From d7774c1b563fd32d21467bd99cec0e96deeff895 Mon Sep 17 00:00:00 2001 From: Tapajyoti Bose Date: Fri, 19 Jun 2020 12:04:43 +0530 Subject: [PATCH 1/2] Added maximum path sum for matrix (top left to bottom right) --- dynamic_programming/mat_max_path_sum.py | 34 +++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 dynamic_programming/mat_max_path_sum.py diff --git a/dynamic_programming/mat_max_path_sum.py b/dynamic_programming/mat_max_path_sum.py new file mode 100644 index 000000000000..87a3aecfac4a --- /dev/null +++ b/dynamic_programming/mat_max_path_sum.py @@ -0,0 +1,34 @@ +from typing import List + + +def matrix_maximum_path_sum(matrix: List[List[int]]) -> int: + ''' + Find the maximum sum of values traced by all the paths from top left to bottom + right in a given matrix + + >>> matrix_maximum_path_sum([[2, 1], [-1, 1], [4, 2]]) + 7 + + >>> matrix_maximum_path_sum([[2, 1, 4], [2, -1, -3], [3, 2, 1]]) + 10 + ''' + + # preprocessing the first row + for i in range(1, len(matrix[0])): + matrix[0][i] += matrix[0][i - 1] + + # preprocessing the first column + for i in range(1, len(matrix)): + matrix[i][0] += matrix[i - 1][0] + + for i in range(1, len(matrix)): + for j in range(1, len(matrix[0])): + matrix[i][j] += max(matrix[i - 1][j], matrix[i][j - 1]) + + return matrix[-1][-1] + + +if __name__ == "__main__": + import doctest + + doctest.testmod() From 345fea4848fa0c8ddddb2c4594495613850cf3bc Mon Sep 17 00:00:00 2001 From: Tapajyoti Bose Date: Thu, 2 Jul 2020 09:45:02 +0530 Subject: [PATCH 2/2] Changed maximum cost path to minimum cost path + added video explaination --- dynamic_programming/mat_max_path_sum.py | 34 ---------------------- dynamic_programming/minimum_cost_path.py | 37 ++++++++++++++++++++++++ 2 files changed, 37 insertions(+), 34 deletions(-) delete mode 100644 dynamic_programming/mat_max_path_sum.py create mode 100644 dynamic_programming/minimum_cost_path.py diff --git a/dynamic_programming/mat_max_path_sum.py b/dynamic_programming/mat_max_path_sum.py deleted file mode 100644 index 87a3aecfac4a..000000000000 --- a/dynamic_programming/mat_max_path_sum.py +++ /dev/null @@ -1,34 +0,0 @@ -from typing import List - - -def matrix_maximum_path_sum(matrix: List[List[int]]) -> int: - ''' - Find the maximum sum of values traced by all the paths from top left to bottom - right in a given matrix - - >>> matrix_maximum_path_sum([[2, 1], [-1, 1], [4, 2]]) - 7 - - >>> matrix_maximum_path_sum([[2, 1, 4], [2, -1, -3], [3, 2, 1]]) - 10 - ''' - - # preprocessing the first row - for i in range(1, len(matrix[0])): - matrix[0][i] += matrix[0][i - 1] - - # preprocessing the first column - for i in range(1, len(matrix)): - matrix[i][0] += matrix[i - 1][0] - - for i in range(1, len(matrix)): - for j in range(1, len(matrix[0])): - matrix[i][j] += max(matrix[i - 1][j], matrix[i][j - 1]) - - return matrix[-1][-1] - - -if __name__ == "__main__": - import doctest - - doctest.testmod() diff --git a/dynamic_programming/minimum_cost_path.py b/dynamic_programming/minimum_cost_path.py new file mode 100644 index 000000000000..93d936656294 --- /dev/null +++ b/dynamic_programming/minimum_cost_path.py @@ -0,0 +1,37 @@ +# Youtube Explaination: https://www.youtube.com/watch?v=lBRtnuxg-gU + +from typing import List + + +def minimum_cost_path(matrix: List[List[int]]) -> int: + ''' + Find the minimum cost traced by all possible paths from top left to bottom right in + a given matrix + + >>> minimum_cost_path([[2, 1], [3, 1], [4, 2]]) + 6 + + >>> minimum_cost_path([[2, 1, 4], [2, 1, 3], [3, 2, 1]]) + 7 + ''' + + # preprocessing the first row + for i in range(1, len(matrix[0])): + matrix[0][i] += matrix[0][i - 1] + + # preprocessing the first column + for i in range(1, len(matrix)): + matrix[i][0] += matrix[i - 1][0] + + # updating the path cost for current position + for i in range(1, len(matrix)): + for j in range(1, len(matrix[0])): + matrix[i][j] += min(matrix[i - 1][j], matrix[i][j - 1]) + + return matrix[-1][-1] + + +if __name__ == "__main__": + import doctest + + doctest.testmod()