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38 lines
926 B
Python
38 lines
926 B
Python
# Youtube Explaination: https://www.youtube.com/watch?v=lBRtnuxg-gU
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from typing import List
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def minimum_cost_path(matrix: List[List[int]]) -> int:
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"""
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Find the minimum cost traced by all possible paths from top left to bottom right in
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a given matrix
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>>> minimum_cost_path([[2, 1], [3, 1], [4, 2]])
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6
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>>> minimum_cost_path([[2, 1, 4], [2, 1, 3], [3, 2, 1]])
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7
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"""
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# preprocessing the first row
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for i in range(1, len(matrix[0])):
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matrix[0][i] += matrix[0][i - 1]
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# preprocessing the first column
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for i in range(1, len(matrix)):
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matrix[i][0] += matrix[i - 1][0]
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# updating the path cost for current position
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for i in range(1, len(matrix)):
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for j in range(1, len(matrix[0])):
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matrix[i][j] += min(matrix[i - 1][j], matrix[i][j - 1])
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return matrix[-1][-1]
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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