Create count negative numbers in matrix algorithm (#8813)

* updating DIRECTORY.md

* feat: Count negative numbers in sorted matrix

* updating DIRECTORY.md

* chore: Fix pre-commit

* refactor: Combine functions into iteration

* style: Reformat reference

* feat: Add timings of each implementation

* chore: Fix problems with algorithms-keeper bot

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* test: Remove doctest from benchmark function

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update matrix/count_negative_numbers_in_sorted_matrix.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* refactor: Use sum instead of large iteration

* refactor: Use len not sum

* Update count_negative_numbers_in_sorted_matrix.py

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 4 people

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

matrix/count_negative_numbers_in_sorted_matrix.py

@@ -0,0 +1,151 @@
+"""
+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.
+
+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
+
+    >>> 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 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 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(grid) for grid in test_grids]
+    [8, 0, 0, 3, 1498500]
+    """
+    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(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 brute force solution above but uses break in order to reduce the
+    number of iterations.
+
+    >>> [count_negatives_brute_force_with_break(grid) for grid in test_grids]
+    [8, 0, 0, 3, 1498500]
+    """
+    total = 0
+    for row in grid:
+        for i, number in enumerate(row):
+            if number < 0:
+                total += len(row) - i
+                break
+    return total
+
+
+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"
+    )
+    for func in (
+        "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:0.4f} seconds")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    benchmark()