#### Matrix Chain Order

p
```import sys

"""
Dynamic Programming
Implementation of Matrix Chain Multiplication
Time Complexity: O(n^3)
Space Complexity: O(n^2)
"""

def matrix_chain_order(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 chain_length in range(2, n):
for a in range(1, n - chain_length + 1):
b = a + chain_length - 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 print_optiomal_solution(optimal_solution, i, j):
if i == j:
print("A" + str(i), end=" ")
else:
print("(", end=" ")
print_optiomal_solution(optimal_solution, i, optimal_solution[i][j])
print_optiomal_solution(optimal_solution, optimal_solution[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, optimal_solution = matrix_chain_order(array)

print("No. of Operation required: " + str(matrix[1][n - 1]))
print_optiomal_solution(optimal_solution, 1, n - 1)

if __name__ == "__main__":
main()
```