Create count negative numbers in matrix algorithm

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 +1,164 @@
+"""
+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.
+
+Leetcode reference: https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix
+"""
+
+
+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 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 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
+    """
+    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:
+    """
+    Similar 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
+    [[1000, ..., -999], [999, ..., -1001], ..., [2, ..., -1998]]
+    """
+    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"
+    )
+    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
+    ):
+        time = timeit(f"{func}(generate_large_matrix())", setup=setup, number=5000)
+        print(f"{func}() took {time} seconds")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    benchmark()