算法导论,动态规划 —— 矩阵链乘法（python代码实现示例）

# coding=utf-8
# 算法导论课本        动态规划  矩阵链乘法
#  矩阵链乘法的最优加括号方案    根据伪码 使用 python实现
# 辅助表 m 保存代价 m[i,j]
# 辅助表 s 记录最优值 m[i,j]对应的分割点 k
def maxChain(p):
# n = len(p) - 1
n = len(p)
m = [[0 for i in range(n)] for j in range(n)]
s = [[0 for i in range(n)] for j in range(n)]
# for i in range(n):
#     m[i][i] = 0
for l in range(2,n):
for i in range(1,n-l+1):
j = i+l-1;
m[i][j] = 9999999999;
for k in range(i,j):
q = m[i][k] + m[k+1][j] + p[i-1] * p[k] * p[j]
if q < m[i][j]:
m[i][j] = q;
s[i][j] = k
return m, s

# 输出矩阵链的最优括号化方法
def printOpt(s, i, j):
if i == j:
print("A", i, end='')
else:
# print("(", end="")
print("(", end='')
printOpt(s, i, s[i][j])
printOpt(s, s[i][j]+1, j)
print(")", end='')
print("start=========")
p = [30, 35, 15, 5, 10, 20, 25]
m, s = maxChain(p)

print(m)
print(s)
print("最优括号化方案为：")
printOpt(s, 1, 6)
print("")
print("其标量乘法次数为：", m[1][6])

print("Over=========")