Python/dynamic_programming/matrix_chain_order.py

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2018-02-26 11:55:09 +00:00
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()