default, python's heapq module implements a min-heap, but we can make it behave like a max-heap by negating the values
+of everything we push onto it.
+
+We add the first k points to the heap by pushing a tuple containing the negative of the distance from the origin, and the
+index of the point. After that is finished, our heap contains the k closest points to the origin that we've seen so far,
+with the point furthest from the origin at the root of the heap.
+
+For each point after the first k, we calculate the distance from the origin and compare it with the root of the heap. If
+the current point is closer to the origin than the root of the heap, we pop the root and push the current point into the
+heap. This way, the heap will always contain the k closest points to the origin we've seen so far.
+
+At the end of the iteration, the heap will contain the k closest points to the origin. We can iterate over each point in
+the heap and return the point associated with each tuple.
+
+![Solution 0](./images/solutions/top_k_closest_to_origin_solution_0.png)
+![Solution 1](./images/solutions/top_k_closest_to_origin_solution_1.png)
+![Solution 2](./images/solutions/top_k_closest_to_origin_solution_2.png)
+![Solution 3](./images/solutions/top_k_closest_to_origin_solution_3.png)
+![Solution 4](./images/solutions/top_k_closest_to_origin_solution_4.png)
+![Solution 5](./images/solutions/top_k_closest_to_origin_solution_5.png)
+![Solution 6](./images/solutions/top_k_closest_to_origin_solution_6.png)
+![Solution 7](./images/solutions/top_k_closest_to_origin_solution_7.png)
+![Solution 8](./images/solutions/top_k_closest_to_origin_solution_8.png)
+![Solution 9](./images/solutions/top_k_closest_to_origin_solution_9.png)
+![Solution 10](./images/solutions/top_k_closest_to_origin_solution_10.png)
+![Solution 11](./images/solutions/top_k_closest_to_origin_solution_11.png)
+
+#### Complexity Analysis
+
+##### Time Complexity: O(n log k)
+
+Where n is the number of points in the array and k is the input parameter. We iterate over
+all points, and in the worst case, we both push and pop each point from the heap, which takes O(log k) time per point.
+
+##### Space Complexity: O(k)
+
+Where k is the input parameter. The space is used by the heap to store the k closest points to the origin.
diff --git a/algorithms/heap/topkclosesttoorigin/__init__.py b/algorithms/heap/topkclosesttoorigin/__init__.py
new file mode 100644
index 00000000..ec62166d
--- /dev/null
+++ b/algorithms/heap/topkclosesttoorigin/__init__.py
@@ -0,0 +1,36 @@
+from typing import List, Tuple
+import heapq
+
+
+def k_closest_to_origin(points: List[List[int]], k: int) -> List[List[int]]:
+    # Max heap will store the top k points closest to the origin in the form (-distance, idx). The distance is negated
+    # because in Python, the heapq module uses min-heap by default. Negating values gives us a maximum heap.
+    # We store the idx of the point for later retrieval from the points array passed in
+    max_heap: List[Tuple[int, int]] = []
+
+    for idx, point in enumerate(points):
+        x, y = point
+        # calculate the distance for this point from the origin
+        distance = x * x + y * y
+
+        # If the contents of the heap are less than the desired top k, then we add the current point's distance and idx
+        if len(max_heap) < k:
+            heapq.heappush(max_heap, (-distance, idx))
+        # We check if the calculated distance of this point is less than the top element in the heap. If this point
+        # is closer to the origin that what is at the root of the heap, we pop the root of the heap and add this
+        # new distance and index.
+        # Note the negation here again to get the actual distance
+        elif distance < -max_heap[0][0]:
+            heapq.heappushpop(max_heap, (-distance, idx))
+
+    # Return the top k points closest to origin. We use 1 to get the index of the point from the original points list
+    # as that is what is stored in the max heap
+    return [points[point[1]] for point in max_heap]
+
+
+def k_closest_to_origin_sorting(points: List[List[int]], k: int) -> List[List[int]]:
+    # Sort the points by the distance from the origin. This incurs a cost of O(n log(n)) and space cost of O(n) due to
+    # timsort
+    sorted_points = sorted(points, key=lambda p: p[0] ** 2 + p[1] ** 2)
+    # Retrieve the top k points closest to the origin
+    return sorted_points[:k]
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diff --git a/algorithms/heap/topkclosesttoorigin/test_top_k_closest_to_origin.py b/algorithms/heap/topkclosesttoorigin/test_top_k_closest_to_origin.py
new file mode 100644
index 00000000..de979b30
--- /dev/null
+++ b/algorithms/heap/topkclosesttoorigin/test_top_k_closest_to_origin.py
@@ -0,0 +1,39 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.heap.topkclosesttoorigin import (
+    k_closest_to_origin,
+    k_closest_to_origin_sorting,
+)
+
+TOP_K_CLOSEST_TO_ORIGIN = [
+    ([[3, 4], [2, 2], [1, 1], [0, 0], [5, 5]], 3, [[2, 2], [1, 1], [0, 0]]),
+    ([[1, 3], [-2, 2]], 1, [[-2, 2]]),
+    ([[3, 3], [5, -1], [-2, 4]], 2, [[3, 3], [-2, 4]]),
+]
+
+
+class TopKClosestToOriginTestCase(unittest.TestCase):
+    @parameterized.expand(TOP_K_CLOSEST_TO_ORIGIN)
+    def test_top_k_closest_to_origin(
+        self, points: List[List[int]], k: int, expected: List[List[int]]
+    ):
+        actual = k_closest_to_origin(points, k)
+
+        sorted_expected = sorted(expected, key=lambda x: (x[0], x[1]))
+        sorted_actual = sorted(actual, key=lambda x: (x[0], x[1]))
+        self.assertEqual(sorted_expected, sorted_actual)
+
+    @parameterized.expand(TOP_K_CLOSEST_TO_ORIGIN)
+    def test_top_k_closest_to_origin_sorting(
+        self, points: List[List[int]], k: int, expected: List[List[int]]
+    ):
+        actual = k_closest_to_origin_sorting(points, k)
+
+        sorted_expected = sorted(expected, key=lambda x: x[0])
+        sorted_actual = sorted(actual, key=lambda x: x[0])
+        self.assertEqual(sorted_expected, sorted_actual)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/pymath/topkfrequentelements/README.md b/algorithms/heap/topkfrequentelements/README.md
similarity index 100%
rename from pymath/topkfrequentelements/README.md
rename to algorithms/heap/topkfrequentelements/README.md
diff --git a/pymath/topkfrequentelements/__init__.py b/algorithms/heap/topkfrequentelements/__init__.py
similarity index 100%
rename from pymath/topkfrequentelements/__init__.py
rename to algorithms/heap/topkfrequentelements/__init__.py
diff --git a/algorithms/heap/topklargest/README.md b/algorithms/heap/topklargest/README.md
new file mode 100644
index 00000000..aa97298e
--- /dev/null
+++ b/algorithms/heap/topklargest/README.md
@@ -0,0 +1,106 @@
+# Top-K Largest Elements in an Array
+
+Given an integer array nums, return the 3 largest elements in the array in any order.
+
+## Example
+
+```text
+Input: nums = [9, 3, 7, 1, -2, 6, 8]
+Output: [8, 7, 9]
+# or [7, 9, 8] or [9, 7, 8] ...
+```
+
+## Solution
+
+Here's how we can solve this problem using a min-heap:
+
+- Create a min-heap that stores the first 3 elements of the array. These represent the 3 largest elements we have seen so 
+  far, with the smallest of the 3 at the root of the heap.
+  ![Solution 1](./images/solutions/top_k_largest_element_in_array_solution_1.png)
+
+- Iterate through the remaining elements in the array.
+  - If the current element is larger than the root of the heap, pop the root and push the current element into the heap.
+  - Otherwise, continue to the next element.
+  
+  ![Solution 2](./images/solutions/top_k_largest_element_in_array_solution_2.png)
+  ![Solution 3](./images/solutions/top_k_largest_element_in_array_solution_3.png)
+  ![Solution 4](./images/solutions/top_k_largest_element_in_array_solution_4.png)
+  ![Solution 5](./images/solutions/top_k_largest_element_in_array_solution_5.png)
+
+After iterating through all the elements, the heap contains the 3 largest elements in the array.
+
+### Complexity Analysis
+
+#### Time Complexity Breakdown
+
+- The heapify function takes O(3) = O(1) time
+- We iterate through all elements in the array once: O(n) time
+- The heappop and heappush operations take O(log 3) = O(1) time each
+
+#### Space Complexity
+
+- We use a heap of size 3 to store the 3 largest elements: O(3) = O(1) space 
+- The algorithm uses constant space regardless of input size
+
+Note: The time and space complexity become more interesting when 3 is a variable number k.
+
+---
+
+# Kth Largest Element in an Array
+
+Write a function that takes an array of unsorted integers nums and an integer k, and returns the kth largest element in
+the array. This function should run in O(n log k) time, where n is the length of the array.
+
+## Examples
+
+```text
+Input:
+nums = [5, 3, 2, 1, 4]
+k = 2
+
+Output: 4
+```
+
+## Solutions
+
+- [Approach 1](#approach-1-sorting)
+- [Approach 2](#approach-2-min-heap)
+
+### Approach 1: Sorting
+
+The simplest approach is to sort the array in descending order and return the kth element. This approach has a time 
+complexity of O(n log n) where n is the number of elements in the array, and a space complexity of O(1).
+
+### Approach 2: Min Heap
+
+By using a min-heap, we can reduce the time complexity to O(n log k), where n is the number of elements in the array and
+k is the value of k.
+The idea behind this solution is to iterate over the elements in the array while storing the k largest elements we've
+seen so far in a min-heap. At each element, we check if it is greater than the smallest element (the root) of the heap.
+If it is, we pop the smallest element from the heap and push the current element into the heap. This way, the heap will
+always contain the k largest elements we've seen so far.
+After iterating over all the elements, the root of the heap will be the kth largest element in the array.
+
+![Solution 2.1](./images/solutions/kth_largest_element_in_array_solution_1.png)
+![Solution 2.2](./images/solutions/kth_largest_element_in_array_solution_2.png)
+![Solution 2.3](./images/solutions/kth_largest_element_in_array_solution_3.png)
+![Solution 2.4](./images/solutions/kth_largest_element_in_array_solution_4.png)
+![Solution 2.5](./images/solutions/kth_largest_element_in_array_solution_5.png)
+![Solution 2.6](./images/solutions/kth_largest_element_in_array_solution_6.png)
+![Solution 2.7](./images/solutions/kth_largest_element_in_array_solution_7.png)
+![Solution 2.8](./images/solutions/kth_largest_element_in_array_solution_8.png)
+![Solution 2.9](./images/solutions/kth_largest_element_in_array_solution_9.png)
+![Solution 2.10](./images/solutions/kth_largest_element_in_array_solution_10.png)
+![Solution 2.11](./images/solutions/kth_largest_element_in_array_solution_11.png)
+
+#### Complexity Analysis
+
+##### Time Complexity: O(n log k)
+
+Where n is the number of elements in the array and k is the input parameter. We iterate over
+all elements, and in the worst case, we both push and pop each element from the heap, which takes O(log k) time per
+element.
+
+##### Space Complexity: O(k)
+
+Where k is the input parameter. The space is used by the heap to store the k largest elements.
diff --git a/algorithms/heap/topklargest/__init__.py b/algorithms/heap/topklargest/__init__.py
new file mode 100644
index 00000000..abc4dddd
--- /dev/null
+++ b/algorithms/heap/topklargest/__init__.py
@@ -0,0 +1,83 @@
+from typing import List
+import heapq
+
+
+def k_largest(nums: List[int], k: int = 3) -> List[int]:
+    """
+    Finds the k largest elements in a given list. K is defaulted to three, but can be used to tweak the k largest
+     elements in the array
+    Args:
+        nums(list): list of elements to check for
+        k(int): number of elements to check, defaulted to 3
+    Returns:
+        list: top k largest elements
+    """
+    # input validation to ensure we don't get unexpected results
+    if not nums or k <= 0:
+        return []
+
+    # Adjust k if it exceeds the length of nums
+    k = min(k, len(nums))
+
+    # create a minimum heap with the first k elements
+    min_heap = nums[:k]
+    heapq.heapify(min_heap)
+
+    # iterate through the remaining elements
+    for num in nums[k:]:
+        # if the current number is greater than the element at the top of the heap
+        if num > min_heap[0]:
+            # Remove it and add this element
+            heapq.heappushpop(min_heap, num)
+
+    # return the top k elements
+    return min_heap
+
+
+def kth_largest(nums: List[int], k: int) -> int:
+    """
+    Finds the kth largest element in a given list
+    Args:
+        nums(list): list of elements to check for
+        k(int): the kth largest element to return
+    Returns:
+        int: the kth largest element
+    """
+    # input validation to ensure we don't get unexpected results
+    if not nums or k <= 0 or k > len(nums):
+        return -1
+
+    # create a minimum heap with the first k elements
+    min_heap = []
+
+    # iterate through the remaining elements
+    for num in nums:
+        if len(min_heap) < k:
+            heapq.heappush(min_heap, num)
+        # if the current number is greater than the element at the top of the heap
+        elif num > min_heap[0]:
+            # Remove it and add this element
+            heapq.heappushpop(min_heap, num)
+
+    # return the top kth element
+    return min_heap[0]
+
+
+def kth_largest_sorting(nums: List[int], k: int) -> int:
+    """
+    Finds the kth largest element in a given list using sorting
+    Args:
+        nums(list): list of elements to check for
+        k(int): the kth largest element to return
+    Returns:
+        int: the kth largest element
+    """
+    # input validation to ensure we don't get unexpected results
+    if not nums or k <= 0 or k > len(nums):
+        return -1
+
+    # Sort the list which incurs a time complexity cost of O(n log(n)). Space complexity is O(n) due to creating
+    # a new sorted list
+    sorted_nums = sorted(nums, reverse=True)
+    # Return the kth largest element
+    return sorted_nums[k - 1]
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diff --git a/algorithms/heap/topklargest/test_top_k_largest_elements.py b/algorithms/heap/topklargest/test_top_k_largest_elements.py
new file mode 100644
index 00000000..1bc6b48c
--- /dev/null
+++ b/algorithms/heap/topklargest/test_top_k_largest_elements.py
@@ -0,0 +1,45 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.heap.topklargest import k_largest, kth_largest, kth_largest_sorting
+
+K_LARGEST_ELEMENTS_TEST_CASES = [
+    ([9, 3, 7, 1, -2, 6, 8], 3, [8, 7, 9]),
+    ([5, 3, 2, 1, 4], 2, [5, 4]),
+]
+
+
+class TopKLargestElementsTestCase(unittest.TestCase):
+    @parameterized.expand(K_LARGEST_ELEMENTS_TEST_CASES)
+    def test_top_k_largest_elements(self, nums: List[int], k: int, expected: List[int]):
+        actual = k_largest(nums, k)
+        self.assertListEqual(sorted(expected), sorted(actual))
+
+
+KTH_LARGEST_ELEMENTS_TEST_CASES = [
+    ([3, 2, 1, 5, 6, 4], 2, 5),
+    ([3, 2, 3, 1, 2, 4, 5, 5, 6], 4, 4),
+    ([1], 1, 1),
+    ([7, 10, 4, 3, 20, 15], 3, 10),
+    ([7, 10, 4, 3, 20, 15], 4, 7),
+    ([7, 10, 4, 3, 20, 15], 5, 4),
+    ([5, 3, 2, 1, 4], 2, 4),
+]
+
+
+class TopKthLargestElementsTestCase(unittest.TestCase):
+    @parameterized.expand(KTH_LARGEST_ELEMENTS_TEST_CASES)
+    def test_top_kth_largest_element(self, nums: List[int], k: int, expected: int):
+        actual = kth_largest(nums, k)
+        self.assertEqual(expected, actual)
+
+    @parameterized.expand(KTH_LARGEST_ELEMENTS_TEST_CASES)
+    def test_top_kth_largest_element_sorting(
+        self, nums: List[int], k: int, expected: int
+    ):
+        actual = kth_largest_sorting(nums, k)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/puzzles/heap/total_cost_hire_k_workers/README.md b/algorithms/heap/total_cost_hire_k_workers/README.md
similarity index 96%
rename from puzzles/heap/total_cost_hire_k_workers/README.md
rename to algorithms/heap/total_cost_hire_k_workers/README.md
index 5d9d5786..a1bcd485 100644
--- a/puzzles/heap/total_cost_hire_k_workers/README.md
+++ b/algorithms/heap/total_cost_hire_k_workers/README.md
@@ -58,32 +58,32 @@ worker, a spot will open up for another worker to be among the first or last m c
 distinguish between the first m candidates and the last m candidates. That way, when we choose a worker, we know if a
 spot was opened in the first m candidates or the last m candidates.
 
-![Step 1](./total_cost_hire_k_workers_step_1.png)
+![Step 1](total_cost_hire_k_workers_step_1.png)
 
 To store the workers in two sections separately, we can use two priority queues, head_workers and tail_workers, where
 the worker with the lowest cost has the highest priority.
 
-![Step 2](./total_cost_hire_k_workers_step_2.png)
+![Step 2](total_cost_hire_k_workers_step_2.png)
 
 Throughout the process, after we hire a worker from a section, we need to add an additional candidate to this section.
 Therefore, we need two pointers, next_head and next_tail, that denotes the next worker to be added to the respective
 queues.
 
-![Step 3](./total_cost_hire_k_workers_step_3.png)
+![Step 3](total_cost_hire_k_workers_step_3.png)
 
 Just like in this situation shown in the picture, if two workers with the same cost appear at the top of both queues, we
 will hire the one from head_workers, since this worker has a smaller index compared with the other one from
 tail_workers. Afterwards, we need to refill head_workers with the worker at next_head to ensure that it still contains
 the first m unselected candidates.
 
-![Step 4](./total_cost_hire_k_workers_step_4.png)
+![Step 4](total_cost_hire_k_workers_step_4.png)
 
 However, if we encounter the condition next_tail < next_head, it indicates that all the workers have been selected as
 candidates and there are no more workers outside the two queues. To avoid double counting, we should not add a worker to
 both queues or update either pointer. Therefore, we can simply move on without making any updates to the queues or
 pointers.
 
-![Step 5](./total_cost_hire_k_workers_step_5.png)
+![Step 5](total_cost_hire_k_workers_step_5.png)
 
 #### Algorithm
 
diff --git a/puzzles/heap/total_cost_hire_k_workers/__init__.py b/algorithms/heap/total_cost_hire_k_workers/__init__.py
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/__init__.py
rename to algorithms/heap/total_cost_hire_k_workers/__init__.py
diff --git a/puzzles/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py b/algorithms/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py
rename to algorithms/heap/total_cost_hire_k_workers/test_total_cost_hire_k_workers.py
diff --git a/puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_1.png b/algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_1.png
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_1.png
rename to algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_1.png
diff --git a/puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_2.png b/algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_2.png
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_2.png
rename to algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_2.png
diff --git a/puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_3.png b/algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_3.png
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_3.png
rename to algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_3.png
diff --git a/puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_4.png b/algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_4.png
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_4.png
rename to algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_4.png
diff --git a/puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_5.png b/algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_5.png
similarity index 100%
rename from puzzles/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_5.png
rename to algorithms/heap/total_cost_hire_k_workers/total_cost_hire_k_workers_step_5.png
diff --git a/algorithms/matrix/__init__.py b/algorithms/matrix/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/algorithms/matrix/isvalidsudoku/README.md b/algorithms/matrix/isvalidsudoku/README.md
new file mode 100644
index 00000000..fbb1f73a
--- /dev/null
+++ b/algorithms/matrix/isvalidsudoku/README.md
@@ -0,0 +1,99 @@
+# Valid Sudoku
+
+Given a 9 × 9 Sudoku board, determine whether it is valid. A board is considered valid if all of the following conditions
+hold (considering only the filled cells):
+
+- Each row contains the digits 1–9 at most once. 
+- Each column contains the digits 1–9 at most once. 
+- Each of the nine 3 × 3 sub-boxes contains the digits 1–9 at most once.
+
+You do not need to check whether the Sudoku is solvable; only whether the current filled entries obey these rules.
+
+> Note:A partially filled Sudoku board can be valid even if it is not necessarily solvable. You only need to verify that
+> the filled cells adhere to the given rules.
+
+## Constraints
+
+- `board.length` == 9
+- `board[i].length` == 9
+- `board[i][j]` is a digit or a `.`
+
+## Examples
+
+![Example 1](images/examples/is_valid_sudoku_example_1.png)
+![Example 2](images/examples/is_valid_sudoku_example_2.png)
+![Example 3](images/examples/is_valid_sudoku_example_3.png)
+
+## Solution
+
+The intuition behind this solution is simple: instead of trying to solve the Sudoku or perform any form of search or
+backtracking, we treat the board as a constraint-checking problem. As we scan the board once, cell by cell, we ensure
+that every filled digit obeys the Sudoku rules, which require no repetition in its row, column, or 3×3 sub-box. To do
+this efficiently, we maintain three arrays of hash sets:
+
+- row_sets[9]: Tracks digits seen in each row.
+- col_sets[9]: Tracks digits seen in each column.
+- box_sets[9]: Tracks digits seen in each 3×3 sub-box.
+
+Each set keeps track of the digits that have already appeared in that specific region. For every filled cell, if the
+digit is already in its row, column, or sub-box set, then we’ve detected a rule violation, and the board is invalid. If
+we finish scanning all 81 cells without encountering duplicates, the board is valid. This transforms the problem into a
+clean, single-pass constraint check, eliminating the need for any kind of search or backtracking.
+
+Using the intuition above, we implement the algorithm as follows:
+- Initialize an empty array, `row_sets`, to track digits in each row.
+- Initialize an empty array, `col_sets`, to track digits in each column. 
+- Initialize an empty array, `box_sets`, to track digits in each 3×3 sub-box. 
+- Use an outer loop to iterate through rows.
+  - Use an inner loop to iterate through columns.
+  - Retrieve the value present at the current rows and columns of the board: `cell = board[r][c].`
+    - If `cell` is a .,
+      - Skip this value
+    - Compute the index of the 3×3 sub-box that contains the current cell using: `(r // 3) * 3 + (c // 3)`.
+    - Check whether `cell` is already present in the corresponding row, column, or box set.
+      - If it is, return False
+    - If no duplicate is found, we insert `cell` into:
+      - `row_set[r]`, 
+      - `col_set[c]`, 
+      - `box_set[box_idx]`.
+- If all cells are processed without conflicts, return TRUE, indicating that the given Sudoku board is valid.
+
+![Example 1](images/solutions/is_valid_sudoku_solution_1.png)
+![Example 2](images/solutions/is_valid_sudoku_solution_2.png)
+![Example 3](images/solutions/is_valid_sudoku_solution_3.png)
+![Example 4](images/solutions/is_valid_sudoku_solution_4.png)
+![Example 5](images/solutions/is_valid_sudoku_solution_5.png)
+![Example 6](images/solutions/is_valid_sudoku_solution_6.png)
+![Example 7](images/solutions/is_valid_sudoku_solution_7.png)
+![Example 8](images/solutions/is_valid_sudoku_solution_8.png)
+![Example 9](images/solutions/is_valid_sudoku_solution_9.png)
+![Example 10](images/solutions/is_valid_sudoku_solution_10.png)
+![Example 11](images/solutions/is_valid_sudoku_solution_11.png)
+![Example 12](images/solutions/is_valid_sudoku_solution_12.png)
+
+### Complexity
+
+#### Time
+
+The time complexity of this algorithm is constant, O(1).
+
+Although we iterate through all 81 cells of a 9×9 Sudoku board, the board size is fixed. In each cell, we perform
+constant-time operations:
+
+- Hash set lookups
+- Hash set insertions 
+- Simple arithmetic for computing the box index
+
+As 81 operations are a fixed constant, the overall runtime is O(1) in terms of theoretical complexity.
+
+#### Space
+
+The space complexity of this algorithm is constant, O(1). This is because we create:
+
+- 9 row sets 
+- 9 column sets 
+- 9 box sets
+
+Each can contain at most 9 digits, so a constant amount of memory bounds the total storage.
+
+Total extra space = 27 sets * max 9 values = 243, which is a constant number. So, the space complexity is O(1).
diff --git a/algorithms/matrix/isvalidsudoku/__init__.py b/algorithms/matrix/isvalidsudoku/__init__.py
new file mode 100644
index 00000000..bef563a2
--- /dev/null
+++ b/algorithms/matrix/isvalidsudoku/__init__.py
@@ -0,0 +1,55 @@
+from typing import List, Set
+
+
+def is_valid_sudoku(board: List[List[str]]) -> bool:
+    """
+    Checks if a given sudoku board is a valid sudoku board. This does not check if the board is solvable. If the board
+    is valid, it returns True, if not returns False. The board is a 9x9 grid with 3x3 cells. Each row only contains
+    digits from 1-9, and each column contains digits from 1-9 repeated once. Each 3x3 cell only contains digits from 1-9
+    repeated once
+    Args:
+        board(list): A 2D grid representing a sudoku board
+    Returns:
+        bool: True if the board provided is valid, False otherwise
+    """
+    # Handles edge cases to check if the board is of length 9
+    if len(board) != 9:
+        return False
+
+    # Validate each row has exactly 9 columns
+    if any(len(row) != 9 for row in board):
+        return False
+
+    number_of_rows = len(board)
+    number_of_columns = len(board[0])
+    row_sets: List[Set[str]] = [set() for _ in range(number_of_rows)]
+    col_sets: List[Set[str]] = [set() for _ in range(number_of_columns)]
+    box_sets: List[Set[str]] = [set() for _ in range(number_of_rows)]
+
+    for row in range(number_of_rows):
+        for col in range(number_of_columns):
+            cell = board[row][col]
+            # if the cell is empty, contains a '.', we don't need to check if, we can skip and continue to the next
+            # iteration
+            if cell == ".":
+                continue
+
+            # Identifying a cell within a sub-box can be found using the formula: i = (r//3)*3+(c//3) where r is the row number
+            # and c is the column number all indexed from 0
+            # The box_idx identifies the box this cell is in
+            box_idx = (row // 3) * 3 + (col // 3)
+
+            # Check if we have seen the digit before in the row, column or the box
+            if (
+                cell in row_sets[row]
+                or cell in col_sets[col]
+                or cell in box_sets[box_idx]
+            ):
+                return False
+
+            # if not there, we add it to the row, column and sub box sets
+            row_sets[row].add(cell)
+            col_sets[col].add(cell)
+            box_sets[box_idx].add(cell)
+
+    return True
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diff --git a/algorithms/matrix/isvalidsudoku/test_is_valid_sudoku.py b/algorithms/matrix/isvalidsudoku/test_is_valid_sudoku.py
new file mode 100644
index 00000000..73664b23
--- /dev/null
+++ b/algorithms/matrix/isvalidsudoku/test_is_valid_sudoku.py
@@ -0,0 +1,88 @@
+import unittest
+from typing import List
+from parameterized import parameterized
+from algorithms.matrix.isvalidsudoku import is_valid_sudoku
+
+IS_VALID_SUDOKU_TEST_CASES = [
+    (
+        [
+            [".", ".", ".", ".", ".", ".", ".", "7", "."],
+            ["2", "7", "5", ".", ".", ".", "3", "1", "4"],
+            [".", ".", ".", ".", "2", "7", ".", "5", "."],
+            ["9", "8", ".", ".", ".", ".", ".", "3", "1"],
+            [".", "3", "1", "8", ".", "4", ".", ".", "."],
+            [".", ".", ".", "1", ".", ".", "8", ".", "5"],
+            ["7", ".", "6", "2", ".", ".", "1", "8", "."],
+            [".", "9", ".", "7", ".", ".", ".", ".", "."],
+            ["4", "1", ".", ".", ".", "5", ".", ".", "7"],
+        ],
+        True,
+    ),
+    (
+        [
+            ["5", "3", "3", "6", "7", "8", "9", "1", "2"],
+            ["6", "7", "2", "1", "9", "5", "3", "4", "8"],
+            ["1", "9", "8", "3", "4", "2", "5", "6", "7"],
+            ["8", "5", "9", "7", "6", "1", "4", "2", "3"],
+            ["4", "2", "6", "8", "5", "3", "7", "9", "1"],
+            ["7", "1", "3", "9", "2", "4", "8", "5", "6"],
+            ["9", "6", "1", "5", "3", "7", "2", "8", "4"],
+            ["2", "8", "7", "4", "1", "9", "6", "3", "5"],
+            ["3", "4", "5", "2", "8", "6", "1", "7", "9"],
+        ],
+        False,
+    ),
+    (
+        [
+            ["6", "4", "5", "9", "8", "2", "1", "3", "7"],
+            ["7", "2", "8", "3", "1", "6", "5", "9", "4"],
+            ["3", "9", "1", "5", "4", "7", "6", "8", "2"],
+            ["9", "8", "7", "1", "5", "3", "4", "2", "6"],
+            ["4", "1", "6", "2", "7", "9", "8", "5", "3"],
+            ["5", "3", "2", "8", "6", "4", "7", "1", "9"],
+            ["8", "7", "3", "6", "9", "5", "2", "4", "1"],
+            ["2", "5", "4", "7", "3", "1", "9", "6", "8"],
+            ["1", "6", "9", "4", "2", "8", "3", "7", "5"],
+        ],
+        True,
+    ),
+    (
+        [
+            ["6", "3", "9", "4", "2", "5", "7", "1", "8"],
+            ["6", "4", "8", "1", "3", "7", "9", "6", "5"],
+            ["5", "7", "1", "9", "6", "8", "3", "4", "2"],
+            ["1", "6", "2", "7", "5", "4", "8", "3", "9"],
+            ["4", "8", "3", "6", "9", "2", "5", "7", "1"],
+            ["9", "5", "7", "3", "8", "1", "6", "2", "4"],
+            ["8", "2", "6", "5", "4", "3", "1", "9", "7"],
+            ["3", "1", "5", "2", "7", "9", "4", "8", "6"],
+            ["7", "9", "4", "8", "1", "6", "2", "5", "3"],
+        ],
+        False,
+    ),
+    (
+        [
+            ["5", "3", ".", ".", "7", ".", ".", ".", "."],
+            ["6", ".", ".", "1", "9", "5", ".", ".", "."],
+            [".", "9", "8", ".", ".", ".", ".", "6", "."],
+            ["8", ".", ".", ".", "6", ".", ".", ".", "3"],
+            ["4", ".", ".", "8", ".", "3", ".", ".", "1"],
+            ["7", ".", ".", ".", "2", ".", ".", ".", "6"],
+            [".", "6", ".", ".", ".", ".", "2", "8", "."],
+            [".", ".", ".", "4", "1", "9", ".", ".", "5"],
+            [".", ".", ".", ".", "8", ".", ".", "7", "9"],
+        ],
+        True,
+    ),
+]
+
+
+class IsValidSudokuTestCase(unittest.TestCase):
+    @parameterized.expand(IS_VALID_SUDOKU_TEST_CASES)
+    def test_is_valid_sudoku(self, board: List[List[str]], expected: bool):
+        actual = is_valid_sudoku(board)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == "__main__":
+    unittest.main()