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45 lines
1.4 KiB
Python
45 lines
1.4 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 = Matrix[a][c] + Matrix[c+1][b] + array[a-1]*array[c]*array[b]
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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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