mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
07e991d553
* 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
|
|
|
|
"""
|
|
Dynamic Programming
|
|
Implementation of Matrix Chain Multiplication
|
|
Time Complexity: O(n^3)
|
|
Space Complexity: O(n^2)
|
|
"""
|
|
|
|
|
|
def matrix_chain_order(array):
|
|
n = len(array)
|
|
matrix = [[0 for x in range(n)] for x in range(n)]
|
|
sol = [[0 for x in range(n)] for x in range(n)]
|
|
|
|
for chain_length in range(2, n):
|
|
for a in range(1, n - chain_length + 1):
|
|
b = a + chain_length - 1
|
|
|
|
matrix[a][b] = sys.maxsize
|
|
for c in range(a, b):
|
|
cost = (
|
|
matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
|
|
)
|
|
if cost < matrix[a][b]:
|
|
matrix[a][b] = cost
|
|
sol[a][b] = c
|
|
return matrix, sol
|
|
|
|
|
|
# Print order of matrix with Ai as Matrix
|
|
def print_optiomal_solution(optimal_solution, i, j):
|
|
if i == j:
|
|
print("A" + str(i), end=" ")
|
|
else:
|
|
print("(", end=" ")
|
|
print_optiomal_solution(optimal_solution, i, optimal_solution[i][j])
|
|
print_optiomal_solution(optimal_solution, optimal_solution[i][j] + 1, j)
|
|
print(")", end=" ")
|
|
|
|
|
|
def main():
|
|
array = [30, 35, 15, 5, 10, 20, 25]
|
|
n = len(array)
|
|
# Size of matrix created from above array will be
|
|
# 30*35 35*15 15*5 5*10 10*20 20*25
|
|
matrix, optimal_solution = matrix_chain_order(array)
|
|
|
|
print("No. of Operation required: " + str(matrix[1][n - 1]))
|
|
print_optiomal_solution(optimal_solution, 1, n - 1)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|