mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 21:59:30 +00:00
49 lines
1.5 KiB
Python
49 lines
1.5 KiB
Python
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()
|