动态规划之矩阵连乘问题Python实现方法

# coding=gbk
# 矩阵连乘问题
__author__ = 'ice'
# row_num 每个矩阵的行数
class Matrix:
  def __init__(self, row_num=0, col_num=0, matrix=None):
    if matrix != None:
      self.row_num = len(matrix)
      self.col_num = len(matrix[0])
    else:
      self.row_num = row_num
      self.col_num = col_num
    self.matrix = matrix
def matrix_chain(matrixs):
  matrix_num = len(matrixs)
  count = [[0 for j in range(matrix_num)] for i in range(matrix_num)]
  flag = [[0 for j in range(matrix_num)] for i in range(matrix_num)]
  for interval in range(1, matrix_num + 1):
    for i in range(matrix_num - interval):
      j = i + interval
      count[i][j] = count[i][i] + count[i + 1][j] + matrixs[i].row_num * matrixs[i + 1].row_num * matrixs[j].col_num
      flag[i][j] = i
      for k in range(i + 1, j):
        temp = count[i][k] + count[k + 1][j] + matrixs[i].row_num * matrixs[k + 1].row_num * matrixs[j].col_num
        if temp < count[i][j]:
          count[i][j] = temp
          flag[i][j] = k
  traceback(0, matrix_num - 1, flag)
  return count[0][matrix_num - 1]
def traceback(i, j, flag):
  if i == j:
    return
  if j - i > 1:
    print(str(i + 1) + '~' + str(j + 1), end=': ')
    print(str(i + 1) + ":" + str(flag[i][j] + 1), end=',')
    print(str(flag[i][j] + 2) + ":" + str(j + 1))
  traceback(i, flag[i][j], flag)
  traceback(flag[i][j] + 1, j, flag)
matrixs = [Matrix(30, 35), Matrix(35, 15), Matrix(15, 5), Matrix(5, 10), Matrix(10, 20), Matrix(20, 25)]
result = matrix_chain(matrixs)
print(result)
# 1~6: 1:3,4:6
# 1~3: 1:1,2:3
# 4~6: 4:5,6:6
# 15125