矩阵链乘法-python实现

原问题出自算法导论第三版15.2的练习题。问题如下：

对矩阵规模序列<5，10，3，12，5，50，6>，求矩阵链最优括号化方案

代码如下：

def matrix_order():
    matrix = (5,10,4,12,5,500,6)
    bignum = 999999999
    cost = []
    s = []
    for i in range(6):
        cost.append([])
        s.append([])
        for j in range(6):
            cost[i].append(bignum)
            s[i].append(-1)
    for i in range(6):
        cost[i][i] = 0
        s[i][i] = i

    for l in range(1,7):
        for i in range(0,6-l):
            j = i + l
            #cost[i][j] = bignum
            for k in range(i,j):
                c = cost[i][k]+cost[k+1][j]+matrix[i]*matrix[k+1]*matrix[j+1]
                if c < cost[i][j]:
                    cost[i][j] = c
                    s[i][j] = k

    return s


def print_order(i,j,s):
    if i == j:
        print(s[i][j],end="")
    else:
        print("(",end="")
        print_order(i,s[i][j],s)
        print_order(s[i][j]+1,j,s)
        print(")",end="")

s = matrix_order()
print_order(0,5,s)