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from __future__ import print_function

import sys

'''

Dynamic Programming

Implementation of Matrix Chain Multiplication

Time Complexity: O(n^3)

Space Complexity: O(n^2)

'''

def MatrixChainOrder(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 i in range(1,N):

Matrix[i][i]=0

for ChainLength in range(2,N):

for a in range(1,N-ChainLength+1):

b = a+ChainLength-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 PrintOptimalSolution(OptimalSolution,i,j):

if i==j:

print("A" + str(i),end = " ")

else:

print("(",end = " ")

PrintOptimalSolution(OptimalSolution,i,OptimalSolution[i][j])

PrintOptimalSolution(OptimalSolution,OptimalSolution[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 , OptimalSolution = MatrixChainOrder(array)

print("No. of Operation required: "+str((Matrix[1][n-1])))

PrintOptimalSolution(OptimalSolution,1,n-1)

if __name__ == '__main__':

main()

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