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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 MatrixChainOrder(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 ChainLength in range(2, N):
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for a in range(1, N - ChainLength + 1):
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b = a + ChainLength - 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 PrintOptimalSolution(OptimalSolution, 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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PrintOptimalSolution(OptimalSolution, i, OptimalSolution[i][j])
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PrintOptimalSolution(OptimalSolution, OptimalSolution[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, OptimalSolution = MatrixChainOrder(array)
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print("No. of Operation required: " + str(Matrix[1][n - 1]))
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PrintOptimalSolution(OptimalSolution, 1, n - 1)
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if __name__ == "__main__":
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main()
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