From daa0c8f3d340485ce295570e6d76b38891e371bd Mon Sep 17 00:00:00 2001 From: Caeden Perelli-Harris Date: Sat, 10 Jun 2023 13:21:49 +0100 Subject: [PATCH] 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 * Update matrix/count_negative_numbers_in_sorted_matrix.py Co-authored-by: Christian Clauss * Update matrix/count_negative_numbers_in_sorted_matrix.py Co-authored-by: Christian Clauss * Update matrix/count_negative_numbers_in_sorted_matrix.py Co-authored-by: Christian Clauss * Update matrix/count_negative_numbers_in_sorted_matrix.py Co-authored-by: Christian Clauss * Update matrix/count_negative_numbers_in_sorted_matrix.py Co-authored-by: Christian Clauss * 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 --- DIRECTORY.md | 2 + ...count_negative_numbers_in_sorted_matrix.py | 151 ++++++++++++++++++ 2 files changed, 153 insertions(+) create mode 100644 matrix/count_negative_numbers_in_sorted_matrix.py 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 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..2799ff3b45fe --- /dev/null +++ b/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()