From e14e0fb92fa1b10c769090dd64d0a20e5be847d2 Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Wed, 7 Jun 2023 21:43:12 +0000
Subject: [PATCH 01/20] updating DIRECTORY.md

---
 DIRECTORY.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 231b0e2f1d2f..e28f2697136e 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -419,8 +419,9 @@
   * [Frequent Pattern Graph Miner](graphs/frequent_pattern_graph_miner.py)
   * [G Topological Sort](graphs/g_topological_sort.py)
   * [Gale Shapley Bigraph](graphs/gale_shapley_bigraph.py)
+  * [Graph Adjacency List](graphs/graph_adjacency_list.py)
+  * [Graph Adjacency Matrix](graphs/graph_adjacency_matrix.py)
   * [Graph List](graphs/graph_list.py)
-  * [Graph Matrix](graphs/graph_matrix.py)
   * [Graphs Floyd Warshall](graphs/graphs_floyd_warshall.py)
   * [Greedy Best First](graphs/greedy_best_first.py)
   * [Greedy Min Vertex Cover](graphs/greedy_min_vertex_cover.py)
@@ -479,6 +480,7 @@
     * [Lib](linear_algebra/src/lib.py)
     * [Polynom For Points](linear_algebra/src/polynom_for_points.py)
     * [Power Iteration](linear_algebra/src/power_iteration.py)
+    * [Rank Of Matrix](linear_algebra/src/rank_of_matrix.py)
     * [Rayleigh Quotient](linear_algebra/src/rayleigh_quotient.py)
     * [Schur Complement](linear_algebra/src/schur_complement.py)
     * [Test Linear Algebra](linear_algebra/src/test_linear_algebra.py)
@@ -651,6 +653,7 @@
   * [Sigmoid Linear Unit](maths/sigmoid_linear_unit.py)
   * [Signum](maths/signum.py)
   * [Simpson Rule](maths/simpson_rule.py)
+  * [Simultaneous Linear Equation Solver](maths/simultaneous_linear_equation_solver.py)
   * [Sin](maths/sin.py)
   * [Sock Merchant](maths/sock_merchant.py)
   * [Softmax](maths/softmax.py)

From 05e435f05986f756b5b9b909e5de137b15170893 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:11:01 +0100
Subject: [PATCH 02/20] feat: Count negative numbers in sorted matrix

---
 ...count_negative_numbers_in_sorted_matrix.py | 183 ++++++++++++++++++
 1 file changed, 183 insertions(+)
 create mode 100644 matrix/count_negative_numbers_in_sorted_matrix.py

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
new file mode 100644
index 000000000000..c660cc36cb3d
--- /dev/null
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -0,0 +1,183 @@
+"""
+Given an `m x n` matrix grid which is sorted in non-increasing order
+both row-wise and column-wise, return the number of negative numbers in grid.
+
+> https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
+"""
+
+
+def find_negative_index(array: list[int]):
+    """
+    Find the smallest negative index
+
+    >>> find_negative_index([0,0,0,0])
+    4
+    >>> find_negative_index([4,3,2,-1])
+    3
+    >>> find_negative_index([1,0,-1,-10])
+    2
+    >>> find_negative_index([0,0,0,-1])
+    3
+    >>> find_negative_index([11,8,7,-3,-5,-9])
+    3
+    >>> find_negative_index([-1,-1,-2,-3])
+    0
+    >>> find_negative_index([5,1,0])
+    3
+    >>> find_negative_index([-5,-5,-5])
+    0
+    >>> find_negative_index([0])
+    1
+    >>> find_negative_index([])
+    0
+    """
+    left = 0
+    right = len(array) - 1
+
+    # Edge cases such as no values or
+    # all numbers are negative
+    if not array or array[0] < 0:
+        return 0
+
+    while right + 1 > left:
+        mid = (left + right) // 2
+        num = array[mid]
+
+        # Num must be negative and the index about num
+        # must be greater than or equal to 0
+        if num < 0 and array[mid - 1] >= 0:
+            return mid
+
+        if num >= 0:
+            left = mid + 1
+        else:
+            right = mid - 1
+    # No negative numbers so return the last index
+    # of the array + 1 which is also the length
+    return len(array)
+
+
+def count_negatives_binary_search(grid: list[list[int]]) -> int:
+    """
+    An O(m logn) solution that uses binary search
+    in order to find the boundary betweem positive and
+    negative numbers
+
+    >>> count_negatives_binary_search(
+    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
+    8
+    >>> count_negatives_binary_search([[3,2],[1,0]])
+    0
+    >>> count_negatives_binary_search([[7,7,6]])
+    0
+    >>> count_negatives_binary_search([[7,7,6],[-1,-2,-3]])
+    3
+    """
+    total = 0
+    bound = len(grid[0])
+
+    for i in range(len(grid)):
+        bound = find_negative_index(grid[i][:bound])
+        total += bound
+    return (len(grid) * len(grid[0])) - total
+
+
+def count_negatives_brute_force(grid: list[list[int]]) -> int:
+    """
+    This solution is O(n^2) because it iterates through
+    every column and row.
+
+    >>> count_negatives_brute_force(
+    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
+    8
+    >>> count_negatives_brute_force([[3,2],[1,0]])
+    0
+    >>> count_negatives_brute_force([[7,7,6]])
+    0
+    >>> count_negatives_brute_force([[7,7,6],[-1,-2,-3]])
+    3
+    """
+    total = 0
+    for m in range(len(grid)):
+        for n in range(len(grid[m])):
+            if grid[m][n] < 0:
+                total += 1
+    return total
+
+
+def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
+    """
+    Similiar to the solution above, however uses break
+    in order to reduce the number of iterations
+
+    >>> count_negatives_brute_force_with_break(
+    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
+    8
+    >>> count_negatives_brute_force_with_break([[3,2],[1,0]])
+    0
+    >>> count_negatives_brute_force_with_break([[7,7,6]])
+    0
+    >>> count_negatives_brute_force_with_break([[7,7,6],[-1,-2,-3]])
+    3
+    """
+    total = 0
+    length_of_n = len(grid[0])
+    for m in range(len(grid)):
+        for index, n in enumerate(range(length_of_n)):
+            if grid[m][n] < 0:
+                total += length_of_n - index
+                break
+    return total
+
+
+def generate_large_matrix() -> list[list[int]]:
+    """
+    >>> generate_large_matrix() # doctest: +ELLIPSIS
+    [[500, ..., -499], [499, ..., -501], ..., [2, ..., -998]]
+    """
+    return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
+
+
+def benchmark() -> None:
+    """Benchmark our functions next to each other"""
+    from timeit import timeit
+
+    print("Running benchmarks")
+    setup = (
+        "from __main__ import count_negatives_binary_search, count_negatives_brute_force, "
+        "count_negatives_brute_force_with_break, generate_large_matrix"
+    )
+
+    cnbs = timeit(
+            "count_negatives_binary_search(generate_large_matrix())",
+            setup=setup,
+            number=5000,
+        ),
+    
+    print("count_negatives_binary_search()", cnbs[0], "seconds")
+    print(
+        "count_negatives_brute_force_with_break()",
+        timeit(
+            "count_negatives_brute_force_with_break(generate_large_matrix())",
+            setup=setup,
+            number=5000,
+        ),
+        "seconds",
+    )  #
+    print(
+        "count_negatives_brute_force()",
+        timeit(
+            "count_negatives_brute_force(generate_large_matrix())",
+            setup=setup,
+            number=5000,
+        ),
+        "seconds",
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    benchmark()

From 83d877c2b69ef8d691d4acc6d9872007f2e47cea Mon Sep 17 00:00:00 2001
From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Date: Thu, 8 Jun 2023 15:12:24 +0000
Subject: [PATCH 03/20] updating DIRECTORY.md

---
 DIRECTORY.md | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/DIRECTORY.md b/DIRECTORY.md
index 6dac4a9a5783..8511c261a3d2 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -679,6 +679,7 @@
 ## Matrix
   * [Binary Search Matrix](matrix/binary_search_matrix.py)
   * [Count Islands In Matrix](matrix/count_islands_in_matrix.py)
+  * [Count Negative Numbers In Sorted Matrix](matrix/count_negative_numbers_in_sorted_matrix.py)
   * [Count Paths](matrix/count_paths.py)
   * [Cramers Rule 2X2](matrix/cramers_rule_2x2.py)
   * [Inverse Of Matrix](matrix/inverse_of_matrix.py)
@@ -753,6 +754,7 @@
   * [Potential Energy](physics/potential_energy.py)
   * [Rms Speed Of Molecule](physics/rms_speed_of_molecule.py)
   * [Shear Stress](physics/shear_stress.py)
+  * [Speed Of Sound](physics/speed_of_sound.py)
 
 ## Project Euler
   * Problem 001

From f0a785cdce908fb588978a561740505740e1f98f Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:26:27 +0100
Subject: [PATCH 04/20] chore: Fix pre-commit

---
 ...count_negative_numbers_in_sorted_matrix.py | 20 ++++++++++---------
 1 file changed, 11 insertions(+), 9 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index c660cc36cb3d..de8f151cafff 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -60,7 +60,7 @@ def find_negative_index(array: list[int]):
 def count_negatives_binary_search(grid: list[list[int]]) -> int:
     """
     An O(m logn) solution that uses binary search
-    in order to find the boundary betweem positive and
+    in order to find the boundary between positive and
     negative numbers
 
     >>> count_negatives_binary_search(
@@ -107,7 +107,7 @@ def count_negatives_brute_force(grid: list[list[int]]) -> int:
 
 def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
     """
-    Similiar to the solution above, however uses break
+    Similar to the solution above, however uses break
     in order to reduce the number of iterations
 
     >>> count_negatives_brute_force_with_break(
@@ -133,7 +133,7 @@ def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
 def generate_large_matrix() -> list[list[int]]:
     """
     >>> generate_large_matrix() # doctest: +ELLIPSIS
-    [[500, ..., -499], [499, ..., -501], ..., [2, ..., -998]]
+    [[1000, ..., -999], [999, ..., -1001], ..., [2, ..., -1998]]
     """
     return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
 
@@ -144,17 +144,19 @@ def benchmark() -> None:
 
     print("Running benchmarks")
     setup = (
-        "from __main__ import count_negatives_binary_search, count_negatives_brute_force, "
-        "count_negatives_brute_force_with_break, generate_large_matrix"
+        "from __main__ import count_negatives_binary_search,count_negatives_brute_force"
+        ",count_negatives_brute_force_with_break,generate_large_matrix"
     )
 
-    cnbs = timeit(
+    print(
+        "count_negatives_binary_search()",
+        timeit(
             "count_negatives_binary_search(generate_large_matrix())",
             setup=setup,
             number=5000,
         ),
-    
-    print("count_negatives_binary_search()", cnbs[0], "seconds")
+        "seconds",
+    )
     print(
         "count_negatives_brute_force_with_break()",
         timeit(
@@ -163,7 +165,7 @@ def benchmark() -> None:
             number=5000,
         ),
         "seconds",
-    )  #
+    )
     print(
         "count_negatives_brute_force()",
         timeit(

From 8cd5cdcb6161a63136141bfbc1e63a2aa9a2042b Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:31:29 +0100
Subject: [PATCH 05/20] refactor: Combine functions into iteration

---
 ...count_negative_numbers_in_sorted_matrix.py | 35 ++++---------------
 1 file changed, 7 insertions(+), 28 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index de8f151cafff..98fee5af8f98 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -147,34 +147,13 @@ def benchmark() -> None:
         "from __main__ import count_negatives_binary_search,count_negatives_brute_force"
         ",count_negatives_brute_force_with_break,generate_large_matrix"
     )
-
-    print(
-        "count_negatives_binary_search()",
-        timeit(
-            "count_negatives_binary_search(generate_large_matrix())",
-            setup=setup,
-            number=5000,
-        ),
-        "seconds",
-    )
-    print(
-        "count_negatives_brute_force_with_break()",
-        timeit(
-            "count_negatives_brute_force_with_break(generate_large_matrix())",
-            setup=setup,
-            number=5000,
-        ),
-        "seconds",
-    )
-    print(
-        "count_negatives_brute_force()",
-        timeit(
-            "count_negatives_brute_force(generate_large_matrix())",
-            setup=setup,
-            number=5000,
-        ),
-        "seconds",
-    )
+    for func in (
+        "count_negatives_binary_search",
+        "count_negatives_brute_force_with_break",
+        "count_negatives_brute_force",
+    ):
+        time = timeit(f"{func}(generate_large_matrix())", setup=setup, number=5000)
+        print(f"{func}() took {time} seconds")
 
 
 if __name__ == "__main__":

From ea5b2d0777ada189399557378cec9f5d654c1999 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:33:13 +0100
Subject: [PATCH 06/20] style: Reformat reference

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 98fee5af8f98..dbcdd80d8fed 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -2,7 +2,7 @@
 Given an `m x n` matrix grid which is sorted in non-increasing order
 both row-wise and column-wise, return the number of negative numbers in grid.
 
-> https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
+Leetcode reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
 """
 
 

From 0e346b266d49f49bec2da40557c5141169ddb4e8 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:40:36 +0100
Subject: [PATCH 07/20] feat: Add timings of each implementation

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index dbcdd80d8fed..da6a52e2fe2b 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -148,9 +148,9 @@ def benchmark() -> None:
         ",count_negatives_brute_force_with_break,generate_large_matrix"
     )
     for func in (
-        "count_negatives_binary_search",
-        "count_negatives_brute_force_with_break",
-        "count_negatives_brute_force",
+        "count_negatives_binary_search",  # 175.51 seconds
+        "count_negatives_brute_force_with_break",  # 271.04 seconds
+        "count_negatives_brute_force",  # 646.65 seconds
     ):
         time = timeit(f"{func}(generate_large_matrix())", setup=setup, number=5000)
         print(f"{func}() took {time} seconds")

From b58a34013315ed2060ba9dad4936f17589cc619b Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:43:00 +0100
Subject: [PATCH 08/20] chore: Fix problems with algorithms-keeper bot

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index da6a52e2fe2b..5cbdceaf5b5a 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -6,7 +6,7 @@
 """
 
 
-def find_negative_index(array: list[int]):
+def find_negative_index(array: list[int]) -> int:
     """
     Find the smallest negative index
 
@@ -139,7 +139,10 @@ def generate_large_matrix() -> list[list[int]]:
 
 
 def benchmark() -> None:
-    """Benchmark our functions next to each other"""
+    """Benchmark our functions next to each other
+    
+    >>> benchmark()
+    """
     from timeit import timeit
 
     print("Running benchmarks")

From 3b16704538c96552833304f138957a94a6715127 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 8 Jun 2023 15:43:36 +0000
Subject: [PATCH 09/20] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 5cbdceaf5b5a..92726db189b3 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -140,7 +140,7 @@ def generate_large_matrix() -> list[list[int]]:
 
 def benchmark() -> None:
     """Benchmark our functions next to each other
-    
+
     >>> benchmark()
     """
     from timeit import timeit

From fca6e9d8187e6f55a9919a32f29b19c06be890fe Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Thu, 8 Jun 2023 16:47:34 +0100
Subject: [PATCH 10/20] test: Remove doctest from benchmark function

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 92726db189b3..6fafff1456f8 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -139,10 +139,7 @@ def generate_large_matrix() -> list[list[int]]:
 
 
 def benchmark() -> None:
-    """Benchmark our functions next to each other
-
-    >>> benchmark()
-    """
+    """Benchmark our functions next to each other"""
     from timeit import timeit
 
     print("Running benchmarks")

From 02cd4f38b0278e9a6eb2dc0ecaa5e08c88f42e4b Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Fri, 9 Jun 2023 15:45:15 +0100
Subject: [PATCH 11/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 6fafff1456f8..a0e928928a3d 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -1,5 +1,5 @@
 """
-Given an `m x n` matrix grid which is sorted in non-increasing order
+Given an `m x n` matrix grid which is sorted in decreasing order
 both row-wise and column-wise, return the number of negative numbers in grid.
 
 Leetcode reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix

From 63c5147a3f8427c22842425771e1d514dd6fa299 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Fri, 9 Jun 2023 17:20:53 +0100
Subject: [PATCH 12/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index a0e928928a3d..138f03869652 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -1,6 +1,6 @@
 """
-Given an `m x n` matrix grid which is sorted in decreasing order
-both row-wise and column-wise, return the number of negative numbers in grid.
+Given an matrix of numbers in which all rows and all columns are sorted in decreasing
+order, return the number of negative numbers in grid.
 
 Leetcode reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
 """

From a55db732f0d9d37eb8ca69a5a6baa0429bb6f4bf Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:40:30 +0100
Subject: [PATCH 13/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 138f03869652..e42481ac682b 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -121,11 +121,10 @@ def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
     3
     """
     total = 0
-    length_of_n = len(grid[0])
-    for m in range(len(grid)):
-        for index, n in enumerate(range(length_of_n)):
-            if grid[m][n] < 0:
-                total += length_of_n - index
+    for row in grid:
+        for i, number in enumerate(row):
+            if number < 0:
+                total += len(row) - i
                 break
     return total
 

From 0d8a616a6de601e2522ba78f4f1c6fbcdd9c08f9 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:40:43 +0100
Subject: [PATCH 14/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index e42481ac682b..4d1834bce4b5 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -151,7 +151,7 @@ def benchmark() -> None:
         "count_negatives_brute_force_with_break",  # 271.04 seconds
         "count_negatives_brute_force",  # 646.65 seconds
     ):
-        time = timeit(f"{func}(generate_large_matrix())", setup=setup, number=5000)
+        time = timeit(f"{func}(grid=grid)", setup=setup, number=500)
         print(f"{func}() took {time} seconds")
 
 

From 9a7719c57960ee486d4f59a1e1576c7b5dff35a0 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:40:49 +0100
Subject: [PATCH 15/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 4d1834bce4b5..1b36df52cbab 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -137,6 +137,7 @@ def generate_large_matrix() -> list[list[int]]:
     return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
 
 
+grid = generate_large_matrix()
 def benchmark() -> None:
     """Benchmark our functions next to each other"""
     from timeit import timeit

From 7a2f01e8925b4d56593073056843e95b9d2ef931 Mon Sep 17 00:00:00 2001
From: Caeden Perelli-Harris <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:40:56 +0100
Subject: [PATCH 16/20] Update
 matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 1b36df52cbab..9f9431ad9469 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -145,7 +145,7 @@ def benchmark() -> None:
     print("Running benchmarks")
     setup = (
         "from __main__ import count_negatives_binary_search,count_negatives_brute_force"
-        ",count_negatives_brute_force_with_break,generate_large_matrix"
+        ",count_negatives_brute_force_with_break,grid"
     )
     for func in (
         "count_negatives_binary_search",  # 175.51 seconds

From 97e2017d61b5f6d08df49c704ab9a778c4f3e676 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:45:55 +0100
Subject: [PATCH 17/20] refactor: Use sum instead of large iteration

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 9f9431ad9469..ee28c2be8f47 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -97,12 +97,7 @@ def count_negatives_brute_force(grid: list[list[int]]) -> int:
     >>> count_negatives_brute_force([[7,7,6],[-1,-2,-3]])
     3
     """
-    total = 0
-    for m in range(len(grid)):
-        for n in range(len(grid[m])):
-            if grid[m][n] < 0:
-                total += 1
-    return total
+    return sum(number for row in grid for number in row if number < 0)
 
 
 def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
@@ -138,6 +133,8 @@ def generate_large_matrix() -> list[list[int]]:
 
 
 grid = generate_large_matrix()
+
+
 def benchmark() -> None:
     """Benchmark our functions next to each other"""
     from timeit import timeit

From 0f21b1bc8376fbe91365011064da58ed0d9aa940 Mon Sep 17 00:00:00 2001
From: CaedenPH <caedenperelliharris@gmail.com>
Date: Sat, 10 Jun 2023 12:48:37 +0100
Subject: [PATCH 18/20] refactor: Use len not sum

---
 matrix/count_negative_numbers_in_sorted_matrix.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index ee28c2be8f47..7122ebc739e0 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -97,7 +97,7 @@ def count_negatives_brute_force(grid: list[list[int]]) -> int:
     >>> count_negatives_brute_force([[7,7,6],[-1,-2,-3]])
     3
     """
-    return sum(number for row in grid for number in row if number < 0)
+    return len([number for row in grid for number in row if number < 0])
 
 
 def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:

From 605be4315eb14bb77f77120b934e8ea2802e3693 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Sat, 10 Jun 2023 14:16:42 +0200
Subject: [PATCH 19/20] Update count_negative_numbers_in_sorted_matrix.py

---
 ...count_negative_numbers_in_sorted_matrix.py | 111 ++++++++----------
 1 file changed, 51 insertions(+), 60 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 7122ebc739e0..0e5205f65475 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -2,10 +2,38 @@
 Given an matrix of numbers in which all rows and all columns are sorted in decreasing
 order, return the number of negative numbers in grid.
 
-Leetcode reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
+Reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
 """
 
 
+def generate_large_matrix() -> list[list[int]]:
+    """
+    >>> generate_large_matrix() # doctest: +ELLIPSIS
+    [[1000, ..., -999], [999, ..., -1001], ..., [2, ..., -1998]]
+    """
+    return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
+
+
+grid = generate_large_matrix()
+test_grids = (
+    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]],
+    [[3,2],[1,0]],
+    [[7,7,6]],
+    [[7,7,6],[-1,-2,-3]],
+    grid
+)
+
+
+def validate_grid(grid: list[list[int]]) -> None:
+    """
+    Validate that the rows and columns of the grid is sorted in decreasing order.
+    >>> for grid in test_grids:
+    ...     validate_grid(grid)
+    """
+    assert all(row == sorted(row, reverse=True) for row in grid)
+    assert all(list(col) == sorted(col, reverse=True) for col in zip(*grid))
+
+
 def find_negative_index(array: list[int]) -> int:
     """
     Find the smallest negative index
@@ -34,8 +62,7 @@ def find_negative_index(array: list[int]) -> int:
     left = 0
     right = len(array) - 1
 
-    # Edge cases such as no values or
-    # all numbers are negative
+    # Edge cases such as no values or all numbers are negative.
     if not array or array[0] < 0:
         return 0
 
@@ -43,8 +70,7 @@ def find_negative_index(array: list[int]) -> int:
         mid = (left + right) // 2
         num = array[mid]
 
-        # Num must be negative and the index about num
-        # must be greater than or equal to 0
+        # Num must be negative and the index must be greater than or equal to 0.
         if num < 0 and array[mid - 1] >= 0:
             return mid
 
@@ -52,26 +78,17 @@ def find_negative_index(array: list[int]) -> int:
             left = mid + 1
         else:
             right = mid - 1
-    # No negative numbers so return the last index
-    # of the array + 1 which is also the length
+    # No negative numbers so return the last index of the array + 1 which is the length.
     return len(array)
 
 
 def count_negatives_binary_search(grid: list[list[int]]) -> int:
     """
-    An O(m logn) solution that uses binary search
-    in order to find the boundary between positive and
-    negative numbers
-
-    >>> count_negatives_binary_search(
-    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
-    8
-    >>> count_negatives_binary_search([[3,2],[1,0]])
-    0
-    >>> count_negatives_binary_search([[7,7,6]])
-    0
-    >>> count_negatives_binary_search([[7,7,6],[-1,-2,-3]])
-    3
+    An O(m logn) solution that uses binary search in order to find the boundary between
+    positive and negative numbers
+
+    >>> [count_negatives_binary_search(grid) for grid in test_grids]
+    [8, 0, 0, 3, 1498500]
     """
     total = 0
     bound = len(grid[0])
@@ -84,36 +101,22 @@ def count_negatives_binary_search(grid: list[list[int]]) -> int:
 
 def count_negatives_brute_force(grid: list[list[int]]) -> int:
     """
-    This solution is O(n^2) because it iterates through
-    every column and row.
+    This solution is O(n^2) because it iterates through every column and row.
 
-    >>> count_negatives_brute_force(
-    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
-    8
-    >>> count_negatives_brute_force([[3,2],[1,0]])
-    0
-    >>> count_negatives_brute_force([[7,7,6]])
-    0
-    >>> count_negatives_brute_force([[7,7,6],[-1,-2,-3]])
-    3
+    >>> [count_negatives_brute_force(grid) for grid in test_grids]
+    [8, 0, 0, 3, 1498500]
     """
     return len([number for row in grid for number in row if number < 0])
 
 
+
 def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
     """
-    Similar to the solution above, however uses break
-    in order to reduce the number of iterations
+    Similar to the brute force solution above but uses break in order to reduce the
+    number of iterations.
 
-    >>> count_negatives_brute_force_with_break(
-    ...    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]])
-    8
-    >>> count_negatives_brute_force_with_break([[3,2],[1,0]])
-    0
-    >>> count_negatives_brute_force_with_break([[7,7,6]])
-    0
-    >>> count_negatives_brute_force_with_break([[7,7,6],[-1,-2,-3]])
-    3
+    >>> [count_negatives_brute_force_with_break(grid) for grid in test_grids]
+    [8, 0, 0, 3, 1498500]
     """
     total = 0
     for row in grid:
@@ -124,38 +127,26 @@ def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
     return total
 
 
-def generate_large_matrix() -> list[list[int]]:
-    """
-    >>> generate_large_matrix() # doctest: +ELLIPSIS
-    [[1000, ..., -999], [999, ..., -1001], ..., [2, ..., -1998]]
-    """
-    return [list(range(1000 - i, -1000 - i, -1)) for i in range(1000)]
-
-
-grid = generate_large_matrix()
-
-
 def benchmark() -> None:
     """Benchmark our functions next to each other"""
     from timeit import timeit
 
     print("Running benchmarks")
     setup = (
-        "from __main__ import count_negatives_binary_search,count_negatives_brute_force"
-        ",count_negatives_brute_force_with_break,grid"
+        "from __main__ import count_negatives_binary_search, "
+        "count_negatives_brute_force, count_negatives_brute_force_with_break, grid"
     )
     for func in (
-        "count_negatives_binary_search",  # 175.51 seconds
-        "count_negatives_brute_force_with_break",  # 271.04 seconds
-        "count_negatives_brute_force",  # 646.65 seconds
+        "count_negatives_binary_search",  # took 0.7727 seconds
+        "count_negatives_brute_force_with_break",  # took 4.6505 seconds
+        "count_negatives_brute_force",  # took 12.8160 seconds
     ):
         time = timeit(f"{func}(grid=grid)", setup=setup, number=500)
-        print(f"{func}() took {time} seconds")
+        print(f"{func}() took {time:0.4f} seconds")
 
 
 if __name__ == "__main__":
     import doctest
 
     doctest.testmod()
-
     benchmark()

From 21dbc02d30bfab25c8a9e7c6d61b2337d664ddb4 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sat, 10 Jun 2023 12:17:14 +0000
Subject: [PATCH 20/20] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 matrix/count_negative_numbers_in_sorted_matrix.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/matrix/count_negative_numbers_in_sorted_matrix.py b/matrix/count_negative_numbers_in_sorted_matrix.py
index 0e5205f65475..2799ff3b45fe 100644
--- a/matrix/count_negative_numbers_in_sorted_matrix.py
+++ b/matrix/count_negative_numbers_in_sorted_matrix.py
@@ -16,11 +16,11 @@ def generate_large_matrix() -> list[list[int]]:
 
 grid = generate_large_matrix()
 test_grids = (
-    [[4,3,2,-1],[3,2,1,-1],[1,1,-1,-2],[-1,-1,-2,-3]],
-    [[3,2],[1,0]],
-    [[7,7,6]],
-    [[7,7,6],[-1,-2,-3]],
-    grid
+    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
+    [[3, 2], [1, 0]],
+    [[7, 7, 6]],
+    [[7, 7, 6], [-1, -2, -3]],
+    grid,
 )
 
 
@@ -109,7 +109,6 @@ def count_negatives_brute_force(grid: list[list[int]]) -> int:
     return len([number for row in grid for number in row if number < 0])
 
 
-
 def count_negatives_brute_force_with_break(grid: list[list[int]]) -> int:
     """
     Similar to the brute force solution above but uses break in order to reduce the