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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
55 lines
1.5 KiB
Python
55 lines
1.5 KiB
Python
import sys
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"""
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Dynamic Programming
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Implementation of Matrix Chain Multiplication
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Time Complexity: O(n^3)
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Space Complexity: O(n^2)
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"""
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def matrix_chain_order(array):
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n = len(array)
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matrix = [[0 for x in range(n)] for x in range(n)]
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sol = [[0 for x in range(n)] for x in range(n)]
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for chain_length in range(2, n):
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for a in range(1, n - chain_length + 1):
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b = a + chain_length - 1
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matrix[a][b] = sys.maxsize
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for c in range(a, b):
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cost = (
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matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
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)
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if cost < matrix[a][b]:
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matrix[a][b] = cost
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sol[a][b] = c
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return matrix, sol
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# Print order of matrix with Ai as Matrix
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def print_optiomal_solution(optimal_solution, i, j):
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if i == j:
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print("A" + str(i), end=" ")
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else:
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print("(", end=" ")
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print_optiomal_solution(optimal_solution, i, optimal_solution[i][j])
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print_optiomal_solution(optimal_solution, optimal_solution[i][j] + 1, j)
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print(")", end=" ")
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def main():
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array = [30, 35, 15, 5, 10, 20, 25]
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n = len(array)
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# Size of matrix created from above array will be
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# 30*35 35*15 15*5 5*10 10*20 20*25
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matrix, optimal_solution = matrix_chain_order(array)
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print("No. of Operation required: " + str(matrix[1][n - 1]))
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print_optiomal_solution(optimal_solution, 1, n - 1)
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if __name__ == "__main__":
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main()
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