Dynamic Programming - Τρόποι πολ/σμού πινάκων

n = 20
# m will be a 20x20 matrix with zeros
m = [[0 for _ in range(n)] for __ in range(n)]

# Initialization
# Diagwnia stoixeia = 1
for i in range(n):
    m[i][i] = 1


'''
for i in range(n):
    for j in range(i+1, n):
        m[i][j] = 0
        for k in range(i, j):
            m[i][j] += m[i][k] * m[k+1][j]
            if m[i][k] == 0 or m[k+1][j] == 0:
                raise Exception('There is a zero element')
'''

# To k "deixnei" tin diagwnio pou eimai
# 1η διαγώνιος το i πάει από 0 ως και το 5
# 2η διαγώνιος το ι πάει από 0 ως και το 4
for diag in range(1, n):
    for i in range(0, n-diag):
        j = i+diag
        m[i][j] = 0
        for k in range(i, j):
            m[i][j] += m[i][k] * m[k + 1][j]
            if m[i][k] == 0 or m[k + 1][j] == 0:
                raise Exception('There is a zero element')


print(m[0][n-1])