Python/dynamic_programming/matrix_chain_order.py

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import sys
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"""
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Dynamic Programming
Implementation of Matrix Chain Multiplication
Time Complexity: O(n^3)
Space Complexity: O(n^2)
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"""
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def MatrixChainOrder(array):
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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)]
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for ChainLength in range(2, N):
for a in range(1, N - ChainLength + 1):
b = a + ChainLength - 1
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Matrix[a][b] = sys.maxsize
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for c in range(a, b):
cost = (
Matrix[a][c] + Matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
)
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if cost < Matrix[a][b]:
Matrix[a][b] = cost
Sol[a][b] = c
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return Matrix, Sol
# Print order of matrix with Ai as Matrix
def PrintOptimalSolution(OptimalSolution, i, j):
if i == j:
print("A" + str(i), end=" ")
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else:
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print("(", end=" ")
PrintOptimalSolution(OptimalSolution, i, OptimalSolution[i][j])
PrintOptimalSolution(OptimalSolution, OptimalSolution[i][j] + 1, j)
print(")", end=" ")
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def main():
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array = [30, 35, 15, 5, 10, 20, 25]
n = len(array)
# 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, OptimalSolution = MatrixChainOrder(array)
print("No. of Operation required: " + str((Matrix[1][n - 1])))
PrintOptimalSolution(OptimalSolution, 1, n - 1)
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if __name__ == "__main__":
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main()